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Imagine there is a water flow through a hollow tube. Assume the pressure inside the liquid is given as 5Kpa. Is there a way to determine the vertical (upward) pressure at the surface of the water flow, that is between the tube wall and the surface of the water column?

This is regarding a biology experiment. I have placed a membrane horizontally in a frame and there is a water flow underneath the membrane. I know the water pressure in side the water column, but I need to determine the effective upward pressure created on the membrane by the water flow.

My suggestion, I believe, technically this should be zero since the vertical (perpendicular to the direction of water flow) velocity of moving water molecules is zero. But in the practical way, there might be some value when you consider turbulent effect of water flow. Is there a way to calculate this in terms of fluid dynamics?

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If you had an open channel flow then, yes, the (gauge) pressure on the fluid surface would be zero. However, as soon as you place a membrane on top of the previously free surface you have viscous flow in a (non-circular) pipe, and the pressure and flow rate may change, in general, depending on whether or not the pipe is horizontal.

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  • $\begingroup$ Thanks Prix. Yes, the pipe remains (or the path of the flow) horizontal. Can you suggest me any reading or key words to find out the calculations associated with this? $\endgroup$ – Kosala Feb 2 '17 at 17:40
  • $\begingroup$ You can google things like "Viscous flow in ducts". The Wikipedia article on Hagen Poiseuille flow may be helpful, too, even though this is for circular pipes. $\endgroup$ – Pirx Feb 2 '17 at 17:45

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