A circular viewing window of diameter D = 0.4m is placed in the Holding tank. The top of

the window is H = 1.2 m below the water surface. Find the hydrostatic force acting on the

window and locate the corresponding centre of pressure (CP).

Answer:

A hydrostatic force is the force caused only by the weight of a body of water (or any liquid) exerting pressure on its container. Without a container the body of water would collapse so the container then must resist the force that tries to collapse the body. The force is static because the body of water and the container are in equilibrium, hence hydrostatic as opposed to hydrodynamic. The centroid of a body would be the location of the average location of all points of a body. The center of pressure on a body would be the location of the average location of all the forces caused by the pressure acting on the body.


Pressure (kPa): p = ρ x g x h ρ

density of water at 20 degrees celsius (kg/m^3)

g acceleration due to gravity (m/s^2) h height (m)

Force (KN): F = p x A where, p = pressure (Pa) A = area (m^2)

Pressure (kPa): p = ρ x g x h

ρ density of water at 20 degrees celsius = 998 kg/m^3

g acceleration due to gravity = 9.81 m/s^2

h height = 1.2m

Force (KN): F = p x A where,

p = pressure A = area = pi(diameter)^2/4 = pi(0.4m)^2/4= 0.12566m^2 --- p = 998 kg/m^3 x 9.81 m/s^2 x 1.2m = 11748.456 N/m^2 = 11.75 kPa F = 11.75 kPa * 0.12566 m^2 = 1.476 KN
for calculation on center of pressure, please refer to the attached document.

To be more precise, the center of pressure is calculated by determining the first moment of the hydrostatic force acting on the window w.r.t. some convenient reference. The c.o.p. = 1st moment of hydrostatic force / total hydrostatic force.

PFA