CodeCogs

Returns the elevation, pressure or velocity inside a fluid given the other two parameters.

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Interface

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

using namespace Engineering::Fluids::Imperial;

inline double Bernoulli_inv(int target, double energy, double density, double elevation, double pressure, double velocity)

This function uses the total energy $E$ within a fluid along with its weight density $\rho$ and, given two out of the three fluid parameters (elevation $Z$ , pressure $P$ , velocity $v$ ) it is able to calculate the third one using the simplifed Bernoulli equation:

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

(1)

where $g$ is the acceleration of gravity, 32.2 ft/s².

The example code below shows how this function acts as the inverse of the \ref{Engineering::Fluids::Imperial::Bernoulli} "Bernoulli" module, by computing each parameter on account of the other two, the total energy and the weight density of the fluid.

In order to return the desired parameter, the function takes a target argument which can be ELEVATION, PRESSURE or VELOCITY correspondingly. The value of the desired parameter as argument in the function call is ingored, but a convenient way is to denote it by a null value as you may notice in the given example code.

Example 1

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

int main()
{
  double
  Z = Engineering::Fluids::Imperial::Bernoulli_inv(ELEVATION,
  214.826817683595, 0.34, 0, 0.5, 2),
  P = Engineering::Fluids::Imperial::Bernoulli_inv(PRESSURE,
  214.826817683595, 0.34, 3, 0, 2),
  v = Engineering::Fluids::Imperial::Bernoulli_inv(VELOCITY,
  214.826817683595, 0.34, 3, 0.5, 0);

  printf("   Energy = 214.826817683595 ft\n");
  printf("  Density = 0.34 lb/ft^3\n\n");
  printf("Elevation = %.10lf ft\n", Z);
  printf(" Pressure = %.10lf lb/in^2\n", P);
  printf(" Velocity = %.10lf ft/s\n", v);

  return 0;
}

Output

Energy = 214.826817683595 ft
  Density = 0.34 lb/ft^3

Elevation = 3.0000000000 ft
 Pressure = 0.5000000000 lb/in^2
 Velocity = 2.0000000000 ft/s

Parameters

target

ELEVATION, PRESSURE or VELOCITY

energy

total head (ft)

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

The numerical value of the desired parameter.

References

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

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