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.

Finding net force on upper half.

Observe the diagram:

If Opposite angles are equal, then opposite sides are also equal.

.

.

The length of the strip is and width is .

Area of the strip is .

Force acting on the strip is .

.

.

.

.

Hydrostatic force as a Riemann sum  .

Set up the integral .

.

Finding force on lower part:

Observe the diagram:

If Opposite angles are equal, then opposite sides are also equal.

.

The length of the strip is and width is .

Area of the strip is .

Force acting on the 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 .