integral calculus
posted by al .
a rectangular plate 12ft long and 8 ft wide is submerged vertically with the longer edge in the surface of the water. Find the force on one side of the plate.

Hydrostatic pressure at depth h
=ρgh
where ρ=density of water = 1000 kg/m³
g=acceleration due to gravity=9.8 m/s²
Total Force = pressure * area
=∫ ∫ ρgh dh dx
x from 0 to 12
h from 0 to 8