Bernoulli's equation - finding the pressure at the top of a tube

AI Thread Summary
The discussion revolves around a fluid dynamics problem involving a horizontal tube with a T-junction and a vertical tube leading to a liquid container. The main inquiry focuses on determining the pressure at the top of the vertical tube when air is forced into the horizontal tube, creating a pressure difference that draws liquid upward. The initial formula proposed for calculating this pressure is P = Po - 1/2 * /rhoA * v^2, where P represents the pressure at the top of the vertical tube, Po is atmospheric pressure, /rhoA denotes the density of air, and v is the air velocity in the tube. The user initially struggles to derive this equation from Bernoulli's principle but later realizes the solution is simpler than anticipated.
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Here's my problem:-

A horizontal tube has a T-junction with a vertical tube coming downwards into a container of liquid, at height h below the T-junction. Air is forced into the horizontal tube which causes a pressure difference which sucks the liquid up the vertical tube.

What is the pressure at the top of the vertical tube?

I have the answer as
P = Po - 1/2 * /rhoA * v^2

where:
P = pressure at top of vertical tube
Po = atmospheric pressure
/rhoA = density of air in tube
v = velocity of air in tube

but I can't seem to derive this equation from Bernoulli's equation. (Or anything else! :confused: )

Any ideas?

Thanks.
 
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s'okay, I've just worked it out. It was embarassingly simple!
 

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