A rectangular tank 1 m × 3 m lies in a vertical plane in water. Calculate the total pressure on the plane surface.

Concept:

Whenever a static mass of fluid comes into contact with a surface the fluid exerts a force upon that surface. The magnitude of this force is known as the hydrostatic force or total pressure force.

The magnitude of the hydrostatic force is given by F = ρ g h̅ A N

Where ρ = Density of the fluid, h̅ = Depth of center of gravity of the surface from the free liquid surface, A = Area of the surface

Calculation:

Given that Square surface = 1 m × 3 m = 3 m2, fluid is water ρ = 1000 kg/m3,

h̅ will be 1.5 m because the plate is vertical and its upper edge is at the water surface and for a square geometry its center of gravity lies at where a is the side of the square.

Now F = ρ g h̅ A = 1000 × 9.81 × 1.5 × 3 = 44145 N