Flow Through a Flat Channel 1

[hogart26]

I am trying to calculate the water level in a flat rectangular channel that has a free discharge (i.e. no backwater effects, flow drops to a lower water surface level downstream of the channel) and a known flow rate. What is the appropriate equation to calculate flow depth?
Thanks.

 

[cvg]

normal depth / mannings equation

http://www.fsl.orst.edu/geowater/FX3/help/8_Hydraulic_Reference/Manning_s_Equation.htm

 

[hogart26]

Thank you CVG for responding to my thread. You appear to be indicating that the Manning Equation should be used for this application (unless I'm missing something). Because the channel slope is zero (flat), I would calculate a flow of zero using this equation (which is not the case). There is a "backwater effect" occurring as the flow backs up in the flat channel and then gets pushed through it as more water comes in. As noted in my first message in this thread, I'm unsure what the control is in this case and how to calculate the depth.

 

[ccor]

For a horizontal channel flow only occurs if there is a difference in head across the channel section. You will need to calculate the water surface elevation at the downstream control section. Then compute the water surface upstream using the standard step or direct step calculations. These are covered in most hydraulic texts on open channel flow.

 

[cvg]

flow cannot backup if the channel is flat with free discharge. Your situation sounds more like a broad crested weir spillway to me.

 

[rcooper]

How I would proceed if you require a reasonably accurate answer is as follows.

1) The free discharge is your control section. The normal equations for the level of the water do not apply in this region as they assume the streamlines are straight and parallel with the base of the channel. As the water goes over the dicharge, they are clearly not. I tend to use energy level rather than actual level in these circumstances. Work out the energy level and depth for critical flow for the channel width and flow rate you have.

2) Calculate the energy gradient and calculate the energy level a small step upstream of the free discharge. From this calculate the water level at subcritical flow. This is easiest to achieve using the Newton method of iteration, starting withthe energy level. The subcritical low level will normally converge within 5 iterations.

3) Keep repeating step 2 using the new level and moving upstream until the changes in depth at each stage are small. Then increase the step size.

With a flat channel, there is no normal depth. The depth will continue to increase as you progress upstream.

This method will not provide you with the perfect profile of the water. Near the discharge the water surface is lower than calculated. As you move upstream the actual profile starts to correlate with the calculated profile.