Determine the total pressure on a circular plate of diameter 2 m, which is placed vertically in water in such a way that the Centre of the plate is 2.5 m below the free surface of the water.

Concept:

When any plate is immersed vertically in water having any arbitrary shape,

total horizontal force is given as 

F_H = ρgAx̅

Where,

ρ = density of the fluid (kg/m3),

g = acceleration due to gravity (m/s2)

x̅ = depth of the center of gravity of the submerged body from the free surface (m)

A = total area of the surface (m2)

Calculation:

Given: Diameter of circular plate d = 2 m, x̅ = 2.5 m, ρ = 1000 kg/m3

\(\begin{aligned} & A=\frac{\pi}{4} \times d^2=\frac{\pi}{4} \times 2^2=3.141 \\ & F_H=\rho g A \bar{x}=1000 \times 9.81 \times 3.141 \times 2.5 \\ & F_H=77047.55 \mathrm{~N} \approx 77048 \mathrm{~N} \end{aligned}\)

 Additional Information

Note: When nothing is given about g, take g = 9.81 m/s2.

Don’t get confused between the centre of gravity and the centre of pressure while calculating F_H.

While calculating F_H centre of gravity is considered but the horizontal force acts at the centre of pressure.

Position of centre of pressure,
\(\bar{h}=\frac{I_{x x} \sin ^2 \theta}{A \cdot \bar{x}}+\bar{x}\)