# Pressure required to lift a weight

Assume all dims in millimeters and kilos and I am working on a hydraulic set up
I have a cylinder Ø200mm diameter x 400 high, it has a hole in the middle Ø10mm going into a capped Ø10mm pipe. The cylinder is filled with water up to 300mm high. There is a bouyant weight that floats on top of the water that weighs 10Kg.

Q1. Firstly, does this bouyant weight increase the pressure at the bottom of the tank (at the Ø10mm cap)? If so, what is the pressure difference if the weight was not there? Or because thre weight floats on top, is the pressure difference negligible?

Q2. If the water was emptied out what pressure/weight/volume of water would be needed in order to fill the cylinder back up with the 10KG weight sitting over the Ø10mm pipe? Assuming that water cannot pass around the weight. ALso, if the tank of water that is being used to fill the cylinder was elevated, would this help in using a smaller tank so the pressure increases?

Any help appreciated. Its been many many moons since I did any physics, hydraulics calculations...

TIA

Ben

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1.-

At any given point inside the water at a depth d, the pressure is simply the weight of the column of water at that point, so, if you take gravity, the volume of water, consider its density, divide that weight by the cross sectional area at that depth...you end up with pressure p = ρgd, where ρ (rho) is water density, g is gravity and d is the depth you are at.

So, does the 10kg floating object increases the pressure? Yes, because it will sink a bit into the water, displacing a certain amount of water where the object itself is and rising the water level in the tank...take this new 'depth' to the bottom of the tank, and you have a new higher pressure.

Or, take the weight of all the water, add 10 kg, divide that force by the cross-sectional area at the bottom of the tank and that is your new pressure...basically, the bottom of the tank needs to carry the weight of everything on top of it...right?

2.-

Again, force is pressure times area and so, if you need to lift a weight of 10kg through a 10mm diameter pipe...you need to calculate the pressure needed so that when multiplied with that cross sectional area...you get 10 kg.

Yes, rising the tank will increase the pressure available.

OK,

So I have worked out a figure for the pressure. (based on the volume of water being 0.003534m3
p = 0.003534m3
therefore P= 0.003534 x 9.81 x 200mm (depth)
therefore P= 6.9337kg/m3

But if i use the other calc taking the weight of water (0.003534) +10Kg / 0.785 (cross sec area of tube @ 10mm) = 12.743Kg/m3

So I am confused to the different results?#?

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cross -sectional area at the bottom = ∏r2

where r = 100 mm = 0.1 m

volume of water is cross - sectional area times height = ∏ r2 h

where h = 300 mm = 0.3 m

weight of such volume of water is density times volume = ρ x volume

where ρ = 1000 kg / m3

OK, I have worked out that the weight of the water is 9.426Kg in a tank that holds Ø0.2 of water x 0.3m high.

I have tank 1, Ø10mm pipe on a u bend going into another tank (tank2) at the other end of the u bend.

so how do I work out and include the acting pressure of what is needed in the u bend in order to lift the weight.

so.. the u bend I/D is 10mm it goes down 0.1m, goes to the right 90° 0.3m, goes up 90° 0.1m into the tank2.

I guess the weight required to lift the weight in tank 1 directly must be 10KG + 9.426.

But, how do we include the reacting pressure from the u bend and also is there a formula to work out how much pressure increases when you elevate the feed tank 2?

TIA