Pressure in Liquid - Example 1

Example 1:

The diagram shows 2 fishes in water. The density of the water is 1025 kg/m³. The surface area of fish A is 300 cm² and the surface area of fish B is 2000cm². Find
a. the pressure exerted by the water on fish A.
b. the pressure exerted by the water on fish B.
c. the force exerted by the water on fish A.
d. the force exerted by the water on fish B.

Answer:
This question would like us to compare the liquid pressure exerted on 2 objects of different size in the same depth of water.

a.
Depth, h = 2m
Density, ρ = 1025 kg/m³
Gravitational Field Strength, g = 10 N/kg

Pressure exerted by water on fish A,
$$\begin{array}{l}P=h\rho g\\ P=(2)(1025)(10)\\ P=20500Pa\end{array}$$
b. Pressure exerted by water on fish B,
$$\begin{array}{l}P=h\rho g\\ P=(2)(1025)(10)\\ P=20500Pa\end{array}$$
(Note: Pressure exerted both fishes are the same. Pressure caused by liquid is not affected by the size or shape of the objects)

c. Surface area of fish A, A₁ = 300 cm² = 0.03 m²

Force exerted by the liquid pressure,
$$\begin{array}{l}F=PA\\ F=(20500)(0.03)\\ F=615N\end{array}$$
d. Surface area of fish B, A₂ = 2000cm² = 0.2 m²

Force exerted by the liquid pressure,
$$\begin{array}{l}P=\frac{F}{A}\\ F=PA\\ F=(20500)(0.2)\\ F=4100N\end{array}$$