When a liquid is contained in a vessel with vertical sides, the pressure at any point of a side depends upon its distance from the surface of the liquid. The total pressure on the sides of the vessel is the sum of all these pressures, which vary from zero at the surface to. a maximum at the bottom.
The pressure of a liquid upon any submerged surface is equal to the weight of a column of the liquid having the area of the surface for its base, and the depth of the center of gravity of the given surface below the surface of the liquid for its height.
NOTE. - In plane surfaces the center of gravity is the center of area. The center of gravity of a triangle, for instance, is a point two thirds of the distance from any angle to the mid-point of the opposite side.
The rule just given applies to all submerged surfaces, whether vertical, horizontal, inclined, plane, or curved. If the surface is the horizontal base of the vessel, the height of the column will be the total depth of the liquid. The law may be expressed in a formula as follows:
Pressure = HaW,
in which H is the height of the surface of the liquid above the center of gravity of the submerged surface, a is the area of the submerged surface, and W is the weight of a unit volume of the liquid.
A cubic foot of water weighs about 62.5 lb., or 1000 oz. Example. - The pressure of water on any submerged body, as in Fig. 1 is found as follow:
Pressure on top (Ha W): = 2 × (2 × 3) × 62.5 = 750 lb.
Pressure on bottom: =3X (2 × 3) X 62.5 = 1125 lb
Pressure on ends.: = 2 X 2.5 X (2 × 1) × 62.5 = 625 lb.
Pressure on sides: = 2 × 2.5 × (3 × 1) × 62.5 = 937.5 lb.
Total pressure = 3437.5 lb.
