What is Hydrostatic Pressure?
Hydrostatic pressure is defined as
The pressure exerted by a fluid at equilibrium at any point of time due to the force of gravity.
Hydrostatic pressure is proportional to the depth measured from the surface as the weight of the fluid increases when a downward force is applied.
The fluid pressure can be caused by gravity, acceleration or forces when in a closed container.Consider a layer of water from the top of the bottle. There is a pressure exerted by the layer of water acting on the sides of the bottle. As we move down from the top of the bottle to the bottom, the pressure exerted by the top layer on the bottom adds up. This phenomenon is responsible for more pressure at the bottom of the container.
Hydrostatic Pressure Formula
Following is the formula used to calculate the hydrostatic pressure:
p = ρgh |
where,
- p is the pressure exerted by the liquid in N.m^{-2}, Pa
- ρ is the density of the liquid in kg.m^{-3}, slugs.ft^{-3}
- g is the acceleration due to gravity taken as 9.81m.s^{-2}
- h is the height of the fluid column in m
Hydrostatic Pressure vs Depth of Water
Following is the table explaining how the depth of water value changes with the pressure:
Depth of water |
Pressure |
||
ft |
m | Pa |
bar |
1 |
0.30 | 2990 | 0.03 |
5 |
1.52 | 14949.99 | 0.15 |
10 | 3.05 | 29899.98 |
0.30 |
15 | 4.57 | 44849.97 |
0.45 |
Hydrostatic Pressure Derivation
Consider a column of water with the total volume V and A as the base surface area.
The weight of the water is:
W = mg
We know that the mass of water is just the density of water with volume X. Therefore,
W = ρVg
Volume is the product of surface area and height. Therefore,
V = Ah
W =ρAhg
Using the formula of pressure:
\(p=\frac{F}{A}\) \(p=\frac{\rho Ahg}{A}\)
p = ρhg
Hydrostatic Pressure Problems
Q1. What is the pressure acting on the water at a depth of 1m at 4°C?
Ans: The depth of water column = 1m
The density of water at 4°C = 1000kg/m^{3}
The formula used is: p = ρgh
= (1000kg/m^{3})(9.81m.s^{-2})(1m)
= 9810 Pa.
Q2. What is the pressure acting on the water at a depth of 3ft at 32°F?
Ans: The depth of water column = 3ft
The density of water at 32°F = 1.940 slugs.ft^{-3}
The formula used is: p = ρgh
= (1.940 slugs.ft^{-3})(32.17405ft.s^{-2})(3ft)
=187.3lb.ft^{-2}.