Energy relationships and the Bernoulli equation

The total energy of a fluid in motion consists of the following components internal, potential, pressure and kinetic energies. Each of these energies may be considered with reference to an arbitrary base level. It is also convenient to make calculations on unit mass of fluid. 

Internal energy This is the energy associated with the physical state of the fluid, ie, the energy of the atoms and molecules resulting from their motion and configuration [Smith and Van Ness (1987)]. Internal energy is a function of temperature. The internal energy per unit mass of fluid is denoted by 17. 

Potential energy This is the energy that a fluid has by virtue of its position in the Earth s field of gravity. The work required to raise a unit mass of fluid to a height z above an arbitrarily chosen datum is zg, where g is the acceleration due to gravity. This work is equal to the potential energy of unit mass of fluid above the datum. 

Pressure energy This is the energy or work required to introduce the fluid into the system without a change of volume. If P is the pressure and V is the volume of mass m of fluid, then PV/m is the pressure energy per unit mass of fluid. The ratio mlV is the fluid density p. Thus the pressure energy per unit mass of fluid is equal to Pip. 

Kinetic energy This is the energy of fluid motion. The kinetic energy of unit mass of the fluid is v2I2, where v is the velocity of the fluid relative to some fixed body. 

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