Hydraulic Jump

University of Greenwich School of Engineering Department of Civil Engineering CIVI-1012-M01 Hydraulics BEng / MEng

Laboratory Report DETERMINATION OF THE PROPERTIES OF A HYRAULIC JUMP WITHIN AN OPEN CHANNEL AND APPRECIATE EXPERIMENTAL AND THEORETICAL ANALYSIS Group 2 Friday 8th February 2013 11:00 – 13:00 Written by; Ihor Moyiseyev Andrew Woods Baris Evran

000675368 000605786 000696354

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Contents 1 Introduction 1.1 Objectives of Experiment 1.2 Theory 1.3 Apparatus 1.4 Procedure 1.5 Health and Safety

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2 2.1 2.2 2.3 2.4

Calculations Hand Booking sheet Tables Graphs Checking spreadsheet calculations

4 5-6 6-8 9 - 16

3 3.1 3.2 3.3

Conclusion Possible sources of error The relationship between experiment and theory The relationship between the concepts explored and practical applications

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References

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5

Group Log

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1

Introduction

In the deep narrow rectangular channel, the flow of water was regulated in the upper end of the channel by a sluice gate in order to develop a shallow and rapid supercritical flow. At the lower end of the channel, another sluice gate was placed to form a barrier which forced the flow of water in front of it to pile up. This was done to create a subcritical flow just before the sluice at the lower end of the channel. The transition from the supercritical flow to the subcritical flow created the phenomenon called the hydraulic jump, which was formed in between of the two flow regimes.

1.1

Objectives of Experiment

The purpose of the Hydraulic Jump Laboratory experiment was to observe the phenomenon of the hydraulic jump, and to develop an understanding of the properties of the hydraulic jump phenomenon. Also, to appreciate the relationship between the experimental results and the theoretical analysis based on the application of continuity and momentum principles.

1.2

Theory

In this experiment, we are trying to create two different types of flow in a small channel. The transition from the supercritical flow to the subcritical flow creates the phenomenon called the hydraulic jump, and in order to observe this phenomenon, we needed to create these two flows. The dynamics of hydraulic jump is governed by the flow continuity and the momentum equation. From the theory we know that a hydraulic jump has the ability to dissipate large quantities of energy. This means that it could have a high number of applications in the modern world. Also, because the energy dissipation is high and the head loss is unknown, we cannot use the energy equation when dealing with a hydraulic jump. Therefore, we will need to use different equations in this experiment. However, in this control environment, the width of the channel, the velocity of the flow and the height of the sluice gates openings are known, than we can assume that Q = bV1h1 = bV2h2 Where Q is the discharge, V is the average velocity and h are the heights of the sluice gate openings, and b is the width of the channel, which is the same everywhere in this particular channel. The numbers represent the locations of the measurements, 1 being in the upper end of the channel, and 2 being in the lower end of the channel. The friction between the sides of the channel can be ignored as it is negligible due to glass being fairly smooth. However, the hydrostatic forces will need to be accounted for in our calculations. Therefore a simplified momentum equation will look like this: 0.5 x ρgbh21 - 0.5 x ρgbh22 = ρQ x (V2-V1) Where ρ is the density of the fluid, and g is the gravity of the earth, which is 9.81 m/s2 Momentum can be defined as M = V2h/2g + h2/2 And by combining the first and the second equations, we can show that M1 = M2 The Froude's number of the upstream flow can be defined as Fr1 = V1/(√gh1) For a hydraulic jump, the upstream flow is supercritical and is Fr1>1, and the downstream flow is subcritical, therefore Fr1<1 there, so Fr2 = V2/(√gh2) < 1 Also, we can calculate the head loss of the hydraulic jump by using the conservation of energy relationship, which is: h1 + V12/2g = h2 + V22/2g + hL Where hL is the Head Loss for the hydraulic jump. After simplifying, we can deduce that: hL = (h2- h1)3/(4h1h2) 2|Page

1.2

Apparatus

(Figure 1.1 – This shows the equipment set up used in the experiment) The following apparatus were used in this experiment:  S16 Hydraulic Flow Demonstrator  F1-10 Hydraulics Bench

1.4 1 2 3 4 5 6

Procedure Make sure that the channel bed is flat by retracting the adjustable central section of the channel bed. Start the pump and set the desired flow of water. Raise the sluice gate in the upper end of the channel to a height of less than that of the water behind it. Make sure that the height of the water behind the sluice gate is higher than the height of the gap under it. Raise the height of the sluice gate in the lower end of the channel to a height of such that the hydraulic jump is formed around the middle of the channel. Record the height of both sluice gates. Also, record the height of water just after the upper channel sluice gate, in the middle of the channel and just before the lower sluice gate. Repeat the previous procedure by adjusting the flow rate of water and the height of the sluice gates.

The flow of water set by the flow control valve is measured in litres per minute (l/m). The flow rates that we chose ranged between 30 and 70 litres per minute. We decided to use the gate opening in the upper end of the channel at 10mm, 15mm and 20mm of height.

1.5

Health and Safety

Health and safety in the laboratory is crucial while conducting a practical experiment. Safety footwear has to be worn throughout working in the lab. Make sure your work space is clear to minimise the risk of trips and falls and minimise the use of electrical equipment around the experiment as we are using water. We must obey the Technicians' laboratory rules. No eating, drinking or jokes allowed. 3|Page

2

Calculations

When conducting our experiment in the laboratory we recorded our results in a hand written booking sheet. Then we inputted those results into an excel spreadsheet which formulated tables of results and graphs to represent the data. To ensure that the calculations carried out in excel were accurate we calculated the results by hand to ensure maximum accuracy in our calculations.

2.1

Hand Booking sheet

(Figure 2.1 – This shows the hand booking sheet from the laboratory)

(Figure 2.2 - This figure shows a diagram that shows the positions of reading from figure 2.1) 4|Page

2.2

Tables

We calculated all our results using information recorded in the hand booking sheet, this enabled a quick easy way to find our data.

(Figure 2.3 – This figure is a table showing our recorded results from the laboratory)

(Figure 2.4 – This is table showing the first half of calculated results in excel)

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(Figure 2.5 – This table is the second half of the calculated results from excel)

2.3

Graphs

We were able to use the data we calculated in the excel spreadsheets (Figures 2.4 – 2.5) to create two graphs. The first graph (Figure 2.6) shows the relationship between the Froude number and y2/y1. The second graph (figure 2.7) shows Froude number compared against percentage relative head loss.

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(Figure2.6 – This shows a graph made from the calculated data from excel)

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(Figure 2.7 – This figure shows a graph comparing percentage relative error against Froude Number)

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2.4

Checking spreadsheet calculations

As we carried out the experiment and completed the calculations we wanted to ensure maximum accuracy therefore we completed a sample of the calculations by hand and them compared them to the excel calculations to see if there was any systematic errors.

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(Figure 2.8 – This figure is showing how to prove the formulas)

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(Figure 2.9 – This figure is showing how to prove the formulas)

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(Figure 2.10 – This figure is showing how to prove the formulas) 12 | P a g e

(Figure 2.11 – This figure is showing how to prove formulas and shows a selection of data needed to prove the excel calculations) 13 | P a g e

(Figure 2.12 – This figure shows the calculation to check against excel) 14 | P a g e

(Figure 2.13 – This figure shows the calculation to check against excel) 15 | P a g e

(Figure 2.14 – This figure shows the calculation to check against excel) 16 | P a g e

3 3.1

Conclusion Possible sources of error

In any experiment there are many different things that can cause errors within an experiment. We usually conduct experiments in a laboratory environment to minimise the factors that cause errors.  Human Error In any experiment there will be always be the factor of human error. In this experiment human errors that could have occurred include the incorrect booking of results. This is a common error within laboratory experiments. The person reading the values off the scale may have read the values incorrectly and therefore cause an error within our collected results. To minimise these errors we used two people reading the values of the scale and instruments to ensure that one person could not mis-read a value and we had two people booking the results, so if one person conducted an error the other person should have the correct readings. We also compared our results against other groups to ensure our results are in the same ball park.  Mis-Reading of the depth of water To record the height of the flow we must record the height of the water using the attached scale on the clear flume. We could have picked up an error if the scale was incorrectly attached to the flume and therefore showing an inaccurate reading of the height of the water. As the flume is rather narrow the water draws up the sides and this causes a meniscus. The meniscus makes it hard to find the true value of water level as you are reading the bottom of the “bubble”, in accurate reading of the “bubble” will cause our results to be off by a few millimetres. The flow after it had undertaken the hydraulic jump was turbulent this meant the true height of the water running through the channel was under interpretation by the person who was reading off the scale. To make our results more accurate we had two people checking the height of the flow so we could compare answers and take an average value. As the equipment was new we would assume the scale had been recently calibrated and therefore should be accurate.  Mis-calculation of the opening below the gate There was no direct way to measure the height of the gate, therefore in the experiment we had to record the height of the top of the gate and then take the height of the gate away from that value. In the experiment we did these calculation in our head to ensure the experiment was done within our time slot. As the calculation were done mentally this could cause an error within our results however because there was three of us conducting the experiment, we could double check each other’s calculations.  Equipment Error In the experiment we used a digital flow meter to record the flow in the pipe and therefore in the open channel. If it has been a long time since the flow metre has been calibrated then it may be slightly inaccurate causing inaccurate results. This would cause a discrepancy in the comparison between experimental and theoretical results. As the flow meter was in fact a digital flow meter this means any minute change of flow would not be noticed this because the digital meter takes immediate readings and therefore the change would not be noticed, however if an analogue flow meter had been used then the change of flow could be noticed more easily.  Turbulent Flow entering pipe As shown in figure 1.1 there is a foam baffle at the exit of the flow input pipe. The baffle is there to absorb the energy from the flow exiting pipe so that we obtain smooth flow in the channel. In the experiment when we the flow rate to 70 l/m the foam baffle was being forced away from the pipe and out of the top of the apparatus. This would mean the effect of the foam baffle would be reduced therefore causing some error within our results. We minimised the risk of this happening by continuing to monitor the effects of the hydraulic jump at flow rates under 70l/s.

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3.2

The relationship between experiment and theory

If we look at figure 2.7 we can see that percentage relative head loss for the theoretical results is higher than that of the practical percentage relative head loss this is because the depth of water level after the hydraulic jump is higher than that of the experimental values. In the practical conditions energy is lost dues to eddies and turbulent flow which means the actual water depth is lower than the theoretical calculations. The trend line in figure 2.6 shows a positive correlation between the increase of Froude number and the y2/y1 values. We can use this positive correlation to show that the Froude number has an impact of value of y2/y1. If we look at figure 2.7 we see that due to the positive correlation of both trend lines as the Froude number increases so does the percentage relative head loss. If we look at figure 2.6 we see that we get some discrepancies however the discrepancies are within a rather limited range. Although the discrepancies do not appear to follow some kind of pattern, they are scattered above and below the trend line. We have a similar trend in figure 2.7 as we have discrepancies scattered above and below the trend however these results are much more widely scattered. These could be a sign of an error we have in our recorded results. The value of the Froude number alters the behaviour of the hydraulic jump, as shown in the table below; Fr No < 1 Jump Impossible Fr No 1 – 1.7 Standing Wave Fr No 1.7 – 2.5 Known as the weak jump, this produces smooth standing wave with some eddies Fr No 2.5 – 4.5 An unstable and oscillating jump this can cause waves that can travel for miles downstream Fr No 4.5 - 9 A stable and steady jump, this is perfect Froude Number range for designing weir and Dam spillways etc. Fr No > 9 A strong jump that is rough but still performs well

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3.3

The relationship between the concepts explored and practical applications

The hydraulic jump is amazing to watch but there are many different practical applications for the hydraulic jump as well.  Dissipation of energy from water flow over a weir or Dam As water passes over a weir or a dam it can gain a large amount of velocity this is because of the height that the water drops. The loss of head creates a large amount of energy within a mass of water and this can cause damage around the dam or weir and it some cases further downstream. The velocity of the water can erode river banks and structures such as bridges further downstream. The hydraulic jump is an ideal way of dissipating the energy build up and therefore stopping the destruction of the local environment.

(Figure 3.1 – This figure shows a spillway from the Haditha dam in Iraq)  Raising water levels in a canal to reduce pumping heads This is useful because it uses a natural process to raise the water level the canal and therefore no or less energy is needed to pump water into the lock. This was useful when canals were first introduced as it was hard to find steam engines big enough to pump enough water. A similar idea can also be used for irrigation of fields.  Creating critical depths for flows going through measurement flumes This is a useful technique to measure the discharge flow from small streams and rivers. The figures below how various techniques to control and measure the flow using the hydraulic jump.

(Figure 3.2 – This shows a flume used in the stream bed to record the streams discharge) 19 | P a g e

 White water parks The hydraulic jump has a very fun use as well. It is commonly used in white water parks to create a nice play spot this can create hours of fun for white water kayakers.

(Figure 3.3 – This shows a hydraulic jump as part of a white water course in Nottingham) 

Retaining walls

You can use the hydraulic jump to increase the factor of safety against overturning on retaining structures such as dams. The factor of safety is increased by increasing the depth water on top of the apron this in turn Increases the weight on apron of a retaining structure.

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References

What?

Source

Date

Research Research

Internet Internet

Research Research Research

Internet Internet Internet

28/03/2013 http://udel.edu/~inamdar/EGTE215/Jump_weirs.pdf 28/03/2013 http://optimist4u.blogspot.co.uk/2011/04/hydraulic-jump-andits-practical.html 28/03/2013 http://hyd.uod.ac/material/CE404_03_Hydraluic_Jump.pdf 28/03/2013 http://www.most.gov.mm/techuni/media/CE_04016_chap8.pdf 28/03/2013 http://www.coastal.udel.edu/~thsu/course/Chap_5_HJ.pdf

Figure 3.1 Figure 3.2 Figure 3.3

Internet Internet Camera

28/03/2013 http://www.politics1.com/usmc5.htm 28/03/2013 http://udel.edu/~inamdar/EGTE215/Jump_weirs.pdf 28/03/2013 Friends photo

5 Ihor Moyiseyev Baris Evran Andrew Woods

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Group Log Introduction Calculations Conclusion

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