Energy Conversions in Fluid Systems

The Bernoulli's equation makes it simple to examine how energy transfers occur among velocity head, elevation head, and pressure head. It is possible to inspect separate components of piping systems and establish what fluid properties are changeable and how the energy balance is exaggerated.

When a pipe containing an ideal fluid endures a steady expansion in diameter, the continuity equation state us that as the diameter and flow region get bigger, the flow velocity should reduce to maintain the similar mass flow rate. As the outlet velocity is less than the inlet velocity, the velocity head of the flow should reduce from the inlet to the outlet. When the pipe lies horizontal, there is no change in elevation head; thus, the reduction in velocity head should be compensated for by a rise in pressure head. As we are considering an ideal fluid which is incompressible, the specific volume of the fluid will not alter. The only way that the pressure head for an incompressible fluid can raise is for the pressure to rise. Therefore the Bernoulli equation points out that a reduction in flow velocity in a horizontal pipe will outcome in a raise in pressure.

When a constant diameter pipe having an ideal fluid undergoes reduction in elevation, the similar total effect results, though for distinct reasons. In this situation the flow velocity and the velocity head should be constant to satisfy the mass continuity equation.

Therefore the decrease in elevation head can only be compensated for by a rise in pressure head. Again, the fluid is incompressible therefore the rise in pressure head should result in a rise in pressure.

However the Bernoulli equation has numerous restrictions placed upon it, there are many physical fluid troubles to which it is exerted. As in the situation of the conservation of mass, the Bernoulli equation might be applied to troubles in which more than one flow might enter or leave the system at the similar time. Of specific note is the fact which series and parallel piping system troubles are resolved by using the Bernoulli equation.