Energy EquationWe now apply the Reynolds Transport theorem (Eqn. 3.27) to derive an equation for energy conservation in a control volume. Now we have,
On the LHS we have
Where Substituting in Eqn.3.27 we have In the above equation, e should include all forms of energy - internal, potential, kinetic and others. The others category will include nuclear, electromagnetic and other sources of energy. But for simple fluid flows these are not important. Fields such as Magneto Hydrodynamics and Relativistic Fluid Dynamics will involve these forms of energy too. We have then Concerning work, we have different kinds - shaft work, Ws, work done by pressure, Wp and work due to shear forces on the control surface. Shaft work includes any work that is directly added to the system by means of a pump, piston etc. Work done by pressure is calculated as where dA ia an elemental area over the control surface, the velocity Vn is into the control volume (hence gets a negative sign). This equation is integrated over the control surface to obtain the total work due to pressure. Thus,
Work due to shear forces is small and is usually neglected. Heat
added
where h is specific enthalpy given by
Subsections (c) Aerospace, Mechanical & Mechatronic Engg. 2005 University of Sydney |