Main question: If you have a column of fluid with a valve as shown on the drawing, what happens to the pressure at the point p when moving from state A to state B and vice-versa?
I'd think it gets suddenly decreased because now it's at a much smaller depth, but I have trouble dealing with the idea of such a sudden change.
Bonus track: What could one say about the force required to open or close that valve? On the 2) section of my silly drawing: what should K be? How close or far away from 1 should it be?
Some thoughts about this problem:
- When closing the valve, the pressure is even aboe and below the valve level, so I'd think closing the valve doesn;t require lots of force. At least, that force shouldn't be depending on the height of the container.
- If the pressure does change from one state to the other, then opening the valve could be tricky. The big pressure difference between sides of the valve could cause a problem there. Maybe the required force will be very high (height depending) or maybe the thing would explode (like suddenly opening a door on a flying plane).
Best Answer
Tricky question (well a little bit tricky).
But the correct answer is - no change in pressure. Assuming the valve is closed very slowly so that it does not act to displace water as it closes, and that the valve creates a perfect seal as it is closed, the water in the container below is essentially trapped at the original pressure, $P=\rho g(H+h)$. When the valve is closed, the lower part of the container is no longer affected by the column of water above it, but it does retain the pressure from the original pressurization.