How to Calculate Fluid Energy

The energy of a fluid comes in the following forms:

  1. Kinetic Energy (if it is moving)
  2. Potential Energy
  3. Pressure Energy

Kinetic Energy

Since energy is required to accelerate a stationary body, a moving mass of fluid flow possesses more energy than an identical, stationary mass. This energy difference is the kinetic energy of the fluid. The kinetic energy of a fluid is generally evaluated per unit mass, which is termed the specific kinetic energy. The equation for specific kinetic energy of a fluid is:

E_v = \frac{v^{2}}{2}\hspace{30px}^{(SI)}
E_v = \frac{v^{2}}{2g_c}\hspace{30px}^{(US)}

Where:
v = velocity (ft/s or m/s)
gc = 32.2 ft/s2

Potential Energy

A mass of fluid at a high elevation will have more energy than an identical mass of fluid at a lower elevation. This energy difference is called potential energy, and like kinetic energy, for a fluid it is usually expressed per unit mass. The reference point (i.e. elevation zero) is arbitrary and it is usually easiest to use the elevation of the lower fluid. The equation is:

E_z = zg\hspace{30px}^{(SI)}
E_z = \frac{zg}{g_c}\hspace{30px}^{(US)}

Where:
z = elevation above reference point (ft or m)
gc = 32.2 ft/s2 (U.S. units) or 9.81 m/s2 (metric)

Pressure Energy

A mass of fluid at high pressure will have more energy than a mass of fluid at lower pressure. This energy difference is the pressure energy.

E_p = \frac{p}{\rho}

Where:
p = pressure (lbf/ft2 or Pa)
ρ = density (lbm/ft3 or kg/m3)

Units

In metric, the units are clearly m2/s2. Since this calculation is per unit mass, multiplying back by mass will result in kg-m2/s2, or N-m.

In U.S. units, the distinction must be made between pounds-force (lbf) and pounds-mass (lbm). The units of the above equations evaluate to:

\frac{(\frac{ft}{s})^{2}}{\frac{lbm\cdot ft}{lbf\cdot s^{2}}} = \frac{ft\cdot lbf}{lbm}

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