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 in-compressible, 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 in-compressible, non-viscous fluid measured using N/m
^{2}. - 𝜌 is the density of the in-compressible, non-viscous fluid measured using kg/m
^{3}. - v is the velocity of the in-compressible, non-viscous fluid measured using m/s.
- g is the acceleration due to gravity measured using m/s
^{2}. - h is the vertical 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. Similarly, if velocity increases, the pressure decreases 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/m
^{2}. - 𝜌 is the density of the propagating medium measured using kg/m
^{3}. - 𝛾 is the adiabatic constant.

Here, velocity is directly proportional to the square root 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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As per Bernoulli’s equation pressure is inversely related to velocity. But lets consider a gardening Hose.

If we reduce the volume of the pipe outlet by covering a part of it with our fingertip, the water gets displaced to a greater distance with a higher velocity and higher pressure. Again if uncover the pipe outlet both velocity and pressure reduces. So here why pressure and velocity and in direct relation??

Bernoulli’s Principle tells us that the higher the velocity of a fluid, the lower the pressure it exerts. Fluid pressure is caused by the random motion of the fluid molecules. When the fluid speeds up, some of the energy from that random motion is used to move faster in the fluid’s direction of motion. This results in lower pressure.

When you are putting a finger across pipe end ,actually you are increasing the pressure and restricting flow inside pipe , so when it releases to atmosphere it has a higher velocity and a higher pressure compared with normal conditions so in actual the velocity is increasing and pressure is reducing comparing the pressure and velocity inside pipe.