Pressure due to a Fluid Column
The pressure exerted by a fluid column at a certain depth is given by P = ρgh, where ρ is fluid density, g is acceleration due to gravity, and h is depth.
What is Pressure due to a Fluid Column?
Force applied perpendicular to the surface of an object per unit area over which that force is distributed.
Key formula / rule: Pressure due to Fluid Column (Gauge Pressure)
Key points
- To understand the factors affecting pressure in a fluid.
- To derive and apply the formula for pressure due to a fluid column.
- To differentiate between gauge and absolute pressure.
- To solve problems involving fluid pressure in various scenarios.
Common exam trap
Confusing gauge pressure with absolute pressure.
Definitions
- Term
Pressure
- Meaning
Force applied perpendicular to the surface of an object per unit area over which that force is distributed.
- Term
Density
- Meaning
Mass per unit volume of a substance.
- Term
Gauge Pressure
- Meaning
The pressure relative to the ambient pressure (usually atmospheric pressure).
- Term
Absolute Pressure
- Meaning
The total pressure, including atmospheric pressure.
Learning objectives
To understand the factors affecting pressure in a fluid.
To derive and apply the formula for pressure due to a fluid column.
To differentiate between gauge and absolute pressure.
To solve problems involving fluid pressure in various scenarios.
Formulae
- Name
Pressure due to Fluid Column (Gauge Pressure)
- Note
ρ = density of fluid, g = acceleration due to gravity, h = depth of the fluid.
- Expression
P = ρgh
- Name
Absolute Pressure
- Note
Patmospheric is the pressure exerted by the atmosphere.
- Expression
Pabsolute = Patmospheric + ρgh
- Name
Density
- Note
m = mass, V = volume.
- Expression
ρ = m/V
- Name
Force due to Weight
- Note
m = mass, g = acceleration due to gravity.
- Expression
F = mg
Prerequisites
Understanding of density (mass per unit volume).
Concept of force and pressure.
Understanding of acceleration due to gravity.
Common mistakes
Confusing gauge pressure with absolute pressure.
Using inconsistent units for density, gravity, and height.
Forgetting that pressure is independent of the shape of the container.
Assuming pressure is only downwards; it acts in all directions.
Keywords
Fluid Pressure
Hydrostatic Pressure
Density
Gravity
Depth
Gauge Pressure
Absolute Pressure
Fluid Statics
Practice preview
What is the pressure exerted by a fluid column of height 'h' and density 'ρ' at a depth 'h'?…
easy
If the density of a liquid is doubled, while the height of the column and acceleration due to gravity remain constant, how does the pressure at the bottom change?…
easy
A rectangular tank of base dimensions 2m x 3m is filled with water to a height of 4m. Calculate the force exerted by the water on the base of the tank. (Density of water = 1000 kg/m³, g = 9.8 m/s²)…
hard