# Open Channel flow with pressure losses - flow depth?

In a horizontal channel that feeds off a river, does the head/pressure loss due to friction, turns etc in the channel translate to a drop in the water level between its inlet and outler? If so, could someone provide a basic insight how?

Thanks.

• If it is an open channel, pressure along the height of the channel is given by the hydrostatic equation. So the momentum source will be the datum head (not the pressure) and the momentum loss is attributed to the friction. Jan 4, 2019 at 6:25

If the channel is horizontal, the flow will set a slope to use the head lost as a potential energy to turn it to kinetic energy that is required to overcome the head loss at the bends and also the viscosity losses.

One can guess a head loss and use it as slope and write the Manning formula for discharge and calculate the flow and from there the height of the water at exit.

If the height is more than say two feet we change our guess by reducing the height to one foot and adding the head as slope, S, recalculating. Until the results become closer and closer to our tolerance.

• My understanding is that Manning formula relates only to friction losses - how is it therefore compatible in calculations taking bend losses into account? Thank you Jan 2, 2019 at 22:32
• Bend losses and changes in geometry of channel is complicated to calculate. There are FEM sofware to do it. But basically any obstacles can be translated into head losses. Jan 2, 2019 at 23:02
• Thanks for the continued help @kamran. I have carried out CFD and obtained a result for the pressure loss in my system. I just don't see how that value can fit with Manning's equation since my losses aren't due to friction. I've looked into other methods and wonder if you can comment on this: Jan 3, 2019 at 0:09
• 1) Create model of a channel on ANSYS. The channel has bends that produce turbulence that causes a pressure drop that can be obtained in the software. 2) Use this pressure drop as the head loss dh to find the Energy Grad Line slope S of the channel (dh/dx = -S) 3) Use S in the Gradually-Varied flow equation to find the drop in flow level in the channel. Jan 3, 2019 at 0:12
• All you say makes sense. Friction could be estimated by assuming your head loss as slope and the height of flow as what is you exit height. Jan 3, 2019 at 0:29

The flow velocity is not uniform over a cross section through the channel because of the viscosity of the water. It is zero at the walls and a maximum in the center of the free surface.

The viscous forces tend to reduce the flow velocity. The work done by the viscous forces is counterbalanced by work done by gravity, as the depth of the stream decreases and the water moves vertically down as well as flowing horizontally.