Just like gases liquids also exert pressure. The pressure in liquid is due to its weight. We will determine that how pressure of incompressible liquid increases with depth.
Consider a column of liquid of height 'h', base area 'A' at the bottom of a tank in liquid and density 'ρ' as shown in figure 5.14. The force acting on a base area is the weight of the cylindrical column of liquid of mass 'm' is, The mass 'm' of the cylindrical liquid, in terms of density 'ρ' is given by,
F = W = mg
or m = ρV
Since the fluid forms a cylindrical volume V shown by dotted lines in the figure which has height h and area of cross section A. Therefore V = Ah, putting equation 3 in equation 2, we get m = ρAh, putting equation 4 in equation 1, we get
F = ρAhg
Since pressure is defined as P = F/A, putting equation 5 in equation 6, we get
P = ρgh
Therefore P = ρgh
From equation 7.3 we deduce that the pressure in a liquid depends on the depth and density of the liquid.
A submarine was moving in the Pacific Ocean (the largest and deepest ocean) at a depth of 8.5 km. How much pressure is exerted upon the submarine if density of water is 1000 kg/m³?
GIVEN
REQUIRED
Pressure P = ?
SOLUTION:
The pressure exerted on a body inside a liquid, can be given by: P = ρgh. Putting values P = (1000 kg/m³) x (9.8 m/s²) x (8500 m) Therefore P = 8.33 x 10⁷ N/m² = 8.33 x 10⁷ Pa
Answer
The water will exert a pressure of 8.33 x 10⁷ Pa or 83.3 MPa on the submarine.