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Summary / Comprehensive Due date:

1

CHAPTER 1 - VISCOSITY

General:

One of the properties of homogeneous liquids is their resistance to motion. A measure ofthis resistance is known as viscosity. It can be measured in different standardized

methods or tests. In this experiment, viscosity will be measured using an LVDV-II+ Pro

viscometer.

Theory:

The absolute viscosity µ is a material property that plays a fundamental role in most fluidflows. In this experiment, the value of µ for a fluid is determined by measuring the torque

T required to rotate a cylinder of length L and radius R in a well containing the fluid. See

Figure 1.1.

Figure 1.1: Spindle Diagram

By definition, the absolute viscosity µ is the coefficient that relates the shear stress τ to

the velocity gradient dV /d y:

V

y

(1.1)

The rotary viscometer used has a narrow gap s between the outer radius R of the cylinder

and the inside of the well wall (Fig. 1.1). The velocity gradient (strain rate) can be

calculated using the small gap assumption. The shear stress can be calculated using thecylinder surface area and the measured torque. On the Brookfield viscometer, the torque

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T is not displayed directly, but rather the fraction β of the maximum torque T maxmeasurable by the instrument:

max

T

T where

max 0.0673 .T mN m (milliNewton meter)

Experimental Procedure:

In this lab we will be using a viscometer to measure viscosities of different fluidsat different temperatures. For each reading of viscosity that the LVDV-II+ Pro

viscometer takes, a corresponding reading of temperature, percent torque, and RPM

speed will be given. A total of 3 different fluids will be tested. One of the fluids will be

tested at 3 different temperatures in order to show how viscosity changes withtemperature. The remaining 2 fluids will be tested to show how viscosities change

between different types of fluids. Therefore a total of 5 samples will be tested.

For each trial the spindle from the viscometer will first be inserted into the fluid

along with the temperature probe, and then a temperature reading taken. Before beginning the experiment the fluid, spindle number, and temperature will be recorded.

Next, at least 5 different RPM values will be used and recorded with their

corresponding torque percentages and viscosity measurements (according to the

viscometer).

See Appendix 1 for instructions on the viscometer. Do not use

viscometer without instructions from (and supervision of) a TA!!

The purpose of the experiment is to calculate viscosities using the torque

percentages and RPM values given by the viscometer, and then compare your calculatedviscosities with the viscosities given by the viscometer.

Table 1.1 - Data for experimental calculations

Spindle #1 Spindle #4

Radius (cm) Radius (cm)

0.9421 0.1588

Effective length (cm) Effective length (cm)9.16 3.396

Spacing (cm) Spacing (cm)

0.448 0.080

*** See Appendix 1 for Viscometer and Warming Bath instructions.

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Data Collection:

Cold Molasses Room Temp.

Molasses

Hot Molasses Corn Syrup Ketchup

Spindle # 4 Spindle # 4 Spindle # 1 Spindle # 4 Spindle # 4

Temp.(°F) Temp.(°F) Temp. (°F) Temp. (°F) Temp. (°F)

µeff RPM %T µeff RPM %T µeff RPM %T µeff RPM %T µeff RPM %T

Some Specific Questions to Address: Viscosity

Plot shear stress vs. strain rate data for each fluid. Find the best fit equation forthe data and determine the viscosity. Explain the errors.

Compare the viscosities calculated using the torque percentages and RPM valuesgiven by the viscometer with the experimental viscosity readings from theinstrument. Calculate the error percentages. Comment on the results.

Plot shear stress vs. strain rate data of all molasses data on the same chart.Explain the impact of temperature on the viscosity of molasses. Compare results

with the curves for other fluids in the textbook and/or online sources. Be sure to

cite these sources.

Identify the 3 fluids tested as Newtonian or non-Newtonian fluids. Explain youranswer.

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APPENDIX 1: SPECIFIC INSTRUMENT INSTRUCTIONS

How to use the LVDV-II + Pro Viscometer

1. After the viscometer is set up and leveled (bubble on top of viscometer), installthe spindle guard. Next, install the temperature probe. Before you install thespindle, the viscometer needs to be turned on. Use the electric cord toconnect to the rear of the viscometer and an electric outlet. Then, using theon/off switch on the rear of the viscometer, turn it on. The viscometer will

display “auto-zeroing” for a few seconds, then will tell you to install the spindle

and press any key.

2. Before installing spindle, remember that the viscometer uses

reverse threads. Therefore, it tightens and loosens in the opposite directionthan the more often used right-handed thread. Also it is important to both lift the

upper half of the drive and keep it from rotating with the thumb and forefinger ofone hand while screwing or unscrewing the spindle with the other hand.

3. Once the spindle is installed, follow the instructions and press any key. After afew seconds, the torque, RPM, viscosity, and temperature categories shouldappear on the display. The temperature should be in Fahrenheit, the viscosity

should be in mPa-s, the torque will be in percentage, and the RPM value will

simply be a number.

4. The next step is to ensure that the viscometer knows what spindle you are using.The number 1 spindle is input as number 61 into the viscometer and the number

4 spindle is input as number 64 in the viscometer. The 1 and 4 numbers arelocated at the top of each spindle. Press the “Select Spindle” button on the

viscometer face. In the top right corner of the display, a number will appear and

start blinking. If the number is the correct number that corresponds to the spindle

you are using, do not touch anything else until it stops blinking. If the numberneeds to be changed, push the up and down arrow keys until you reach the

correct num ber. Next, push the “Select Spindle” button again to lock in the

change. If you do not push the “Select Spindle” key a second time to confirm thespindle selection, the number will not be recognized in the viscometer.

5. Once the spindle is properly installed and the viscometer has the correct spindle

number input, you can insert the spindle into the fluid that is being tested. On both spindles, there is an indentation on the shaft. The fluid that you are testing

should cover the spindle up to the middle of the indentation to the point where

there is a raised groove. In order to receive accurate data, the fluid

cannot go over or below this point. The 600 ml flasks can be filled toaccomplish this, along with moving the viscometer up and down its track. It isimportant to keep the spindle close to the center of the flask. If the spindle is

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closer to the edge of the beaker than it is to the guard, the calibrated spacing

value that we need will be thrown off.

6. Finally, it’s time to start taking measurements. To begin, press the “motoron/off” button on the viscometer face. The spindle should begin to rotate at the

designated RPM speed. In order to change the RPM speed, press the “Set Speed” button. Then, press the Up or Down arrows according to which value of RPMyou are trying to reach. The value of RPMs will appear just to the right of the

currently running RPM value. Once you find an RPM that you wish to reach,

press the “Set Speed” button again and that RPM value will become thecurrently running speed. There will be a different torque percentage for each

RPM value. In order for the values to be valid, the torque percentage must be

above 10% and below 100%. If the torque reaches 100% or above, the screen

will display “EEEE”. If this occurs, simply reduce the RPM speed.

7. About RPM speeds. There are two sets of RPM speeds. To test and

understand what this means, scroll through the RPM speeds and when you reachthe maximum, continue upward and another set of speeds will begin. Any speed

can be used that keeps the torque within its allowable range. A good idea is to

start at the lower RPMs and work up to faster velocities. The viscometer reachesequilibrium faster that way.

8. To finish and shut off, press the “motor on/off” button and the spindle will stoprotating. Remove the spindle and viscometer from inside the fluid. At this time

the viscometer can be shut off. The spindle can then be removed. Remember

that the spindle is a reverse thread. Also remember to press upwards onthe upper drive and hold while unscrewing the spindle.

9. Next, clean the spindle and the viscometer and return it to its case. Warm waterand paper towels will be sufficient for cleaning. Be sure to remove all of the

material from the spindle to avoid contamination.

IMPORTANT!!!!

This Viscometer costs over $1200. The most tedious part

of using the viscometer is installing and removing the spindle.The spindle has reverse threads and can easily be ruined. The

shaft of the motor is also sensitive to pushing and pulling and

can be bent out of alignment easily if one does not take care

removing the spindle.

SO BE CAREFUL!!!

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How to use the TC-102 Water Bath

1. Unless Water Bath is already filled, fill with water to within 1 inch of the surfaceof the device. This is the maximum level for the water. Since a 600 ml flask will

be inserted to warm fluids, the level of water should be a little less to allow for

displacement.

2. Attach electric wire and plug into outlet. Using on/off switch on the back of thedevice, turn the device on. 3 dots will then appear on the display screen.

3. In order to reach the desired temperature, press and release the turn-knob once.The current temperature will appear (Fahrenheit should be displayed as thetemperature). Then, turn the knob either left or right until the desired temperature

displays on the screen. Once the desired temperature is displayed on the screen,

do not touch the turn-knob again. In a few seconds the display will return to thecurrent temperature. The circulation pump will turn on at this point and the

temperature will begin to change. To see the temperature that you are trying to

reach, simply press and release the turn-knob, and it will be displayed again.

4. Allow sufficient time for the water bath, and fluid that you are testing, to reachthe desired temperature.

5. IMPORTANT!!!! Remember that the fluid and flask is going to be hot afterheating and to take proper precautions not to injure yourself or damage the

equipment.

6. After testing is complete, and you are finished with the water bath, simply turn thedevice off using the on/off switch on the back of the display panel.

7. If the bath is not going to be used for a significant period, empty the water.

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CHAPTER 2 – PRESSURE AND FORCE

General:

The objective of this lab is to observe the relationship between pressure and force.Pressure gauges and weights will be used to observe pressure. These readings will be

compared to predicted pressure values. This lab will briefly discuss trend line selection.

Theory:

Pressure is defined as force per unit area. Since this is a general relationship, the unit

system (U.S. or SI) must be consistent within the equation. See Equation 2.1.

F P

A (2.1)


This experiment will use multiple weights applied to a water-filled cylinder of knowngeometry. The cylinder is connected to a Bourdon-tube pressure gauge which will

provide the recorded pressure readings. See Figure 2.1 below.

Figure 2.1: Experimental Apparatus

The weights are applied on the cylinder side. The diameter of the cylinder of eachapparatus is listed on the instrument ID tag. At least 5 weight combinations must be

tried, and each combination must be applied three times. The trials should be performed

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in a random order (i.e., do not add the weight and then read the gauge three times without

doing anything). The intermediate fluid is water. Water is selected because it is nearly

incompressible and does not dissipate pressure within the fluid.

Experimental errors should be listed and accounted for. “Human error” is not an error.

Using that phrase means that an unknown mistake was made and no effort was made toidentify it, remove it, or quantify it. This is unacceptable. An idea of the magnitude ofthe errors should also be mentioned (one error may change the values by 0.1% while a

different one may change the values by 10%).

Data Collection:

Weight (kg) Pressure (kN/m2 or lbf/in2)

Weight combination Trial #1 Trial #2 Trial #3

Some Specific Questions to Address:

*All plots should include an appropriate trend line with equation and coefficient of

determination unless otherwise stated. This applies to all labs.

** All plots are given as “Y versus X” notation.

A data table should compare the recorded pressure with the calculated pressure.Percent Error should be used.

Include a plot of Experimental pressure versus Theoretical pressure. Is theexperiment consistent? Does it over-predict or under-predict values?

Make a plot of force versus Experimental pressure. Does it behave as isexpected? Does the slope of the line match the expected value?

Plot percent error against applied force. Discuss any trends.

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CHAPTER 3 – MANOMETRY

General:

Manometry utilizes the change in pressure with elevation to evaluate pressure. There are severalinstruments available to measure pressure depending on the magnitude of the pressure and the

characteristics of the fluid to be studied.

Theory:

By measuring the height of liquid in a simple manometer, it is possible to compute the gage

pressure at the center of the vessel to which the manometer is connected. A manometer uses adifferent fluid than the one in the main vessel (i.e. water). By measuring the deflection of the

manometer fluid (e.g. mercury) in a U-tube, the pressure in the main vessel can be calculated if

the specific weights of the two fluids are known. In this lab we will use a U-tube manometer

(Figure 3.1).

Figure 3.1: The Manometer

The hydrostatic pressure equation states that there is no horizontal variation in pressure in a static

fluid. Therefore,

A B P P (3.1)

The change in pressure with height in a fluid is given by P h (3.2)

where Δ is the increase in pressure due to moving down a distance Δ in a fluid of specific

weight . Note that the pressure at points 1 and 2 in Figure 3.1 is P=0.

h1

h3

h2

A B

1 2

oil

water

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In this lab we will calculate the specific weight of vegetable oil and a salt water solution.

First, you will use the vegetable oil and water in the manometer. Fill the tube mostly with water,

then some oil and measure the heights h1, h2, h3 as shown in Figure 3.1. Add a little more oil andrepeat three times. Be sure not to have the oil-water interface near the bottom of the tube. If itis, then oil could possibly come out the other side of the tube, causing two unknowns.

After cleaning the tube out, use the salt water solution and oil. The tube should be mostly full ofsalt water now, with some vegetable oil on one side like before. Take your measurements of

heights and add increments of oil just like the previous step. This time, the known specific

weight will be the newly calculated value of vegetable oil. You will use this value to calculate

the specific weight of the salt water.

Data Collection:

h1 (cm) h2 (cm) h3 (cm)

Clear Water 1.

2.

3.

Salt Water 1.

2.

3.

Some Specific Questions to Address: - Manometry

Determine the specific weight of the cooking oil and the salt water. Compare the specificgravity calculated for the cooking oil with values that you look up from an outside source

(textbook or internet, cited appropriately).

Are these results as expected? Do they correspond to our knowledge of certain fluids being less dense/more dense than other fluids?

Describe in your own words how the principles of manometry are applied in thisexperiment.

What problems would have to be overcome if we were to measure the unit weight of saltwater only using the equipment specified, without the cooking oil? What are some

possible solutions?

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CHAPTER 4- THE CENTER OF PRESSURE

General:

In this lab you will verify the location of the "center of pressure" due to the force of a

liquid on a submerged plane surface.

Theory:

At any point below its free surface, the liquid exerts a pressure onto any surface in

contact with the liquid, given by

p h (4.1)

Where p = pressure at any point; = specific weight of the liquid; and h is the vertical

distance from the surface to the point where pressure is measured. Any surface in contact

with a liquid, therefore, experiences a force that can be calculated from:

pdA zdAw w w c w

area area

F h A (4.2)

Where F w = the total force exerted by the fluid on the area, dAw = the elemental area on

which the pressure p is applied, hc = the depth to the centroid of the surface; and Aw = the

area of interest. If the total force of the fluid could be represented by a force acting at one point on the surface, this point would be known as the "center of pressure." Knowing the

specific weight of the fluid, the shape of the plate, the location of the plate under the fluid

surface, and the orientation of the plate, the magnitude and location of the force of the

fluid on the submerged area can be determined using Equation 4.2.

Table 4.1 - Dimensions of the Test Apparatus

Radius of inner cylinder 10.0 cm

Radius of outer cylinder 20.0 cm

Width of the plate (w) 7.5 cm

Length of the plate 10.0 cm

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Figure 4.1: Definition sketch of force of fluid on a plate. Note that all the forces

acting on the curved surface of the Plexiglas act along lines passing through the

pivot point (A). Therefore, only the hydrostatic force acting on the flat surface

creates a moment about (A).

Experimental Apparatus:

Figure 4.2 shows the test apparatus (a) and the measurable for the tank (b). Table 4.1

gives its required dimensions. The apparatus consists of counterbalancing weights to

zero the instrument, a scaled lever arm to measure the distance to the added moment, a

quadrant tank to contain the water, and a gradation plate to read elevations for the tank.

Figure 4.2(a) Schematic of the Test Apparatus, (b) explanation of measured

variables

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exp200

if S 200mm:cos

p d

S y I

(4.7b)

Figure 4.3 Schematic of the momentum calculation of force of water about (A) ( for

submerged case)

Experimental procedure:

1. Set the lever arm distance and use the rotating slider to level the apparatus at the

desired .

2. Record St, Sh, and 3. Add weights, ensuring that the hanger has not moved from its set distance.

4. Pour water into the quadrant tank until balance is restored.

5. Measure and record S for the specified angle and weight W.

6. Repeat steps 3 and 4 for 6 different weights. Use a total of at least two weight

combinations below 3 N and at least four combinations above 3 N.

7. Empty the quadrant tank .

8. Repeat steps from 1 to 7 for =20o, and 40 o.

Be sure to use the same combination of weights for each angle.

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Data Collection:

Angle o

Lever Arm [mm]

-------------------------

Lowest Gate Level St [mm]

-------------------------

Highest Gate Level Sh [mm]

----------------------

Weight [N] Water level reading S [mm]

Angle o

Lever Arm [mm]

-------------------------


-------------------------


----------------------

Weight [N] Water level reading S [mm]

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Angle o

Lever Arm [mm]

-------------------------


-------------------------


----------------------Weight [N] Water level reading S [mm]

Some Specific Questions to Address – Center of Pressure

Calculate the moment about point A due to the hydrostatic pressure on the plate

using (4.6) and plot this moment vs the moment due to the weight.

Plot the distance between the center of area and the center of pressure (

exp p c y h ) vs. (S-St) for all three angles on the same graph. Explain the

falling limb of the graph using equations as necessary. What number(s) should ε

approach?

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CHAPTER 5 - VENTURI METER ANALYSIS

General:

In this lab, Bernoulli's equation will be applied in steady state condition to the study of venturi

flow meter. We will also calibrate the venturi meter as a flow measurement device.

Theory:

The conversion of energy for an inviscid, incompressible fluid in a stream-tube is given by

Bernoulli’s equation as:

P V z

g

(5.1)

where P = pressure (F/L

2

); = specific weight of fluid (F/L

3

); V = mean velocity of fluid (L/t);z = elevation of fluid above datum (L); and H = total head (ft-lb/lb or N-m/N).

If we assume no energy is lost between two points, the total head along a streamline is the same(H1 = H2). Substituting Bernoulli’s equation in for total head, we get Equation 5.2.

2

1 1 P V P V

z z g g

(5.2)

Figure 5.1 shows a closed conduit system with an inviscid, incompressible fluid flowing through

it. Sections 1 and 3 have the same diameter, and section 2 has a smaller diameter.

Figure 5.1: Inviscid, incompressible flow through a contraction

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The continuity equation also applies, giving

1 2 1 1 2 2Q Q V A V A (5.3)

where A1 and A

2 are the areas of sections 1 and 2. For a given geometry (A1, A2), one can solve

for up to two unknown using Equations. 5.2 and 5.3 (V1, V2) and hence the flow rate.

Figure 5.2: Actual fluid flow through a contraction


We will measure pressure from all of the pressure taps at three flow rates to get profiles of the pressure along the venturi. Non-dimensional parameter “φ” will be used to normalize these

values. “Normalizing” values means that various dissimilar values that follow the same trend are

modified by a constant parameter within each dataset. This allows the data points to plot on top

of each other, showing that the trend is common between them.

1

2

2

2

nh h

v

g

(5.4)

For the remaining runs we will only measure the pressure difference between the entrance

section and the throat.

Δh

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Some Specific Questions to Address – Venturi Meter

For a given Q, calculate the dimensionless parameter in expression (5.4). Plot (φ) vs.distance along the Venturi for all 3 profile runs on the same chart. No trend line is

necessary, just connect the points.

Plot the velocity head and pressure head along the Venturi Meter for your profile data on

the same plot (one plot per profile for each of the three full profiles). Be sure to plot the

velocity head on top of the pressure head like it was shown in lab and in Figure 5.1.Identify the Energy Grade Line. The best fit lines should reflect the behavior of the fluid,

but it is not necessary to show the equations.

For all the seven readings,

I. Calculate h1-h2 using the measured flow rate and Bernoulli’s Equation

II. Plot (h1-h2)calc vs. (h1-h2)measured III. Plot Qcalc from (h1-h2)measured vs Qmeasured IV. Plot (h1-h2)measured - (h1-h2)calc (= head loss) vs. Q and fit both a straight line and a

quadratic curve

V. Comment on which it the most appropriate fit and why.

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Venturi Meter Data Sheet

ManometerReading

Flow a (1) b c d (2) e f g h j k l

(gpm) (mm) (mm) (mm) (mm) (mm) (mm) (mm) (mm) (mm) (mm) (mm)

1

2

3

4

5

6

7

No measurements will be taken in the grey areas.

You do not need to calculate the values either.

Figure 5.3: Venturi Meter Dimensions

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APPENDIX 2: HOW TO USE THE SELF-CONTAINED LAB BENCHES

The lab benches in the Fluids lab are fiberglass basins with an internal sump pump to provideflow. The top of the bench has openings which all return water should be directed through.

Figure A2.1 shows the operations side of the bench.

Figure A2.1: Lab Bench Diagram

The bench has one red knob in the center of the bench. This is the on/off control. Towards theright side of the bench is the red flow control valve.

To turn the bench on, first open the flow control knob at least three turns. This prevents the pump from running without flowing water. It is a standard globe valve, so turning CCW opens

the valve and turning CW closes the valve. Most pumps are self-cooling, so running a pump in a

closed system (valves closed, pump isolated) will cause the pump to overheat and burn out. Thisapplies to almost every pump you will work with. To turn the pump on, twist the red knob CCW

and it should pop out. To turn the pump off, push the red knob in – no twisting is necessary.

Adjusting the flow rate is done with the globe valve. Just like any valve, it has sensitive control

over certain ranges of % open and less sensitive control elsewhere. This means that when youfirst begin opening the valve, you may turn it multiple complete turns to achieve a rise of 1 gpm.

As you continue opening the valve, you will find that opening the valve a quarter of a turn will

increase the flow by 2 gpm. All valves behave similarly, so be aware of this behavior.

All equipment and test sections should be connected to the system using standard hose clamps.

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CHAPTER 6 – DETERMINING COEFFICIENT OF DISCHARGE

General:

The objective of this lab is to determine the coefficient of discharge of a tank’s outlet consideringthe outlet as an orifice.

Theory:

The usual purpose of an orifice is the measurement or control of flow from a reservoir. It can

also be used to make a pressure differential (drop). When there is no inflow, conservation of

volume is given by

T out

dh A Q

dt , (6.1)

where AT=Area of tank and Qout=outlet flow rate given by

2out D oQ C A gh (6.2)

where CD is the discharge coefficient and Ao is the orifice area.


A bucket, stop watch, and yard stick will be supplied in the lab.

1. Measure the diameter of the smallest outlet and make sure all the holes are plugged.

2. Fill the square bucket with water from the table sump.

3. Once the tank is full, turn off the water supply and remove the smallest plug at the bottomof the tank and let it drain.

4. Record the depth (measured from the center of the outlet) as a function of time at one

minute intervals.

5. Repeat steps 2-3 two more times so that you have 3 sets of time – depth data for the

smallest orifice. Do not remove any of the larger plugs as you will likely cause a flood.

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Figure 6.1: Experimental Setup

Data Collection:

Diameter of outlet (cm) = Cross sectional area of tank (cm2) =

Time

(min)

Head, h (cm)

1st run

Time

(min)

Head, h (cm)

2nd run

Time

(min)

Head, h (cm)

3rd run

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Assuming that the outlet can be treated as an orifice with discharge coefficient CD,

calculate the theoretical height as a function of time by solving equations (1) and (2).

Note that substituting (2) into (1) gives you a first order ordinary differential equation.

Use the analytical equation from the previous step to fit it an appropriate curve through

your measured height vs time data and estimate CD

Comment on any possible sources of error.

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CHAPTER 7 – FLOW OVER A V-NOTCH WEIR

General:

A weir is an overflow control structure built across an open channel for the purpose ofmeasuring the flow discharge. V-notch weirs are sharp crested weirs.

Theory:

Consider the V-notch shown in the figure 7.1. Let H be the height of water surface and ϴ

be the angle of notch. Then, W is width of the notch at the water surface

2 tan2

W H

(7.1)

Figure 7.1: Flow over V-notch

Consider a horizontal strip of the notch of thickness dh under a head h. Then, width of thestrip,

2( ) tan2

W H h

(7.2)

Bernoulli’s equation can be used to show that the theoretical discharge through the strip

is

dQt = area of the strip x velocity = 2( ) tan 2

2

H h dh gh

(7.3)

Integrating between the limits 0 and H and simplifying, the total theoretical discharge

over the notch is given by5 5

2 28

2 tan15 2

t Q g H KH

(7.4)

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where,

82 tan

15 2 K g

(7.5)

Let Qa be the actual discharge. Then the coefficient of discharge, Cd, is given bya

d

t

QC

Q (7.6)

5

2

a d Q KC H (7.7)

The co-efficient of discharge depends on relative head (H/P), relative height (P/W) and

angle of the notch (ϴ).



1. Position the weir plate at the end of the approach channel, in a vertical plane, with thesharp edge on the upstream side.

2. Admit water to the channel until the water discharges over the weir plate.

3. Close the flow control valve and allow water to stop flowing over weir.

6. Admit water to the channel and adjust flow control valve to obtain heads, H, increasingin steps of 0.5 cm.

7. Use the flume orifice equation ( 0.4648

0.2041*Q h ) to calculate the flow rate for

each measured head.

8. For each flow rate, stabilize conditions, measure and record H.

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Due date:

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Data Collection:

Angle of the notch, ϴ =

Head from datum to vertex, P =

Observation Distance from

bottom,Y=P+H

Head,H

Theoretical Discharge5

28

2 tan15 2

t Q g H

Flume orifice

plate headdrop(Δh)

Actual Discharge

0.4648

0.2041*aQ h

a D

t

QC

Q

1

2

3

4

5

6

7

8

9

10

11

12


Find Cd for the V-notch.

Plot Qt vs. H in a plain graph paper.

Plot Qa vs. H in a log-log paper and to findo the power-law relationship between your measured H and Qao Cd for the V-notch weir

Discuss the sources of error.

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CHAPTER 8 – FORCE ON A SLUICE GATE

General:

A sluice gate is a vertical gate installed in open channels to control the discharge. It

allows water to pass underneath the gate. This device may be used as a flow measuring

device. We will also use it to illustrate the momentum theorem.

Theory:

In hydrostatics, the force on a submerged gate was easily calculated from the linear

increase of pressure with depth. We now know from Bernoulli’s equation that as velocity

increases, pressure decreases. The water just upstream of a sluice gate may be moving,

so typical hydrostatic equations do not apply anymore and we must go to the Momentum

equation. The momentum theorem comes from Newton’s Second Law of Motion

(Equation 8.1)

F the rate of change of momentum (8.1)

The force of water on the sluice gate may be computed from the momentum theorem

assuming one-dimensional flow and neglecting shear stresses along the channel bed and

the side walls. See Figure 7.1 for a diagram shoving forces and velocities.

Figure 8.1 Definition sketch of a sluice gate in operation

V1

y1

ys

Fg

y2 V2

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The downstream depth will be hard to measure due to the highly unstable flow. In the lab

you will measure the downstream depth and observe the difficulties. You will check

your measured depth using a contraction coefficient Cc, such that

2 theo c s y C y

(8.2)

Values of Cc have been calculated by von Mises by assuming flow through a sluice gate

to be inviscid flow through the upper half of a two dimensional slot, as shown in Table

6a.1.

Table 8.1: von Mises’ Contraction coefficients for Equation 6a.2

ys/y1 Cc = y2/ys

0.0 0.611

0.1 0.612

0.2 0.616

0.3 0.622

0.4 0.631

0.5 0.644

Experimental Procedure: Sluice Gate as Verifier of Momentum Equation

The sluice gate that will be used has a number of piezometer holes along the center of the

upstream face. These are located at various z elevations above the bottom edge of the

sluice gate. The height of water in each manometer tube (h + z) may be read on the scale

attached to the sluice gate. See Figure 8.2.

Figure 8.2: Measurement of head at different locations on the sluice gate

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With a conceptual knowledge of physics and fluid mechanics, the gate force is simply the

integral of the pressure over the gate area. See Equation 6a.3. In our case, pressure

varies over the height of the gate.

max

0

z

g F PdA (8.3)

Here dA bdz . Since piezometers measure pressure head instead of actual pressure, the

values muse be converted by multiplying h by the specific weight of water (remember

P h ). This leads to Equation 7.4.

max

0

z

g F hdA (8.4)

Here, the actual pressure head, h, can be found with the equation:

reading correction tap elevationh (8.5)

Knowledge of integrals allows the user to recognize that the integral of the pressure head

variation per unit width with depth is equal to the area under the curve of a plot of

pressure head (h) against depth (z). Thus, Equation 8.4 becomes Equation 8.6. See

Figure 8.3 for an example plot. The dots represent pressure head readings from

piezometers located at various elevations. Correct locations for the y-axis intercepts are

critical.

* g Area under the curve F width (8.6)

Figure 8.3 Plot of pressure variation on the gate in the vertical direction

Elevation,

z (ft)

Pressure=γh

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Experimental Procedure: Sluice Gate as a Flow Measurement Device

Flow through a sluice gate can be calculated by simultaneously solving the energy

equation with conservation of volume. It can also be expressed empirically as:

12 sQ Kby gy (8.7)

Here K is a flow coefficient which is a function of 1 s y y . That is,

1

coefficientarea velocity

* 2 * sQ by gy K (sluice equation) (8.8)

Note that this is similar to the empirical equation for the flume’s orifice plate:

0.4648

0.2041*Q h (orifice equation) (8.9)

Values of K are given by Rouse and provided in Table 7.2. Using this information and

the relatively simple measurements of sluice gate opening size and upstream depth, the

flow rate can be calculated.

Table 8.2: Values of flow coefficients for use in Equation 8.8

ys/y1 K

0.00 0.611

0.05 0.5990.10 0.588

0.15 0.578

0.20 0.568

Note: In the case of the specific apparatus that we use in this lab, there is a variation in

the scale attached to the sluice gate. The piezometer tubes for the taps near the bottom of

the gate take up some space, so the scale was attached 0.4 inches (0.0333 ft) above the

bottom of the gate. The tap locations listed (z) are the correct actual distances from the

bottom of the gate but the values read from the gradation behind the piezometers will beless than their true values. For example, a water level reading of 0.1 ft on the scale is

actually 0.133 ft from the bottom of the gate. Thus, the correction needs to be applied to

the piezometer readings as shown in Figure 8.4.

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Figure 8.4: Measurements and scale of the sluice gate

Some Specific Questions to Address – Sluice Gate

Compare the measured value of downstream depth (y2) with the value derivedfrom Equation 8.2.

Determine the flow rate using the energy equation, the calibrated Orifice equation

8.9 and the Sluice gate equation 8.8.

Calculate the theoretical value of the net force of water acting on the sluice gate

from the momentum equation. Determine velocities V1 and V2 using all three Q

estimates calculated previously. Hence, you will determine three theoretical

values of force. (Note: Use the theoretical value of y2 from Equation 8.2 in your

calculations of theoretical force.)

Make a plot of z vs. pressure on the gate similar to that shown in Figure 8.3. Pass

a smooth curve through the data points. Don’t forget to extend the line to

intersect with the appropriate points on the axis. On the same graph plot the

hydrostatic pressure equation max

P z z

Calculate the experimental value of the force on the gate by integrating the

pressure distribution numerically.

Calculate the percent difference between the values of force on the gate

determined by experiment and the three theoretical forces.

Analyze your results and draw your conclusions regarding the validity of the experiment

results. Refer to each of the items you have been asked to determine

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Data collection:

Units:

Upstream depth, Y1: ____

Gate opening, Ys: ____

Downstream depth, Y2: ____

Channel Width, b: ____

Orifice Manometer reading: ____

Tap Number Piezometer

Tap Location (z)

(ft)

Piezometer

Reading

(ft)

1 (near bottom of gate) 0.008

2 0.017

3 0.025

4 0.042

5 0.083

6 0.125

7 0.167

8 0.208

9 0.2510 0.333

11 0.417

12 0.5

13 0.625

14 0.75

15 (near top of gate) 0.875

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APPENDIX 3: AREA UNDER THE CURVE

Approximate Integration

Integration is often referred to as the “area under the curve.” Mathcentre is a UK -based

organization that provides support for subjects, and they have a good reference onintegration by summation that is reproduced below.(http://www.mathcentre.ac.uk/resources.php/80 - reproduction is acceptable for student

distribution and educational purposes only)

To integrate, we take the limit of the summation. This requires knowledge of the

function’s behavior at every x-value. In an experiment, we only have data at specific points and do not know the actual function (we’re trying to determine/prove it). If we

cannot integrate we must revert to the summation process.

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Adding up the area of our known rectangles will provide the area under the curve. The

final value may not be as accurate, but it is incredibly easy to perform in a spreadsheet.

The distance between two recordings is calculable from the cells, and this will give the

“dx” value. “f(x)” is the value of the function – the reading that we have taken and will

be plotting as “y.” This is another cell’s value in the spreadsheet. Each row will then

have an associated “dx” and “y” so a differential area can be found. The summation ofall of those differential areas will be the area under the curve! Obviously, if morerecordings are made then the accuracy will increase because the distance between

recordings (dx) will decrease.

Figure A3.1: Max Value Figure A3.2: Trapezoids

There are various sub-methods for the area of the differential element. Figure A3.1

shows the area of the element calculated from the highest of the two functional values ofthe element. This consistently over-estimates the area. A similar method is to always

take the first value (functional value on the left side of the element). This method can

have varying error, as the behavior may lead to a mix of over- and under-estimations,

making the accuracy uncertain. Another method is to make a trapezoidal shaped element,which assumes linear behavior within the element – see Figure A3.2. This method is

very accurate is the preferred method for approximate numerical integration. A third,

more complex method involves looking at the adjacent elements and finding a moregeneral trend (think of a decaying function). For the purposes of this lab, the extra

accuracy of this method is not worth the extra computation.

Alternate methods of area determination

There are other methods of finding the area under the curve that require more work by

hand. One method is to plot a line through each of the data points and use a planimeter totraverse a scaled plot. This provides good results but is limited to the accuracy of the

data points. Another method is to again plot the data with connecting lines onto graph

paper or plotted with gridlines. The area of each square is known, so adding up the area

of all of the squares under the curve will also yield the total area. This method is verytedious and the squares must be small to avoid large errors in area estimation, but it has

been around much longer than computers and planimeters.

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CHAPTER 9 – VELOCITY PROFILES IN PIPES

General:

In this laboratory session, we will compare theoretical and experimental velocity profilesin pipes for turbulent flow situations.

Theory:

Flow in pipes can occur under laminar and turbulent conditions. The transition from

laminar to turbulent flow is a function of the Reynolds number ( Re UD where

U Q A ). Under normal engineering conditions, transition occurs in pipes at Reynolds

numbers of 2000 to 3000. Below 2000, the flow is completely stable and will always be

laminar.

Turbulent flow occurs at Reynolds number greater than 3000. For turbulent flow, theoryand empirical results give us:

1/

max max

m n y y

V V V R R

(9.1)

Where Vmax is the velocity at the centerline of the pipe and y and R being defined by

Figure 9.1. Some engineers approximate m as 1/7. Others vary m with the Reynolds

number according to Table 9.1. This lab will use the table.

Table 9.1: Reynolds number versus velocity exponent

Re m = 1/n

4.0 x 103 1/6

2.3 x 104 1/6.6

1.1 x 105 1/7

1.1 x 106 1/8.8

3.2 x 106 1/10

Remember that the Reynolds number includes a velocity term. This velocity is the

average velocity over the cross section, not the point velocities that are to be compared.

Figure 9.1: Definition sketch of velocity distribution in pipes

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Experimental Procedures:

This lab will use a manometer connected to a stagnation tube to measure pressuredifferences at various points through a pipe cross section as shown in Figure 5a.2.

Assuming no energy loss due to the stagnation tube (H1 = H2), Bernoulli's equation can

be inserted to get Equation 9.2.

1 P V P V

z z g g

(9.2)

It was previously learned how to evaluate pressure differences from manometer readings,so the velocity at point 2 can easily be computed for the horizontal pipe system. By

moving the stagnation tube across the pipe, the velocity at various locations across the pipe can be measured. In this lab, the setup uses a standard water differential manometer.

Figure 9.2: The stagnation tube arrangement for velocity determination

The discharge will be measured using the orifice plate and manometer in the main supply pipe. To calculate the discharge with orifice plate manometer reading, use Equation 9.3:

0 4

2

1 D

g hQ C Ad

(9.3)

Here 0.82 DC for this orifice plate, 0 A is the orifice plate cross sectional area, h is

the orifice plate manometer reading, and0

d D D is the ratio of orifice plate diameter to

pipe line diameter.

1 2

Air

Δh

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The theoretical velocity profile requires a maximum velocity to base its calculations

around. Use the maximum experimental velocity in the theoretical equation. This will

ensure that the two profiles overlay correctly and the shapes of the profiles can becompared.

To calculate the flow rate using experimental manometer readings along the cross sectionshown in Figure 8.3, use Equation 8.4

ii ave iQ Q V dA (9.4)

Figure 9.3 Schematic for flow rate calculation using manometer readings

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Data Collection:

Units

Brass Pipe Diameter: 2.00 in

Mainline Diameter: 2.00 in

Orifice Diameter: 1.40 inOrifice Plate Δh: in

Tube position Vernier reading

(in.)

y

(in)

Manometer reading

(in.)

1 2.1 0.05

2 2.2 0.15

3 2.3 0.25

4 2.4 0.35

5 2.5 0.45

6 2.6 0.557 2.7 0.65

8 2.8 0.75

9 2.9 0.85

10 3.0 0.95

11 3.1 0.95

12 3.2 0.85

13 3.3 0.75

14 3.4 0.65

15 3.5 0.55

16 3.6 0.45

17 3.7 0.35

18 3.8 0.25

19 3.9 0.15

20 4.0 0.05

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Some Specific Questions to Address – Velocity Profile

Calculate the flow rate from the orifice plate’s differential manometer reading.

Record manometer readings for all Vernier scale positions. Calculate

experimental and theoretical velocity for each Vernier position.

Plot experimental and theoretical velocity profiles on the same graph. Remember

to use data points only with no line to indicate the experimental data, and a line

with no point markers for the theoretical.

Fit a power law curve through the experimental data and comment on exponents.

Calculate the flow rate from the experimental readings. Compare this to the flowrate calculated using the orifice plate.

Calculate the average velocity from the experimental readings using anappropriate method. Compare this to the average velocity calculated from the

flow rate using the orifice plate.

Draw your conclusions from the results.

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APPENDIX 4: INTEGRATION OVER AN AREA (3 DIMENSIONS)

Integration by summation yields a 2 dimensional area with the units of whatever the axes

were. Some things require integration of a 3 dimensional quantity, so it must be handled

carefully to preserve the meaning of the integration.

The first instance this will be used where 3 dimensional areas are required in Chapter 9

(Velocity Profiles) for finding the flow rate within a pipe. A velocity profile provides the

velocity for a certain portion of the flow but the actual calculation procedure may bedifficult to visualize. The first step in doing this calculation is to simply use half of the

velocity profile. We use only half the profile because the area under the curve must be

rotated around the centerline axis of the pipe, and this simplifies the calculation.

Secondly, it is incredibly easier to work this problem in cylindrical coordinates.

Another situation this will be used if to find the Force on a Sluice Gate in Chapter 6A.

This chapter requires the calculation of force on a submerged plate. Pressure is forceover area, so if we can find the pressure acting on the plate, we can find the force.

Piezometers are used to find the pressure, numerical integration is performed, and the

area under the curve is found. This area is for a unit width, so the area must be multiplied

by the width of the plate to get the total pressure “volume” in units of ft^3. Specificweight provides the relationship between force and volume, so the force can be easily

found. This procedure is described in detail in Chapter 6A.

In cylindrical coordinates, the flow rate can be calculated according to the integral

0

2 ( ) R

Q r V r dr

For our data, the location of the reading (y) is the independent variable and the calculated

velocity (V) is the dependent variable. Thinking back to Appendix 3’s ( ) * f x x , thisessentially makes the f(x) value the velocity and the “delta” value the distance betweenrecordings. When rotating this area through 2*pi, you make the simple but incredibly

bad mistake of rotating the area around the radius line (x-axis) instead of the pipe

centerline (y-axis). This error is shown in Figure A4.1.

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Figure A4.1: Incorrect Rotation

To revolve the area correctly, the incremental areas must be calculated a different way.

See Figure A4.2.

Figure A4.2: Correct Method of Revolution

The problem with this method is that the differential areas are not easily calculated. They distance can be calculated easily, but the “delta” value for the summation is now a

“delta velocity” and is not as intuitive to define.

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An easier method is the Shell or Cylinder method of volumes. This allows our original

differential areas to be used. Again, think about the cylindrical coordinate system. See

Figures A4.3 and A4.4.

Figure A4.3: Shell Method (picture from online source)

** the “a” value in the figure is the radius of the pipe **

Figure A4.4: Calculation of Area for Shell

From the flow rate integral, ( )V r dr is equal to the incremental area and the radius of

rotation, r, of each segment is calculated by: ( )r R y . So, writing the Shell Rotation

integral as a summation yields:

Incremental Area Under Curve 2 ( )Q R y

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CHAPTER 10 – FLOW R ESISTANCE

General:

The resistance caused by a fluid as it flows along a pipe results in a continuous loss ofenergy of the fluid. This laboratory session will determine the energy losses due to flow

resistance for turbulent flow.

Theory:

The energy equation for the flow of viscous fluids between two points in a pipeline is

given by:

2 2

1 1 2

1

2 L

V P V P z z h

g g

(10.1)

The term hL represents the energy (head) lost (converted to heat) per pound of flowing

fluid due to the viscous nature of the fluid. The energy loss is a function of the pipe size,velocity of the fluid, length between the two points and viscosity of the fluid. The most

widely used expression relating head loss to the physical properties of the pipeline and

fluid (attributed to Darcy-Weisbach) is

2

2 L

L V h f

D g (10.2)

where L = length; V = mean velocity; D = diameter; g = acceleration of gravity; and f =resistance coefficient. The resistance coefficient varies with Reynolds number andrelative roughness of pipe, where Reynolds number is defined as

Re UD

v (10.3)

where U = mean velocity; D = diameter; and = kinematic viscosity. The roughness of

the pipe is also of importance. The roughness height, k s or ε, is known for certain typesof pipes and is tabulated many places. The relative roughness of the pipe is noted as k s/D

or ε/D. This relationship between resistance coefficient and Reynolds number is

represented graphically by the Moody diagram. This diagram is found in more places

than you can shake a stick at.

The first thing to note a bout Moody’s diagram is that although turbulent flow starts at

Reynolds numbers greater than 3000, the lines representing a particular relativeroughness tend to curve downwards until becoming horizontal. When the given relative

roughness line flattens out, the friction factor for a given relative roughness does not

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change with Reynolds number. The flow is then said to be fully turbulent. This is where

most civil engineering applications operate, and these friction factors are often used as a

first estimate in iterative solutions.

In 1939, Colebrook developed an implicit equation that can be used to solve for the

friction factor of a pipe. His equation covers hydraulically smooth, hydraulically rough,and the in-between areas of turbulent flow. Implicit equations require iterative solutionsfor the variable of concern because it is on both sides of the equation. See Appendix 5

for a description of the solution of implicit equations. Colebrook’s equation is as follows

1 2.512.0*log

3.7 Re*

D

f f

(10.4)


This lab will experimentally determine resistance coefficients (f) for the test pipe forseveral different flow rates (and therefore several Reynolds numbers) in a setup shown inFigure 10.1. The head loss can be determined by simplifying Equation. 10.1.

First, turn on the pipe and wait 3 minutes to get steady. Read the pressure difference forfirst length of pipe (12ʹ). This will give head loss for that flow rate. The procedure

should be repeated for four flow rates. Also, this lab will determine head loss as a

function of length. Set the flow rate to maximum, and record the manometer reading fordifferent pipe lengths provided in experimental data sheet.

Figure 10.1: Schematic drawing of pipe head loss setup

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Data Collection:

Units

Brass Pipe Diameter: 2.00 in

Mainline Diameter: 2.00 in

Orifice Diameter: 1.40 in

Pipe is made of brass and the corresponding roughness height is

0.00005 0.015 ft mm

Run No. Manometer Reading

(Orifice plate)

Pipe Length Manometer

Reading (head loss)

(in) (ft) (in)

1 12

2 12

3 12

4 12

5 4

6 See run 5 8

7 See run 5 12

8 See run 5 14

9 See run 5 16

10 See run 5 18

Some Specific Questions to Address – Flow Resistance Determine the experimental friction factor for each of the runs using Darcy-

Weisbach friction loss equation.

Determine the theoretical friction coefficient for each of the flows using the

Moody diagram from textbook.

Determine the theoretical friction coefficient for each of the flows using theColebrook equation.

Compare the experimentally determined f value with the two theoretical f values.

Comment on your results. If the experimental f value varies from the theoretical f

values, explain why this might be so.

Make a plot of head loss as a function of flow rate, fit an appropriate curve andcomment on the type of function.

Make a plot of head loss ( Lh ) as a function of distance along the pipe using the

5th discharge only, fıt a curve and comment on the function.

Do the changes in distance along the pipe and discharge produce expected

resultant head losses? Give your reasons.

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APPENDIX 5: IMPLICIT EQUATION SOLUTION PROCEDURE

An Implicit equation is one that has the variable of interest in two locations and cannot be

simplified to one. For example, Colebrook’s equation for fr iction factor (used in Chapter

5b) is:

1 2.512.0*log

3.7 Re*

D

f f

The friction factor, f, is unknown while the other parameters have been calculated. Astandard solution procedure is as follows:

1) Guess a value for the variable of interest. (f = something)

2) Using the guessed value of f and the known values, solve one side of the equation.

(f = something, e/D = something, Re = something right hand side of theequation = something)

3) Solve for the variable of interest. (f on the left hand side of the equation =something)

4) Compare the guessed value of the variable of interest to the one you justcalculated. (f guess ?=? f something)

5) If the values are the same within some tolerance margin, the value of the variableof interest is the one just calculated. If the two values are not close enough, repeat

these steps. The recently calculated variable of interest now becomes yourguessed value. (f something f guess; insert this value on right hand side of equation)

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CHAPTER 11 – PUMP CHARACTERISTICS CURVE

General:

The objective of this lab is to calculate the pump performance curve for the pump, Ep(Q),and to compare it to the curve provided with this lab manual.

Theory:

The performance of a pump can be represented graphically by characteristic curve. A

typical characteristic curve shows the total head rise over the pump as a function of pump

discharge.


A bucket, a submersible aquarium pump, some tubing, stop watch, tape measure and a

measuring cup will supplied in the lab. Measure the flow rate produced by the pump for a

range of heights (at least 9) above the water surface, including the height for which there

is no flow rate


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Data Collection:

Diameter of Pipe = Length of pipe =

Observation Head,

H(cm)

Volume

ofwater in

the cup,

(ml)

Time

(sec)

Q (ml/s) Outlet

velocity(cm/s)

Head loss

(cm)

1

2

3

4

5

67

8

9

10


Calculate outlet velocity for each measurement case.

Calculate friction factor f for each flow rate assuming the tube is a smooth pipe.

Calculate head loss for each discharge using Darcy-Weisbach formula.

Apply the work energy equation from point 1 to point 2, and calculate pump

performance curve that is, Ep(Q).

Plot your calculated points on the supplied pump performance curve (plot by

hand).

Discuss briefly any sources of error.

Note that the bucket supplied has a flow rate meter attached. This is for a different lab

and should not be connected during this experiment or used to measure the flow rate.

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Ep (cm)

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In-class calculations will be submitted after lab session

51

CHAPTER 12 – HYDRAULIC JUMP

General:

The hydraulic jump is an open channel phenomenon whereby water (or any liquid)

flowing at a small depth y1 abruptly jumps to a larger depth y2 and continues to flow atthe new depth. The phenomenon is a chaotic, turbulent one and is associated with loss of

energy.

Theory:

Water flowing in open channels will occur in one of two velocity states, subcritical or

supercritical. Supercritical flow is characterized by a high velocity and is relativelyunstable. Subcritical flow has a lower velocity and is stable. A dimensionless ratio

which allows the definition of these conditions is the Froude number, given by:

* m

V V Fr A gy

g T

(12.1)

where V = velocity; g = acceleration of gravity; A = cross-sectional flow area; T = top

width of flow; ym =A/T= hydraulic mean depth (ym=y for a rectangular channel).Supercritical conditions occur when Fr > 1 and subcritical conditions occur when Fr < 1.

When supercritical flow encounters insufficient energy gradient, which causes it to

become subcritical, it undergoes an abrupt change in depth, known as the hydraulic jump.In this transition, considerable loss of energy occurs. The simplest analysis of this

situation involves a control volume approach in which the momentum equation is

applied.

This lab will use a rectangular open channel. A side-view of the water surface is shown

in Figure 12.1. If the body of water between sections 1 and 2 is considered as a controlvolume, the only horizontal forces acting on it are the hydrostatic forces from the

adjacent masses of water and a small shearing force along the perimeter. Neglecting the

bed shear stress, since the length between the sections is small, the momentum equation

is

1 2 2 1 F F QV QV (12.2)

Here F1 and F

2 are hydrostatic forces as shown in Figure 6b.1. The conservation of

volume equation of the system gives:

1 1 2 2Q V A V A (12.3)

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hL

F2

EGL

y2

V22

2gV

2

1

2g

1 y1

Figure 12.1: Schematic drawing of a hydraulic jump

Solving the equations 12.2 and 12.3 simultaneously the depth at section 2 can be

calculated:

2

1

2 3

1

81 1

2

y q y

gy

(12.4)

Equation 12.4 can be used to give either jump depth (the conjugate depth) if the other

depth is known. Subscripts can be interchanged if y1 is desired and y

2 is known.

Equation 12.4 can also be expressed in terms of the Froude number:

21

2 11 1 8

2

y y Fr

(12.5)

or

221 2

1 1 82

y y Fr

(12.6)

The energy lost in the jump can be determined having solved for the depths by writing

the energy equation between sections 1 and 2

2 2

1 2

1 2

2 2 L

V V y y h

g g (12.7)

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Theoretical discharge can be calculated using orifice manometer reading –

0.4648

0.2041*Q h (orifice equation) (12.8)


This lab will use a rectangular flume provided with a flow measuring device. By

allowing water under a sluice gate and raising an obstruction at the downstream end ofthe flume, we will cause a hydraulic jump to occur at one flow rate. We can then

measure y1, y2, and discharge for the jump Q. So, by using any two of these parameters

(y1, y2, and Q), we can find the third from one using 12.2 and 12.3 and compare thetheoretical value to the measured value.

The selected values for y1 and y2 should be away from the jump where the depth is not

changing. Theoretically, these two depths are the normal channel depths before and afterthe jump happens, so they should be taken where they are near constant values on either

side of the jump.

Data Collection:

Units

Orifice Manometer Reading*

Channel width

Upstream depth

Downstream Depth

Required In-Class Calculation Set

This should be done like an extended set of sample calculations with a narrative. Don’tforget to list the equations used before numbers are substituted into it.

1) State known parameters and measured parameters.

2) Calculate Q using both: the flume’s orifice plate, equation 12.8 (theoretical)

using equations 12.2 and 12.3 (experimental)

Using the estimate of discharge calculated from orifice plate equation and measured y1and y2 values

3) Calculate the Velocity and Froude Number at each section (Upstream andDownstream).

4) Calculate the head loss across the jump.

5) State any observations about the results.

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6) Calculate y1 from the conjugate depth equation 12.6. What is the percentagedifference from the measured value?

If the percent difference was less than 2%, finish the calculations with a y1 value 2%higher than the measured value. If the error was greater than 2%, use the calculated y1

value for the final steps. This will show the sensitivity of the final numbers to errors.

7) Re-calculate velocity and Froude Number at point 1.

8) Re-calculate the head loss across the jump.

9) Comment on your observations and calculations.

ce 3411 manual- spring2016

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