Table of ContentsINTROCUCTION2Experiments2Chapter 1: Rapidly varied steady flow21. A-1Hydraulic Jump21.1.Introduction21.2.Apparatus21.3.Procedure41.4.Observations51.5.Lab Results61.6. Calculations of the data71.7 Results discussion131.8. Errors151.8 Conclusion16A-2 Flow through a venturi flume162.1. Introduction162.2 Apparatus162.3 Procedure172.4 Observations172.5 Lab Results182.6 Calculations of the data192.7 Results discussion212.8 Conclusion21Chapter 2: Backwater curve22Rectangular channel221.1.Data221.2.Calculation:221.3.Spread sheet23Trapezoidal channel242.1.Data242.2.Calculation:242.3.Spread sheet24REFERENCES25

INTROCUCTIONThe main purpose of this experimental report is on the hydraulic jump phenomena where hydraulic jump equipments has been used and the amount of water that passes through the sluice gate is measured and analysed.(Chadwick et al, 2009) defines a hydraulic jump as a jump of water established when a supercritical flow slows down due to friction from the wetted perimeter until it becomes a subcritical flow and there is a rapid movement of water and this rapid movement causes turbulence in the water that result in an energy loss.The report will also experiment on the flow of water through a venture flume; the main aim of this experiment is to: demonstrate the flow of water from a subcritical flow to a super critical flow. When water is allowed to pass on a venturi flume the flow goes from a sub to supercritical flow as it passes through the constriction.

ExperimentsChapter 1: Rapidly varied steady flow1. A-1Hydraulic Jump1.1. IntroductionThe hydraulic jump phenomenon is a rather abrupt change from super critical to sub critical flow. This change in momentum in real life often occurs after a flow through a dam, or flow from a steep to a mild slope and finally flow from a reservoir. To mimic the real life hydraulic jump a set up was done that included the apparatus as elaborated below.

1.2. Apparatus

Sump tank, Flow meter, upstream tank, Downstream tank, Pipes, Pump, Open channel, Horizontal scale, Point gauge, Sluice gate, Rule.

Figure 1: Hydraulic jump apparatus1.3. Procedure

The hydraulic bench was filled with enough water to connect to the H23 Flume water Intake. The channels dimensions were measured and recorded The flume was levelled and the sluice gate installed at the upstream end with the required aperture. A baffle block is placed at a suitable location just upstream of the gate to streamline the flow. The depth gauge was then used to set the channel bed as the datum. The discharge control was then adjusted to establish a stable hydraulic jump The volumetric flow rate was then measured The water depth immediately after upstream and downstream y1 and y2 respectively of the sluice gate. The water depth of the sluice gate is then measured i.e. y3 (upstream) and y4 (downstream).

1.4. Observations

1. A centrifugal pump was used to increase the pressure of fluid in the open channel by using a rotating propeller.2. The hydraulic jump phenomena is observed as an obstruction of the flow of water that forces a super critical flow to change to a subcritical flow.

Figure 2: Picture showing hydraulic jump

Y1LY2

Figure 3: Figure showing hydraulic jump, length of jump, upstream and downstream

1.5. Lab Results

Time 1 [sec]Time 2 [sec]Time Av.[sec] per 5L

28.8328.7128.77

23.3523.2523.3

19.2419.4519.35

17.3417.4817.41

23.1023.3023.31

19.0218.7418.88

15.7016.1015.9

13.8313.5713.7

Table 1: Table showing the Hydraulic jump experiments done and the time taken

y1 [m]y2 [m]y3 [m]y4 [m]

10.060.00620.0120.026

20.0850.00630.0120.030

30.1150.00610.0140.033

40.1430.00630.0120.041

50.0580.00810.0110.033

60.0830.00800.0130.037

70.1200.00830.0100.053

80.150.00820.0110.056

Table 2: Table showing values of Y1, Y2, Y3 and Y4

1.6. Calculations of the data1.6.1. Calculating Yc, discharge Q and discharge q

y1 [m]y2 [m]y3 [m]y4 [m]yc [m]L[m]Discharge, Q (m^3/s)q [m^2/sec]

10.060.00620.0120.0260.0210.730.00050.00954

20.0850.00630.0120.0300.0230.550.00060.011

30.1150.00610.0140.0330.0280.5750.00080.0152

40.1430.00630.0120.0410.0310.710.00090.0171

50.0580.00810.0110.0330.0230.150.00060.011

60.0830.00800.0130.0370.0290.630.00080.015

70.1200.00830.0100.0530.0311.150.00090.0171

80.150.00820.0110.0560.0361.210.00110.021

Table 3: Table showing values of L and discharge q

In order to calculate the value of yc the values of discharge Q and q are calculated, to calculate the discharge Q the following formulae is used:

Thus, to calculate Q for values of row 1

The discharge q is obtained by using the following formula

Again to calculate q for values of row 1:

Now to work out yc the following formula is used.

Therefore, the yc value for the first row is

1.6.2. Calculating Specific Energy (E)The specific energy is the mechanical energy that is relative to the bottom of the channel.Specific Energy, E

E1 [m]E2 [m]E3 [m]E4 [m]Ec [m]

0.0630.0750.0330.0390.042

0.0850.1130.0380.0350.031

0.1180.1600.0440.0380.035

0.1440.2100.0590.0450.036

0.0620.0680.0430.0360.031

0.0860.09730.0560.0410.033

0.120.1350.110.0540.038

0.1530.1790.1210.0620.042

Table 4: Table showing specific energy values

The head losses are determined by the energy equation as follows:

Therefore the specific energy E value of the first row in the table is calculated as:

1.6.3. Calculating E for theoretical values of y and obtaining y/yc [Ratio] and E/yc [Ratio]y [m]E[m]y/yc [Ratio]E/yc [Ratio]

0.2398900.00322114.1132970.189499

0.2187390.00337712.8688990.198652

0.2003400.00353211.7864680.207805

0.1842400.00368810.8392580.216958

0.1700740.00384310.0058230.226111

0.1575460.0039999.2688060.235264

0.1464170.0041548.6140390.244417

0.1364870.0043108.0298620.253571

0.1275930.0044667.5066120.262724

0.1195980.0046217.0362240.271877

0.1123860.0047776.6119240.281030

0.1058600.0049326.2279900.290183

0.0999380.0050885.8795620.299336

0.0945480.0052445.5624880.308489

0.0896310.0053995.2732080.317642

0.0851340.0055555.0086500.326795

0.0810130.0057104.7661590.335949

0.0772270.0058664.5434240.345102

0.0737420.0060214.3384300.354255

0.0705300.0061774.1494130.363408

0.0675620.0063333.9748210.372561

0.0648160.0064883.8132880.381714

0.0622720.0066443.6636060.390867

0.0599110.0067993.5247010.400020

0.0577170.0069553.3956210.409174

0.0556760.0071103.2755150.418327

0.0537740.0072663.1636230.427480

0.0520000.0074223.0592630.436633

0.0503440.0075772.9618230.445786

0.0487960.0077332.8707520.454939

0.0473470.0078882.7855530.464092

0.0459910.0080442.7057750.473245

0.0447210.0082002.6310110.482399

0.0435290.0083552.5608910.491552

0.0424100.0085112.4950790.500705

0.0413590.0086662.4332670.509858

0.0463660.0080002.7278020.470658

0.0424850.0085002.4994820.500074

0.0393140.0090002.3129120.529490

0.0367070.0095002.1595400.558906

0.0345540.0100002.0328940.588322

0.0290510.0120001.7091620.705987

0.0254960.0169971.5000001.000000

0.0261390.0200001.5377881.176645

0.0327280.0300001.9254751.764967

0.0415350.0400002.4435762.353290

0.0509820.0500002.9993952.941612

0.0606820.0600003.5700623.529935

0.0705010.0700004.1477384.118257

0.0803840.0800004.7291514.706580

0.0903030.0900005.3127365.294902

0.1002460.1000005.8976705.883225

0.1102030.1100006.4834866.471547

0.1201710.1200007.0699017.059869

0.1301450.1300007.6567407.648192

0.1401250.1400008.2438858.236514

0.1501090.1500008.8312578.824837

0.1600960.1600009.4188029.413159

0.1700850.17000010.00648010.001482

0.1800760.18000010.59426310.589804

0.1900680.19000011.18212811.178127

0.2000610.20000011.77006011.766449

Table 5: Table showing y/yc [Ratio] E/yc [Ratio]

The values of q are then used to determine the specific energy E for a range of theoretical values of depth y of up to 200mm.The values of E are obtained via a summation of E values plus a constant value of 0.00016i.e. E2 = E1 + 0.00016

1.6.4. Froude numbers

y4/y3 [Ratio]v1 [m/sec]v2 [m/sec]v3 [m/sec]v4 [m/sec]F1F2F3F4

2.1670.1591.5390.7950.3670.216.242.320.73

2.500.1291.1750.9160.3670.144.732.670.69

2.3570.1321.2491.0860.4610.125.112.930.81

3.4170.1202.7141.4250.5520.10 10.94.150.87

3.4230.1891.3580.3330.4780.253.862.400.53

2.8460.1811.8751.1540.4050.184.832.550.55

4.8180.1432.061.710.3230.135.734.820.33

5.090.142.3611.9090.5850.096.564.770.35

Table 6: Table showing Froude numbers

y4/y3 [Ratio] is first obtained by dividing the values of y4 by y3.The different Froude numbers are then calculated using the following formula.

Therefore F1 is obtained for the 2nd row as follows:

1.6.5. y4/y3 Ratio for theoretical and experimental valuesExperimentalTheoretical

y4/y3 Ratioy4/y3 Ratio

2.1671.95

2.502.65

2.3572.35

3.4173.50

3.4233.52

2.8462.91

4.8185.32

5.096.23

Table 6: Table showing Froude numbers

Theoretical values of y4/y3 are calculated using the following formula:

1.6.6. Theoretical head lossesTheoretical

y4 [m]hL [m]

0.0230.0012

0.0320.0052

0.0310.0048

0.0490.0140

0.0400.0068

0.0370.0099

0.0520.0520

0.0650.0523

Table 7: Table showing theoretical values of y4 and Hl

Theoretical values of y4 are calculated using experimental values of y3 and the Froude numbers already calculated.The values of head loss are calculated using the following formula:

The head loss formula to calculate theoretical head loss is modified to:

i.e. 1.6.7. Experimental head lossesExperimental

y4 [m]hL [m]

0.0260.0022

0.0300.0042

0.0330.0038

0.0410.0120

0.0330.0061

0.0370.0083

0.0530.0421

0.0560.0467

Table 8: Table showing experimental values of y4 and Hl

The head loss value using the experimental data is calculated the same way as the theoretical values, the only difference being that this time the experimental values are used.

1.6.8. L/y4 for experimental and theoretical valuesExperimentalTheoretical

L/y4 RatioL/y4 Ratio

24.328.1

17.218.33

18.2117.58

14.517.32

3.754.55

17.0317.05

22.1221.7

17.2321.60

Table 8: Table showing theoretical and experimental values of L/y4

The values of L/y4 are obtained by dividing the length to the respective y4 values.

1.7 Results discussion The hydraulic jump phenomena was observed in the experiment where flow from a supercritical to subcritical conditions were experienced. 1.7.1 Specific energy

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Graph 1: Specific energy curve

Graph 2: Specific energy curve dimensionless

The graph 1 shows the specific energy against the depth: Between 1 & 2 the flow was subcritical and at 3 the flow was supercritical. At 1-4 there is a massive reduction in depth, but a relatively small energy loss At 2-4 the energy loss increases with an increase in depth

1.7.2. Froude numberpartFroude numberType of flow

1Fr< 1 : Subcritical flow

2Fr> 1 : Supercritical flow

3Fr> 1 : Supercritical flow

4Fr< 1 : Subcritical flow

A stable jump requires the Froude number to be in between 4.5 9, from the Froude number values depicted in the table above the hydraulic jump experienced was a stable jump.

Graph 3: y4/y3 ratio against Fr

The depth ratio y4/y3 of experimental and theoretical values are shown in graph 3, the graph sows that the depth ration of theoretical values is higher compared to the experimental values.

1.8. Errors

1.8.1. Human errorsThere is a big chance that the results read of the scales were not accurate. Measures were taken to ensure that the readings were as accurate as possible, this measures included: Counterchecking with other groups Having two people taking readings1.8.2. Misreading the depth and width of waterThe depth and width may have been misread which might results to erroneous results. The error is minimal hence might not really affect the results as much.1.8.3. Equipment errorThe equipment used in the experiments may have an error, from not being calibrated well. The discrepancies in measurement may yield different results for experimental and theoretical values.1.8 ConclusionThe experiment has demonstrated the hydraulic jump phenomena where flow changes from supercritical to subcritical conditions. This change in flow results in a considerable amount of energy loss.From the tables and graphs it can be seen that the theoretical values were slightly higher than the experimental values, this difference may have been caused by errors experience whilst carrying out the laboratory experiment.A stable jump was obtained this was proved from the Froude values calculated.The hydraulic jump phenomena is used practically in weirs, dams and spillways etc. In weirs and dams the hydraulic jump is used effectively to dissipate energy, the water flows down from a weir or dam at very high velocity, without loss of energy the water may corrode dams and cause damage to the structures.

A-2 Flow through a venturi flume2.1. IntroductionThe flow through a venture flume reduces the flow of water by restricting the width of water basing through the channel.2.2 Apparatus

Venturi flume, trapezoidal liners, Vernier clip, rule, scale.

2.3 Procedure

The venturi flume comprising of the two smooth trapezoidal liners that fit to the side of the panels was placed in a position upstream of the channel outlet. The depth gauge was then used to set the channel bed as the datum. The volumetric flow rate, water depth upstream in the throat and downstream on the venture flume was then measured starting with the maximum flow and then reducing in 3 steps. The pitot tube was then used to measure the specific energy across the channel 2.4 Observations

1. The flow of water moved from a subcritical flow to a super critical flow.2. In the subcritical flow the wave velocity is greater than the flow velocity, whereas in the supercritical flow the flow velocity is greater than the wave velocity which is the exact opposite of the latter.

2.5 Lab Results2.5.1. Time to collect 5litres of water in seconds

2.6 Calculations of the data

2.6.1. Mean time in secondsThe mean time in seconds is calculated by taking the average of the flow measurements and the experimental recorded time.

2.6.2. Standard deviation of timeThe standard deviation in time is calculated by using the mean time already calculated, and subtracting it by the mean and square results of each value. The mean of those squared differences is then calculated and finally the value obtained is square rooted to obtain the standard deviation.

2.6.3. Specific energyThe specific energy is calculated using the height and the pitot value obtained, the following formula was used:

i.e.

2.6.4. Mean flowThe mean flow in m3is calculated by taking the total flow and dividing it by the mean time.

i.e.

2.6.5. Froude valueThe Froude value is calculated using the modified Froude formula

i.e.

2.6.6. Energy loss through the venture flume

2.7 Results discussion A subcritical to a supercritical flow is experienced as depicted from the calculated Froude number values.i.e. Fr 0.2557 0.5518 2.5527

The specific energy also increases with the decrease in height and the increase in length of the measuring position.The drag coefficient was calculated as elaborated on the table above, this shows that the drag coefficient is negligible and doesnt affect the results obtained.

2.8 ConclusionThe reduction in width (constriction) causes a change in velocity and height as wasdepicted in the analysis3. Health and safetyIn order to ensure that the experiments are carried out efficiently and effectively, health and safety is a priority. The health and safety measures that need to be carried out are: Managing the water level in the channel to avoid over flowing Cables to be effectively fitted on poles to avoid tripping All cables should be insulated to avoid danger of electrocution Emergency stop button to be located in a precise location and to inform students of its location and use.Chapter 2: Backwater curveRectangular channel1.1. DataRectangular channel

Q (m^3/s)=10

b(m)=5

L (m)=200

q [m^2/sec] =2

y_cr =0.741532735

So=0.0005

n=0.033

z=0

1.2. Calculation: Area: b x h = 5 x 3.2 = 16 m^2 Perimeter: b + 2h = 5 x (2 x 3.2) = 6.4 m R = = R^4/3 = 2.54/3= 3.39 E = h + y2/2 = 3.2 + 0 = 3.2 Delta = E2 E1 = 3.1 - 3.2 = - 0.1 Delta Ax = delta / b = 5/-0.1 = -0.02 X = summation of delta Ax Bed level = 100 + (b x) = 100 + ( 5 x -0.02) = 99.9 Water surface level = bed level + respective height = 100 +3.2 = 103.2

1.3. Spread sheet

Graph 4: Backwater curve for a relief channel

Trapezoidal channel2.1. Data

Trapezoidal channel

Q (m^3/s)=10

b(m)=5

L (m)=200

q [m^2/sec] =2

y_cr =0.741532735

So=0.0005

n=0.033

z=0

2.2. Calculation:Area (b + mh)h = (5 + 3 x 3.2)3.2 = 46.72 m^2Perimeter: b + 6.4 h = 5+ (6.4 x 3.2) = 25.48m

2.3. Spread sheet

REFERENCES1. Chadwick, A., MORFETT, J.& BORTHWICK, M.(2004) Hydraulics in Civil and Environmental Engineering, 4th ed, London and New York, Spon.2. MASSEY, B.S. (1989) Mechanics of Fluids, 6th ed, London, Chapman and hall.3. HAMILL L ,(2001), Understanding hydraulics, 2nd edition, Palgrave Macmillan

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