CE 1501 CE 150 Fluid Mechanics G.A. Kallio Dept. of Mechanical Engineering, Mechatronic Engineering & Manufacturing Technology California State University, Chico

CE 1502 Finite Control Volume Analysis Reading: Munson, et al., Chapter 5

CE 1503 Conservation of Mass The conservation of mass principle states that Applying the RTT with B = m and b = 1:

CE 1504 Special Cases Moving control volume - replace V with relative velocity W = V-V cv, where CV is moving at constant velocity V cv Deforming control volume – replace V with relative velocity W + V cs, where CS is moving at constant velocity V cs

CE 1505 Newton’s 2 nd Law: Linear Momentum Eqn. Newton’s 2 nd law for a system is Applying the RTT with B = mV (linear momentum) and b = V :

CE 1506 Newton’s 2 nd Law: Linear Momentum Eqn. The first LHS term represents the time rate of change of linear momentum of the control volume The second LHS term represents the net outflow of linear momentum across the control surface The RHS term represents all body and surface forces acting on the control volume

CE 1507 Newton’s 2 nd Law: Linear Momentum Eqn. Important notes regarding the linear momentum equation: –this is a vector equation; it can have components in as many as three orthogonal directions –the first LHS term is zero for steady flow through a nondeforming CV –the V n product determines whether there is an inflow or outflow of linear momentum –the integral operations in the second LHS term are simplified if the flow is incompressible and the velocity is uniform over the control surface

CE 1508 Newton’s 2 nd Law: Linear Momentum Eqn. Important notes, continued: –the CV is normally chosen to be perpendicular to inflows and outflows; this further simplifies the analysis –if an anchoring force is sought, then the CV should contain the fixture that imposes the anchoring force; this normally allows the atmospheric pressure to cancel out over all surfaces –the external forces in the RHS term typically include anchoring or reaction forces, pressure forces, and fluid weight forces

CE 1509 Moment-of-Momentum Equation This material is omitted (sections 5.2.3, 5.2.4, and 5.3.5)

CE The Energy Equation The conservation of energy equation, or 1 st Law of Thermodynamics, for a (closed) system is

CE The Energy Equation The total energy stored in the system, E, consists of internal, kinetic, and potential energy:

CE The Energy Equation Applying the RTT with B=E or b=e: The first RHS term represents the time rate of change of the energy stored within the CV The second term represents the net loss of energy by fluid flow across the control surface

CE The Energy Equation Combining terms, Work is transferred across the CV boundary in several ways; when analyzing fluid machinery such as pumps, fans, compressors, turbines, etc., rotating shaft work is common Heat transfer occurs by the modes of of conduction, convection, and radiation under the influence of a temperature difference

CE The Energy Equation Work also occurs where flow enters and leaves the CV; this is associated with the pressure and is often called flow work; since it acts along the control surface, it can be combined with the flow of stored energy term: h is the fluid enthalpy per unit mass (J/kg or Btu/slug)

CE The Energy Equation Combining terms once again, we obtain a useful form of the energy equation for a control volume experiencing fluid flow: