CE 230-Engineering Fluid Mechanics Lecture # 17 Reynolds transport equation Control volume equation

Definitions System Control volume Intensive versus extensive property B extensive property and b is the corresponding intensive property b= B/mass Examples

Flow into/out of a CV Net rate of outflow =Σ V.A For a certain extensive property B= Σ b m= b ρ V. A

Derivation of control volume equation

Time rate of change of a system extensive property = time rate of change of that property in CV + Net outflow rate of that property across CS Property B can be selected as mass, momentum, energy etc

Derivation of Euler’s equation Consider a cylindrical fluid element being accelerated in direction l and neglect viscous effects Use equilibrium equation Σ F = m a

Derivation of Euler’s equation