CEE 331 Lab 2 Page 1 of 10 Lab #2 Conservation Equations and the Hydraulic Jump CEE 331 Fall 2006 Safety The major safety hazard in this laboratory is a shock hazard. Given that you will be working with water and items running on standard line voltages (the computer) you should pay attention to the possibility of electric shock. The flume has a few very small leaks and there may be a few wet spots under and around the flume. If water gets near a 110-Volt electrical connection DO NOT clean it up. Seek a TA, Cowen, or one of the CEE technicians (Tim Brock, Paul Charles, or Cameron Willkens who have offices across from the lab) for help. The flow rates in this lab are sufficient to generate moderate forces. Take care with the pressure transducer, Pitot tube, rulers, and any other items that you bring in contact with the flowing water as they may receive sufficient force to knock them around to unexpected locations. Always work with a minimum of two people. Objectives In this laboratory you 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 in pipe flow). You will get a chance to look at this flow analytically using the conservation equations (mass, linear momentum and energy) in Problem Set #6 but for the lab we will focus on the observational evidence. You will be introduced to the hydraulic phenomenon known as the hydraulic jump (see Figure 1) – 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). This is your chance to get a tangible sense of the conservation equations and concepts such as the energy grade line and the 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. Theory The Flow We will use a sluice gate to convert potential energy to kinetic energy and create what is known as supercritical flow. We will study supercritical flow in some detail in the final weeks of the semester. The concept of supercritical flow is fairly straightforward (and covered in your text in Chapter 10 sections 10.1 and 10.2), and simply defined means that waves can only travel downstream. As an example consider throwing a rock into a slowly moving river. A circular wave pattern forms initially and propagates radially outward (until the banks 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. Now, if the river speed increases eventually 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. Another way of thinking about this is that in subcritical flow the information (waves) saying the flow wants to get deeper canCEE 331 Lab 2 Page 2 of 10 propagate both up and down stream so you can influence a flow's depth (in fact you can set it) 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. For waves that have a long wave length in comparison to their flow depth the wave speed c is simply cgh= 2.1 where h is the local flow depth and g is the acceleration of gravity. Hence we can express the condition that the wave speed is equal to the flow speed as V = c or Fr 1Vgh== 2.2 where Fr is known as the Froude number and V is the local flow velocity. As suggested above a flow can exist in a supercritical (Fr > 1), subcritical (Fr < 1) or critical (Fr = 1) state. For a flow, such as in our case just after the sluice gate, that is locally supercritical, downstream conditions may require the flow to increase its depth, say to get over a sill or weir. Because of the conservation of linear momentum and the conservation of mass (as you will see in Problem Set #6), there is only one valid supercritical and one valid subcritical depth for a given flow rate, so if the flow must adjust its depth it must transition to the subcritical state, which is slower and hence deeper. Now, normally over short reaches of a river it is reasonable to ignore energy loss and assume energy is constant. However, there is no way for a flow to decelerate smoothly and adjust to a subcritical state (note that it can accelerate smoothly from sub- to supercritical as it did beneath the sluice gate). It accomplishes this transition to deeper flow depth by a feature known as a hydraulic jump (see section 10.6 of your text), which as you will see is a highly turbulent event and dissipates significant energy. In this lab we have set up a weir (an overflow gate as opposed to a sluice gate which is an underflow gate) at the outlet of our teaching flume in the environmental fluid mechanics teaching laboratory. This weir requires that the flow be at minimum 3 cm deep to get out of the flume and return to the pumps that supply the flume with water. Hence if we use a sluice gate to deliver a supercritical flow of depth about 1 – 2.5 cm to the flume, it must transition to a deeper state to get over the weir and out of the flume and it does this via a hydraulic jump. Figure 1 below shows a schematic of the flow. Constant Head Tank The flow is established via a constant head tank. This is a simple source condition that establishes a constant elevation head of water in a reservoir to drive a steady flow. The facility we are using (sketched in Figure 1) creates a constant head tank by filling the metal head box with water from a pump at a rate greater than the water flows out under the sluice gate. Excess flow is drained out of the head box by an overflow pipe installed approximately 0.75 m above the facility’s test section bottom elevation. The overflow pipe returns excess water to the inletCEE 331 Lab 2 Page 3 of 10 tank (the white plastic cylindrical tank sitting next to the metal head box) which delivers water to the pump. Hence we have a roughly constant head in the metal head box as long as the PVC overflow pipe is draining some water into the white cylindrical inlet tank. Hydraulic Jump If