Development
We apply the Law of Conservation of Energy to a control volume. To do so, we must identify the forms of energy in the control volume. Consider the following system
The forms of energy in this system are:
· Pressure energy: The pressure in a fluid also does work by generating force on a cross section which then moves through a distance. This is energy since work is energy.
· Kinetic energy: This is due to the motion of the mass of fluid.
· Potential energy: This is due to the height above an arbitrary datum
Pressure Energy
Kinetic Energy
From classical physics, the kinetic energy of the mass entering is:
Potential Energy
The potential energy of the mass entering, due to the height above the datum is:
Total Energy
The total energy at the entry to the system is just the sum:
Final Form
It is more usual to consider the energy per unit weight, and so we divide through by
