Summation of Accumulative Physical Quantity

The application of integration can also be applied to other mechanical quantities by expressing the mechanical quantity in the form of accumulative mechanical quantity.

Hydrostatic Force

Hydrostatic force is the normal force exerted on an submerged object due to the hydrostatic pressure of the fluid. Hydrostatic pressure is defined as the force per unit area. Therefore hydrostatic force is equal to

Since hydrostatic pressure is the equilibrium pressure at a point exerted by a fluid, the hydrostatic pressure at a point is a function of the depth of the point below the fluid surface. Imply the hydrostatic pressure is equal to

Hydrostatic force on the horizontal bottom of a rectangular tank

For a rectangular tank, the horizontal plate of the bottom is submerged at a constant depth in the fluid. Imply

Hydrostatic force on one vertical end of a rectangular tank

For a rectangular tank, the vertical end of a tank is submerged at a variable depth in the fluid. Imply

Hydrostatic force on a vertical triangular window of a rectangular tank

For a rectangular tank, the vertical triangular window of a tank is submerged at a variable depth in the fluid. Imply

Hydrostatic force on a vertical triangular window of a rectangular tank

For a rectangular tank, the vertical triangular window of a tank is submerged at a variable depth in the fluid. Imply

Hydrostatic force on a vertical circular window of a rectangular tank

For a rectangular tank, the vertical circular window of a tank is submerged at a variable depth in the fluid. Imply

By substitution:

And: