# Relation Between Pressure And Velocity

Pressure and velocity both are the macroscopic parameters governing plenty of natural phenomena. Pressure is the measure of force per unit area. Velocity is the measure of the rate of change of displacement. The relation between pressure and velocity can be given through two independent equations/formulation.

## Pressure And Velocity Relation

In thermodynamics, for any incompressible, non-viscous fluid, the relation between pressure and velocity is given by Bernoulli’s equation,

 $P+\frac{1}{2}\rho v^{2}+\rho gh=Constant$

Where,

• P is the pressure of the incompressible, non-viscous fluid measured using N/m2.
• 𝜌 is the density of the incompressible, non-viscous fluid measured using kg/m3.
• v is the velocity of the incompressible, non-viscous fluid measured using m/s.
• g is the acceleration due to gravity measured using m/s2.
• h is the verticle height of the pipe from the reference level measured using m.

Pressure and velocity are inversely proportional to each other. If pressure increases, the velocity decreases to keep the algebraic sum of potential energy, kinetic energy, and pressure constant. Similarely if velocity increases teh pressure decreases to so as to keep the sum of potential energy, kinetic energy, and pressure constant.

In mechanics, the relation between pressure and velocity is given by Laplace correction for Newton’s equation for the velocity of sound as-

 $v=\sqrt{\frac{\gamma p}{\rho }}$

Where,

• v is the velocity of sound waves measured using m/s.
• p is the pressure of the propagating medium measured using N/m2.
• 𝜌 is the density of the propagating medium measured using kg/m3.
• 𝛾 is the adiabatic constant.

Here, Velocity is directly proportional to the squareroot of pressure. Similarly, the pressure is proportional to the square of velocity. As they are directly proportional to each other. When pressure increases, velocity will also increase and vise-versa.

Hope you understood the relation and conversion of Pressure and Velocity in various disciplines of physics.

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