A vertical plate is submerged in water as indicated in the figure.

Find the hydrostatic force on one end of the aquarium:

.

, where is the depth of the aquarium.

At any time, the plate is depth from the surface.

Thus, .

Strip area of one side of the plate is , as depth increases then also increases.

Thus, consider width as .

Find the length of the strip.

Redraw the figure.

Observe the similar triangles:

.

Length of the strip .

Area of the strip is .

Force acting on that strip is .

.

.

Hydrostatic force as a Riemann sum .

Set up the integral .

.

Hydrostatic force on one end of the aquarium is .

Hydrostatic force on one end of the aquarium is .