Engineering Bernoulli Equation

The energy equation for a steady flow incompressible fluid flow through a system with a stationary boundary is as follows:

The term (ΔÛ – Q) is referred to as friction loss per unit mass and is designated as Ê_V. This represents the irreversible degradation of mechanical energy into thermal energy. Thus the above Equation 5 is expressed as follows:

 

This is known as the Engineering Bernoulli Equation.

Example

Water is pumped from a large reservoir to an elevation of 20m through a pipe of diameter 10cm as shown in the figure below and issues out of a nozzle to form a free jet. Assuming negligible frictional losses, calculate the power required to accomplish this task.

Solution

Simplification of the Engineering Bernoulli Equation

Static Fluid

For a static fluid, v = 0, thus the Engineering Bernoulli equation simplifies as follows:

This is the basic equation of fluid statics. The positive z-direction of the equation above should be taken in the direction opposite to gravity.

Perfect Fluid

A perfect or inviscid fluid has zero viscosity. Thus, under these circumstances the Engineering Bernoulli equation simplifies as follows:

The above equation is known as the Bernoulli Equation.