Question

Determine the net force due to pressure from the fluid on a 10 cm tall cylinder sitting at the bottom of a 3 m pool of water. Is this value equal to the buoyant force acting on the cylinder? Assume the radius of the cylinder is 4 cm.

Answer 1

The buoyant force is the force equal to the weight of water displaced and does not vary with depth of immersion.
Pressure at 3 metres = (1,000 x g) x 3 = 29,400Pa. gauge, or add atmospheric pressure of 101,325Pa. = 130,725Pa., or 130.725kPa. absolute.
If the radius of the cylinder is 4cm., 4cm. = 0.04m., and 10cm. = 0.1m.
Surface area = (pi r^2 *h) + (pir^2) = 0.00553 m^2.
Force due to absolute pressure at 3m. = (pressure x area) = 130,725 x 0.00553 = 722.90925N.

For gauge pressure, the pressure on the cylinder at the surface would be 0, while for absolute, it will still be 101.325kPa. due to air pressure.

Fresh water density is 1,000 kg/m^3, so weight becomes (1,000 x g) = 9,800N. per metre depth.
So, (9,800 x 3m) = the 29,400N/m^2, = 29,400Pa. change (gauge) in pressure.