Note that z is the height of the port above some datum level and g is the acceleration due to gravity. The specific energy e can include kinetic and potential energy, however will always include the combination of internal energy ( u) and flow work ( Pv), thus we conveniently combine these properties in terms of the property enthalpy (as was done in Chapter 3a), as follows: The total power in due to heat and mass flow through the inlet port (1) must equal the total power out due to work and mass flow through the outlet port (2), thus: Furthermore with a constant mass flow rate, it is more convenient to develop the energy equation in terms of power rather than energy as was done previously. Under steady flow conditions there is no mass or energy accumulation in the control volume thus the mass flow rate applies both to the inlet and outlet ports. The Complete ENergy Equation for a Control VolumeĬonsider the control volume shown in the following figure. In the following section we can now develop the complete energy equation for a control volume. It is of interest that the specific flow work is simply defined by the pressure P multiplied by the specific volume v. In order to evaluate the flow work consider the following exit port schematic showing the fluid doing work against the surroundings through an imaginary piston: These include four types of energy – internal energy ( u), kinetic energy ( ke), potential energy ( pe), and flow work ( w flow). The fluid mass flows through the inlet and exit ports of the control volume accompanied by its energy. Thus finally the mass flow rate can be determined as follows: Furthermore the term Control Volume indicates that there is no boundary work done by the system, and typically we have shaft work, such as with a turbine, compressor or pump.Ĭonsider an elemental mass dm flowing through an inlet or outlet port of a control volume, having an area A, volume dV, length dx, and an average steady velocity, as follows. We will only consider Steady Flow conditions throughout, in which there is no energy or mass accumulation in the control volume, thus we will find it convenient to derive the energy equation in terms of power rather than energy. In addition to the energy flow across the control volume boundary in the form of heat and work, we will also have mass flowing into and out of the control volume. Fortunately we will be able to separately analyze each component of the system independent of the entire system, which is typically represented as follows: In this course we consider three types of Control Volume Systems – Steam Power Plants, Refrigeration Systems, and Aircraft Jet Engines.

The First Law of Thermodynamics for Control Volumes

Turbine thermodynamics calculator