AcademyFluids
Academy
Pressure in Fluids
Level 1 - Physics topic page in Fluids.
Principle
Fluid pressure acts normal to surfaces and increases with depth in a static fluid.
Notation
\(p\)
pressure
\(\mathrm{Pa}\)
\(F_\perp\)
normal force on area
\(\mathrm{N}\)
\(A\)
surface area
\(\mathrm{m^{2}}\)
\(\rho\)
fluid density
\(\mathrm{kg\,m^{-3}}\)
\(h\)
depth below a reference level
\(\mathrm{m}\)
\(p_0\)
pressure at the reference level
\(\mathrm{Pa}\)
Method
Pressure is force per area, and in a static fluid the deeper level must support the weight of fluid above it.
Pressure definition
\[p=\frac{F_\perp}{A}\]
Column equilibrium
\[pA-p_0A-\rho ghA=0\]
Take a fluid column of area \(A\) and height \(h\).
Hydrostatic result
\[p=p_0+\rho gh\]
Pressure force
\[F_\perp=pA\]
The graph shows the linear hydrostatic increase when density is constant.
The slope of the line is \(\\rho g\), so denser fluids produce larger pressure changes per metre.
Rules
These are the compact pressure relations for static fluids.
Pressure
\[p=\frac{F_\perp}{A}\]
Hydrostatic pressure
\[p=p_0+\rho gh\]
Pressure change
\[\Delta p=\rho gh\]
Pressure force
\[F_\perp=pA\]
Examples
Question
Find the gauge pressure
\[3.0\,\mathrm{m}\]
below the surface of water \[(\rho=1000\,\mathrm{kg\,m^{-3}})\]
Answer
\[\Delta p=\rho gh=1000(9.8)(3.0)=2.94\times10^4\,\mathrm{Pa}\]
Checks
- Pressure is a scalar, even though the force it produces has direction.
- In the formula used here, \(h\) is measured downward from the reference level.
- Gauge pressure ignores atmospheric pressure; absolute pressure includes it.
- Pressure force is perpendicular to the surface it acts on.