Hydraulic Jump
Objectives
In this laboratory you will investigate an open-channel flow (flow down a channel with a free surface, e.g., not confined by a rigid surface as would be the case in pipe flow) using conservation equations (mass, linear momentum and energy). You will be introduced to the hydraulic phenomenon known as the hydraulic jump (see Figure 1-1) – the sudden transition from a higher energy state to a lower energy state while conserving momentum (analogous to a shock wave in compressible gas flows). This is your chance to get a tangible sense of these conservation equations and concepts such as the energy grade line and hydraulic grade line. You will also get a chance to think about the energy equation and when the assumptions of the Bernoulli equation are valid and when they are violated[1].
Theory
Flow through a sluice gate can be reasonably modeled using the Bernoulli equation. The potential energy of the water behind the sluice gate is converted into kinetic energy as the water passes under the gate. Thus the velocity of the water can be calculated directly from the height of the water behind the sluice gate. Hydraulic jumps occur in open channel flow when the flow transitions from supercritical to subcritical flow. A description of the phenomena can be found in Munson, et al. page 653. The upstream (y1) and downstream (y2) depths are related by equation 1.2.
1.2
where the upstream Froude number (Fr1) is defined as
1.3
The velocity in the channel can be determined by applying the Bernoulli equation in the region where velocity is increasing between the reservoir and immediately downstream of the sluice gate. The velocity can also be measured with a stagnation tube connected to a pressure sensor. The stagnation tube will be filled with water prior to connecting to the pressure sensor and the pressure sensor output will be zeroed with the stagnation tube held vertically (in the same orientation used for taking measurements.) Thus the pressure sensor will measure the pressure at point 3 (Figure 1-2). From the Bernoulli equation across streamlines we can obtain the following relationship.
1.5
Since =0 we have
1.6
From the Bernoulli equation along streamlines we have
1.7
where will be measured using a pressure transducer. Since is zero and we can obtain
1.8
Thus the stagnation pressure head includes both the static head based on the submergence of the stagnation tube tip as well as the velocity head.
Experimental Methods
Height of water in the reservoir (cm)Stagnation pressure head at the opening of the sluice gate (cm)
Stagnation pressure head just upstream of the hydraulic jump (cm)
Depth of submergence of the stagnation tube for previous measurement (cm)
Depth of water just upstream of the hydraulic jump (cm)
Depth of water downstream of the hydraulic jump (cm)
A small flume will be set up with a stable hydraulic jump. Your goal is to measure the flume dimensions and fluid velocity upstream and downstream from the hydraulic jump.
Make the following measurements using the bottom of the channel as your elevation datum. In addition to these measurements you should play with the stagnation tube and the hydraulic jump so you can answer the questions for the lab report.
Questions
Before doing lab:
1)Roughly plot the EGL to see what kind of energy changes you expect to happen.
2)Think about a way to calculate the fluid velocity right outside the sluice gate without having to use a Pitot or stagnation tube. Also, since we won’t be taking measurements in the region after the hydraulic jump, figure out a way to find the velocity there.
After the lab:
1)Calculate the velocities and Froude numbers in the super and sub critical regions.
2)Create a more exact EGL plot using your test data. Was it similar to what you expected? If not, what are the reasons for this?
3)Why was the weir important in generating the hydraulic jump?
4)Explain which equations you can or can’t use to analyze the different sections of the set-up. Why?
5)Describe the properties of the sub and super critical regions. If you had no instruments, what could you do to differentiate between sub and super critical flows.
6)What happens if you measure the stagnation pressure at the very bottom of the channel? Explain based on the properties of real fluids.
[1]Adapted from Lab #3 Conservation Equations and the Hydraulic Jump, CEE 331 Fall 2001, Professor Cowen, CornellUniversity)