total_head — Imperial

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

Interface

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

using namespace Engineering::Fluids::Imperial;

inline double total_head(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 constant total energy of fluid 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 piping system.

Example 1

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

int main()
{
  double energy = Engineering::Fluids::Imperial::total_head(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 –