This is The general equation of conservation of energy for a fixed control volume.įor a lot of problems. Plugging these into the above equation yields Plug all of these back into the energy equation, but put the pressure work term on the right hand side:īut, and from the definition of enthalpy (per unit mass).If we define vector as the resultant shear stress acting on the C.S., it turns out that. Rate of viscous work, = rate of work done by viscous stresses at the control surface.Rate of Pressure Work, = rate of work done by pressure forces at the control surface.Note: is positive for a turbine (work done by the fluid), and is negative for a fan (work done on the fluid). a turbine (extracts energy from a flow) : The turbine takes energy from the fluid and converts it into rotation of the shaft. Rate of Shaft Work, = rate of work done by the fluid on a shaft protruding outside the C.V.Į.g.Let's look at each of these terms individually: Has dimensions of = Power (so these are actually power terms). , where: = rate of shaft work, = rate of pressure work, = rate of viscous work. Generally, what is done is to split the work term up into 3 parts:.= kinetic energy per unit mass, gz = potential energy per unit mass. Where e = total energy of the fluid per unit mass,, = internal energy per unit mass, Thus, the right side of the above equation can be called the General Integral Equation for Conservation of Energy in a Control Volume, The left side of the above equation applies to the system, and the right side corresponds to the control volume. In the Reynolds Transport Theorem (R.T.T.), let.Where = rate of change of total energy of the system, = rate of heat added to the system, = rate of work done by the system ![]() Recall, the First Law of Thermodynamics:.
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