Executive Summary 3
Introduction 3
Analysis and Results 6
Discussion of Results 8
Conclusion 8
Appendix 9
Executive Summary
In this lab, we will investigate an open-channel flow (flow down a channel with a free-surface, i.e. not confined by a rigid surface as would be the case with a pipe flow). You will get a chance to look at this flow analytically using the conservation equations (mass, linear momentum and energy), but the lab will focus on the observational evidence. You will be introduced to the hydraulic phenomenon known as hydraulic jump – the sudden transition from a higher energy state to a lower energy state constrained by the conservation of momentum (analogous to a shock wave in compressible gas flows). You will get to tangibly experience the equations of conservation and concepts such as the energy grade line and the hydraulic grade line. One will also get a chance to analyze the energy equation and when the assumptions of Bernoulli equation are valid and when they are violated.
We will use a slice gate to convert kinetic energy into potential energy and create a supercritical flow. The concept of supercritical flow says that the waves can only travel downstream. For waves that have a long wavelength in comparison to their flow depth, the wave speed c is: c = √gh,
Where h is the local depth of the flow and g is the acceleration of gravity.
Hence, we can express the condition when the wave speed is equal to the flow speed as V = c or
Where Fr is the Froude Number and V is the local flow velocity.
Introduction
We will use a sluice gate to convert potential energy into kinetic energy and create what is known as supercritical flow. As an example, consider throwing a rock into a slowly flowing river. A circular wave pattern forms initially and propagates radially outward (until the blanks are hit at least). If the river flow is slow, then a significant portion of the circular wave pattern will propagate upstream i.e. the waves make progress back against the river current if viewed from the river bank. This state is known as the subcritical state. However, if the river speed gradually increases, it will flow fast enough that none of the circular wave pattern will make progress upstream. When this scenario is true the river flow is said to be supercritical. In other words, in subcritical flow, the waves get deeper and can propagate both up and down stream, so it can influence a flow’s depth from downstream. Conversely, when the flow is supercritical, there is no way from the downstream side to tell the flow that it should get deeper – this information must come from the upstream side.
A flow can exist in a supercritical, subcritical or critical state. For a flow that is locally supercritical, the conditions for a downstream flow may require the flow to increase its depth, say to get over a sill or weir. Because of the conservation of the linear momentum and the conservation of mass, there is only one valid supercritical and one valid subcritical state, which is slower and hence, deeper. Now, normally over short reaches of a river, it is reasonable to ignore energy losses and assume that the energy stays constant. Also, there is no way for a flow to decelerate smoothly and adjust to a subcritical state. It accomplishes that this transition to deeper slow depth by a feature known as a hydraulic jump is a highly turbulent event and dissipates significant energy.
Procedure
- Check that the water level in the flume (with the pumps turned off) is just below the red tape on the piezometer at the flume outlet end.
- Turn on the pumps by first turning on the master power switch (whiteboard side of the flume) and then hitting “run” on the three pumps. The pumps should spin up and go up to a reading of 30Hz, which means ½ (30/60) of full speed. Make sure you do not adjust any of the pumps.
- The hydraulic jump should position itself around mid-flume. If even after a minute or two it does not, ask for the TA’s help, he can help you to correctly position it.
- Take measurements and record them in the data analysis sheet.
- Observe the velocity as monitored by the acoustic Doppler Velocimeter only in the subcritical section of the flow. This instrument is used to measure the Doppler shift of sound to measure all three components of the velocity. Record the average u, v and w components of the velocity (the 30 second average is reported in the table on the screen) and notice how turbulent the flow is (how much the velocity varies about its mean).
Note: the ADV measures 15 cm below the head of the instrument, and it must be submerged when the data is being recorded; do NOT mount the ADV closer than 15 cm from the bed (ideally, the ADV head should be ~20 cm above the bed). The ADV cannot be used in the supercritical section of the flow because the flow is too shallow.
- Before you turn off the flume, produce waves in the supercritical and subcritical regions of the flow. Can you get the waves to propagate upstream in each region? Now try to make waves just after the weir. Note your observation about the flow over the weir - is it subcritical or supercritical?
- After you have taken all of your measurements, hit “stop” on the pump controllers (all three) and then turn off the master power switch.
Analysis and Results
Below are the graphs:
Y1 vs Et
Y2 vs Et
Yc Vs Et
hL vs Q
Discussion of Results
For each gate opening, different discharge levels were used to maintain the upstream depth below the critical depth of the flow from the channel.
The values of specific energy also fall in line with the theoretical knowledge, because as the values for Yc increase, the Et values increase as well.
In general, the Yc values varied in each trial because of the variation in the height of the hydraulic jump produced. If the wave produced is smaller, the Yc value is also smaller.
The specific diagram figures created against the different values of y match closely to the ideal picture.
We also observe that the values of Froude number increase with an increase in the levels of discharges.
Scientists have been continually experimenting on the effects of viscosity of the liquid on the hydraulic jumps, which have led to upcoming of various man-made hydraulic jumps. One such use of hydraulic jump is energy dissipation in a hydraulic jump stilling basin. In this basins, horizontal and sloping aprons are used to dissipate more than half of the energy released from the flow of the incoming water. The effectiveness of the devices used in the basin is highly dependent of the Froude number of the flow.
Conclusion
The procedure for measuring the sequent depth ratio of the hydraulic jump was simple and easy to understand.
This experiment helped analyze all the theoretical concepts studied in the classrooms. It gave the opportunity to actually observe the conservation of energy and apply the knowledge to understand the actual process behind the jump.
It also helped understand the interdependence of different parameters of the jump on each other. The results obtained after the experiment are more or less in sync with the theoretical results expected.
Appendix
Raw data of the experiment:
