Hydrostatic Pressure Formula and Sample Problems
What is Hydrostatic Pressure?
Pressure is commonly defined as force per unit area. But in liquids, the column of liquid exerts a constant force downward due to its weight. The pressure exerted by a column of liquid is called hydrostatic pressure.
This force due to the liquid's weight can be computed using the liquid's density and height. This is the reason why hydrostatic pressure has a different formula than pressure in solids.
Hydrostatic Pressure Formula
Hydrostatic pressure can be computed by multiplying the density of the fluid by the acceleration due to gravity and the depth. In symbols,
P = pgh
where P is the hydrostatic pressure, p (rho) is the density of the liquid, g is the acceleration due to gravity and h is the height from the surface or the depth.
Hydrostatic Formula in Action
How much is the hydrostatic pressure experienced by a scuba diver at 30 meters below the surface of the ocean?
To solve this problem, we have to enumerate the given. But the only given is the height from the surface or the depth which is 30 meters.
The rho or the density of the fluid must be also given or we can rely with our previous knowledge that the density of seawater is 1,030 kilograms per cubic meters.
The acceleration due to gravity is of course 9.8 meters per second squared.
Now, let's solve the problem.
P = pgh Hydrostatic Pressure Formula
P = (1,030 kg/m^3)(9.8 m/s^2)(30 m) Substitution
P = 302,820 Pascals Multiplication
Therefore, the hydrostatic pressure at 30 meters below the surface of the ocean is 302,820 Pascals.