CodeCogs

Returns the total energy within a fluid using the simplified Bernoulli equation.

Interface

#include <codecogs/engineering/fluids/imperial/bernoulli.h>

using namespace Engineering::Fluids::Imperial;

inline double Bernoulli(double density, double elevation, double pressure, double velocity)

The simplified Bernoulli equation is basically expressing the application of the law of conservation of energy to the flow of fluids in a conduit. It is given by the following formula:

$Z + \frac{144 P}{\rho} + \frac{v^2}{2g} = E \mbox{ (constant)}$

(1)

where $Z$ is the elevation head, $P$ is the pressure head, $v$ the velocity head and finally $E$ is the total energy of fluid constant at any particular point, above some arbitrary horizontal datum plane. Also $g$ is the acceleration of gravity, 32.2 ft/s².

It is assumed that friction losses are neglected and no energy is added to, or taken from the system.

Example 1

#include <stdio.h>
#include <codecogs/engineering/fluids/imperial/bernoulli.h>

int main()
{
  double energy = Engineering::Fluids::Imperial::Bernoulli(0.34, 3, 0.5, 2);
  printf("Total energy: %.12lf ft\n", energy);

  return 0;
}

Output

Total energy: 214.826817683595 ft

Parameters

density

weight density of fluid (lb/ft³)

elevation

potential head or elevation above reference level (ft)

pressure

pressure (lb/in²)

velocity

mean velocity of flow (ft/s)

Returns

Total energy of fluid (ft).

References

The Engineering Division, Crane Co., "Flow of fluids through valves, fittings, and pipe", Chicago, 1957

Interactive Calculator

density

elevation

pressure

velocity

Result –