Formulae of Hydrostatic Pressure
Let us derive the formula for Pressure on an object submerged in a fluid.
We know that,
Pressure = Force/Area = F/A & Force = mass x acceleration = m × g (acceleration due to gravity)
So: Pressure = F/A = mg/A ……………. (1)
Now Density = Mass/Volume;
So, Mass= Density x Volume ……………. (2)
From equation 1 & 2,
Pressure = (density x volume x acceleration)/area.
P = (ρ * g * v)/A
P = ρ * g * h
Here
h = v/A = Height of fluid above the object
ρ (rho) is the density of the fluid,
g is the acceleration of gravity
Pressure on an object submerged in a fluid is-
P = ρ * g * h
Hydrostatic Pressure
Hydrostatic pressure can be stated as the pressure exerted by a fluid at equilibrium at a given point within the fluid, due to the force of gravity. Hydrostatic pressure is proportional to the depth measured from the surface as the weight of the fluid increases with a downward force applied.
The fluid pressure can be caused by gravity, acceleration, or forces when in a closed container. Consider a container filled with water or any other fluid along with a ball in the bottom. Now consider the ball from the top of the container. There is pressure exerted by the layer of water acting on the ball. As we move down from the top of the container to the bottom, the pressure exerted by the top layer on the ball adds up. This phenomenon is responsible for more pressure at the bottom of the container.
As we can see in the above figure a ball is completely submerged in a fluid. Here force applied by the fluid on the ball equals to Hydrostatic pressure. Top Layer of the fluid exerts the most pressure on the ball. When we move the ball upside, the pressure applied by the top layer starts to reduce.