Find the force on the plate due to hydrostatic pressure?

Question

A rectangle plate of radius 4 m is submerged horizontally

Answer 1

Step 1) Write out what you know:

Water density: ρ = 10³ kg/m³

Acceleration of gravity: g = 9.81 m/s²

Water height: h = 8 m

Radius of plate: r = 2 m

Step 2) Use the hydrostatic pressure equation:

Hydrostatic pressure = Water density * Acceleration of gravity * Water height

P = ρgh

P = (10³ kg/m³) (9.81 m/s²) (8 m)

P = 78480 kg/m-s² (this unit is also called a Pascal)

Step 3) Find the force:

Pressure = Force / Area

P = F/A

F = P * A (recall that the area of a circle is: A = π r²)

F = P (π r²)

F = (78480 kg/m-s²) π (2 m)²

F = 986208.76 kg-m/s² (this unit is also called a Newton)