Pressure in a Fluid Formula
The pressure exerted by a static fluid or hydrostatic pressure, is the pressure in an equilibrium system that depends only upon the depth of the fluid, the density of the fluid, and the acceleration of gravity. Its units are the same as pressure in general, N/m2. The formula for pressure in a fluid is given:
Pressure in a fluid = (density) * (acceleration of gravity) * (depth of the fluid)
P = ρ g h
Where we have:
ρ: Density of the fluid
g: Acceleration of gravity
h: Depth of the fluid
Pressure in a fluid Formula Questions:
1) A 3 m height container, sealed, is half filled by fluid. The density of the fluid is ρ = 1.5 Kg/m3. What is the pressure at the bottom of the container?
Answer: The pressure is given by the formula: P = ρ g h,
P= 1.5 Kg/m3 * 9.8 m/s2 * 1.5 m = 22.05 N/m2
The pressure of the fluid at the bottom is then,
P = 22.05 Pa.
2) A 20 m height container is filled with a fluid. The container is open. The density of the fluid is ρ = 50 Kg/m3. What is the pressure at the bottom of the container?
Answer: The pressure is given by the formula: P = ρ g h, but an additional pressure must be added, the pressure PA exerted by the atmosphere at the top of the open container, then P = PA + ρ g h
P= 50 Kg/m3 * 9.8 m/s2 * 20 m = 9800 N/m2 = 9800 Pa = 9.8 kPa
The atmospheric pressure at the level of the sea is 101.325 kPa
The pressure of the fluid at the bottom is then,
P = 101.325 kPa + 9.8 kPa = 111.125 kPa.
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