Non-Uniform Flow 2

Now you are the engineer, and you have been given this design and your task is to analyze the channel to determine the flow depth in the channel from start to finish. This is a single channel with a constant geometry and roughness. The only change in the channel is the slope. Water enters the channel through a sluice gate at the top of the channel. At the bottom of the channel the water is backed up by the water ponding behind a dam. The first step is to complete the steady / uniform analysis. Start by calculating the critical depth. Since this is a rectangular channel with a base width of 15 feet and a design flow rate of 500 cfs, then we can calculate the critical depth directly using this formula. I get a critical depth of 3.26 feet. Next calculate the normal depth for each segment of the channel. The normal depth is found using the iterative approach to Manning's equation. For the mild channel I get 4.58 feet for the normal depth, and for the normal depth in the steep channel I get 1.47 feet. It helps to visualize the solution better if you sketch in the normal and critical depth to your design drawing. Completing this step allows us to classify each segment of the channel as mild or steep. The next step is to qualitatively assess the actual channel flow depth. We do this by sketching how we predict the flow will change as it navigates the changes in slope. For example, at the downstream end, just before the dam, the flow depth will have to increase in order to match the ponded water depth behind the dam. This is a gradually varied flow section. Because the flow depth is supercritical, and the dam is ponding the water to a depth above critical depth, then just before the GVF profile there will be a hydraulic jump. When the slope transitions from Mild to Steep we should expect to see a GVF profile in the mild and steep sections. We assume that the flow will pass through the critical depth at the grade break. Finally, as the water enters the channel, the sluice gate has an opening less than the normal depth, so it is possible that there may be a gradually varied flow section followed by a hydraulic jump. For this to happen the depth of flow in the mild channel can not be so deep that it buries the jump. We can use the conjugate depth equation to determine if the jump will occur or not. To organize our calculations it is important to classify each of the GVF profiles. Starting with the GVF just downstream of the sluice gate we know that it is an M profile because it is in a Mild channel.