Force Due to Liquid Pressure: Physics Principles and Applications, Slides of Differential and Integral Calculus

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Force Due to

Liquid Pressure

Force Due to Liquid Pressure

• (^) The force F on an area A at a depth h in a liquid of density w is given by F = w h A
• (^) The force will increase if the density increases, or if the depth increases or if the area increases.
• (^) So if we have an unevenly shaped plate submerged vertically in a liquid, the force on it will increase with depth. Also, if the shape of the plate changes as we go deeper, we have to allow for this.

In integral form,

dF  whdA

In differential form, 

b a

F w hdA

Where h is the distance of the element or the strip from the liquid surface.

Example 1 A trough having a trapezoidal cross section is full of water. If the trapezoid is 3m wide at the top, 2m wide at the bottom and 2m deep, find the total force owing to liquid pressure on one end of the trough.

w

answer N

Example 3 Find the force on one side of a cubical container 6.0 cm on an edge if the container is filled with mercury. The weight density of mercury is 133 kN/cubic meters.

Example 4 A right triangular plate of base 2.0 m and height 1.0 m is submerged vertically, with the top vertex 3.0 m below the surface. Find the force on one side of the plate.

Example 6 The bottom of a swimming pool is an inclined plane. The pool is 2m deep at one end and 8m deep at the other end. If the width of the pool is 25m and the length is 40m, find the force due to liquid pressure on the bottom. answer 250 409 w N