The energy balance for systems involving a simple flow of a fluid is characterized by the lack of conversion of chemical, thermal, or any other kind of energy into mechanical energy. Essentially, the resulting mathematical formulation is simply a mechanical energy balance wherein the energy contributions arise from the potential and kinetic energy terms and flow work [3]. For an incompressible (constant density) fluid that does not experience any friction, the mechanical energy balance is given by equation 5.1 [1]:
where P is the pressure, V is the velocity, ρ is the density of the fluid, and z is the elevation of the fluid in the gravitational field, g being the acceleration due to gravity. The terms in the equation have the units of J/kg (energy per unit mass), and this equation is known as the Bernoulli equation [1]. The validity of the Bernoulli equation is limited to frictionless flow, but in reality, frictional effects need to be accounted for. Applying the Bernoulli equation between points 1 and 2 yields equation 5.2 [1]:
where hf represents the frictional losses. It is assumed that the fluid flow is accomplished by means of a pump between the two points, and win is simply the work input from this pump. It should be clear from equation 5.2 that the power requirement for transferring a fluid from one point to another depends on the following four factors:2
2. A student will encounter the detailed analysis while conducting the mechanical energy balance in later curriculum.
• The difference in the hydrostatic pressure between the two points
• The difference in the elevation of the two points
• The difference between the fluid velocities at the two points
• The frictional losses in the piping system
The frictional losses depend on the flow regime, and the accounting of the frictional losses requires an understanding of the concept of viscosity.
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