Bernoulli`s Equation Calculator

How does this Bernoulli's Equation Calculator work?

This tool can be used to calculate any variable from the Bernoulli’s formulas as explained below:

Bernoulli's Equation: P₁ + 0.5 * ρ * v₁² + h₁*ρ*g = P₂ + 0.5 * ρ * v₂² + h₂*ρ*g

- If the value of P₁  or the one of the P₂ should be computed then the equations used are:

P₁ = (P₂ + 0.5 * ρ * v₂² + h₂*ρ*g) – (0.5 * ρ * v₁² + h₁*ρ*g)

P₂ = (0.5 * ρ * v₂² + h₂*ρ*g) – (P₁ + 0.5 * ρ * v₁² + h₁*ρ*g)

- In case h₁ or h₂ should be estimated then the formulas applied are:

h₁= [(P₂ + 0.5 * ρ * v₂² + h₂*ρ*g) – (P₁ + 0.5 * ρ * v₁²)]/( ρ*g)

h₂= [(P₁ + 0.5 * ρ * v₁² + h₁*ρ*g) – (P₂ + 0.5 * ρ * v₂²)]/( ρ*g)

- If either v₁ or v₂  is the unknown variable then to calculate it the following expression is used:

v₁ = √[(P₂ + 0.5 * ρ * v₂² + h₂*ρ*g - h₁*ρ*g - P₁)/( 0.5 * ρ)]

v₂ = √[(P₁ + 0.5 * ρ * v₁² + h₁*ρ*g – h₂*ρ*g – P₂)/( 0.5 * ρ)]

- In case ρ should be obtained then the formula is:

ρ = (P₁- P₂)/(0.5 * v₂²+ h₂*g – 0.5 * v₁²+ h₁*g)

Where:
g is the acceleration due to gravity and by default is considered to be 9.80665 m/s²;
ρ is the fluid density measured in Kg/m³;
P₁ represents the fluid pressure measured in Pa at point 1;
P₂ refers to the fluid pressure measured in Pa at point 2;
v₁ is the fluid speed expressed in meter/second at point 1;
v₂ stands for the fluid speed in meter/second at point 2;
h₁ is the height in meters at point 1;
h2 is the height in meter at point 2.
As it can easily be observed this Bernoulli`s Equation calculator allows choosing between multiple units depending on the variable type as detailed here, while the conversion rates are:
- For fluid pressure the measurement units available are:

- For fluid speed the supported measurement units are:

- For fluid density the measurement units that can be used:

- For height these are the units available: