This Bernoulli's Equation Calculator can help you determine any unknown variable from Bernoulli’s principle formula by giving 6 out of the 7 figures (height, pressure, fluid speed and density). You can discover more on this topic below the tool.

## 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: P _{1} + 0.5 * ρ * v_{1}^{2} + h_{1}*ρ*g = P_{2} + 0.5 * ρ * v_{2}^{2} + h_{2}*ρ*g**

- If the value of P_{1 } or the one of the P_{2 }should be computed then the equations used are:

P_{1} = (P_{2} + 0.5 * ρ * v_{2}^{2} + h_{2}*ρ*g) – (0.5 * ρ * v_{1}^{2} + h_{1}*ρ*g)

P_{2} = (0.5 * ρ * v_{2}^{2} + h_{2}*ρ*g) – (P_{1} + 0.5 * ρ * v_{1}^{2} + h_{1}*ρ*g)

- In case h_{1} or h_{2 }should be estimated then the formulas applied are:

h_{1}= [(P_{2} + 0.5 * ρ * v_{2}^{2} + h_{2}*ρ*g) – (P_{1} + 0.5 * ρ * v_{1}^{2})]/( ρ*g)

h_{2}= [(P_{1} + 0.5 * ρ * v_{1}^{2} + h_{1}*ρ*g) – (P_{2} + 0.5 * ρ * v_{2}^{2})]/( ρ*g)

- If either v_{1} or v_{2 }is the unknown variable then to calculate it the following expression is used:

v_{1 }= √[(P_{2} + 0.5 * ρ * v_{2}^{2} + h_{2}*ρ*g - h_{1}*ρ*g - P_{1})/( 0.5 * ρ)]

v_{2 }= √[(P_{1} + 0.5 * ρ * v_{1}^{2} + h_{1}*ρ*g – h_{2}*ρ*g – P_{2})/( 0.5 * ρ)]

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

ρ = (P_{1}- P_{2})/(0.5 * v_{2}^{2}+ h_{2}*g – 0.5 * v_{1}^{2}+ h_{1}*g)

Where:

g is the acceleration due to gravity and by default is considered to be 9.80665 m/s^{2};

ρ is the fluid density measured in Kg/m^{3};

P_{1} represents the fluid pressure measured in Pa at point 1;

P_{2} refers to the fluid pressure measured in Pa at point 2;

v_{1 }is the fluid speed expressed in meter/second at point 1;

v_{2 }stands for the fluid speed in meter/second at point 2;

h_{1} 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:

From: | To: Pa |

Pa | 1 |

Kpa | 1000 |

bar | 100000 |

Atm | 101325.01 |

mmHg | 133.32238 |

mbar | 100 |

- For fluid speed the supported measurement units are:

From: | To: m/s |

m/s | 1 |

m/min | 0.016667 |

km/hr | 0.277778 |

yd/s | 0.9144 |

ft/s | 0.3048 |

mile/hr | 0.4470405 |

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

From: | To: Kg/m^{3} |

Kg/m^{3} |
1 |

oz/in^{3} |
1730 |

g/cc(ml) | 1000 |

lbs/liter | 453.5923 |

lbs/yd^{3} |
0.5932763 |

lbs/ft^{3} |
16.018461 |

- For height these are the units available:

From: | To: m |

m | 1 |

dm | 0.1 |

cm | 0.01 |

mm | 0.001 |

yd | 0.9914 |

ft | 0.3048 |

in | 0.0254 |