# Would it take an equal amount of lb-force as the total water weight weighing down on the piston to be at equilibrium? Pascals principle

Pascals principle sounds simple, but I'm a bit confused on this.

A cylinder that's 24" in diameter by 5 ft in height filled with 117 gallons(980 lb) that's connected to 1" diameter pipe going up 300 ft high filled with 12 gallons(100 lb).

I know that with deeper depth the water pressure increases, but I'm a little lost on this question about how much lb-force I'd need to lift this water upwards.

I have 129 gallons of water or (1080 lb) in total weight weighing down on a piston that's set at the very bottom of the 24"D cylinder. Considering the height of the smaller pipe is 300 ft high, would I need an equal amount of weight (1080 lb) force up to have this piston at equilibrium?

And to lift this piston up I'd assume the lb-force should be slightly over equilibrium if I used a lever.

• Thanks Aaron for the edit!
– Rip
Sep 22, 2019 at 21:33

So we just need to find the force of the water on the piston. At the very top of the tube the pressure is atmospheric pressure. The change in pressure due to the depth of the water is given by $$\Delta P=h\rho g$$, where $$h$$ in this case is 305 feet. So to obtain the pressure at the very bottom, you can add simply add this change to the initial atmospheric pressure.
Finally it suffices to use the expression $$F = PA$$ where $$A$$ is the area of the piston in order to determine the force.