BERNOULLI'S EQUATION: for Ideal Fluid Flow
- The fluid is incompressible and nonviscous.
- There is no energy loss due to friction between the fluid and the wall of the pipe.
- There is no heat energy transferred across the boundaries of the pipe to the fluid as either a heat gain or loss.
- There are no pumps in the section of pipe under consideration.
- The fluid flow is laminar and steady state.
Bernoulli's Equation is basically a statement of the conservation of energy per unit volume along the pipe.
Energy Density or Energy per unit Volume (SI: J/m3):
For an ideal fluid flow the energy density is the same at all locations along the pipe. This is the same as saying that the energy of a unit mass of the fluid does not change as it flow through the pipe system.
* A compressed fluid or gas has the ability to do work if it is allowed to expand, i.e. it has stored energy. The magnitude of the pressure P is equal to the Potential Energy per unit volume due to the Hydrostatic Pressure in the fluid. Note that the unit of pressure even can be expressed at a unit of energy density, Pa = N/m2=(N. m)/(m2 . m) = J/m3.
* The kinetic energy density can be though of a pressure exerted by the fluid due to its motion.
* We have already seen that gravitational potential energy density, ρgh, is just the pressure of a fluid due to its weight.