Consider the general form of the Reynolds transport theorem (RTT) as stated in Prob. 4–93. Let B_sys be the linear momentum mV(vector) of a system of fluid particles. We know that for a system, Newton’s second law is

Use the RTT and Newton’s second law to derive the linear momentum equation for a control volume.

Data from Problem 93

Consider the general form of the Reynolds transport theorem (RTT) given by

where V_r(vector) is the velocity of the fluid relative to the control surface. Let B_sys be the mass m of a closed system of fluid particles. We know that for a system, dm/dt = 0 since no mass can enter or leave the system by definition. Use the given equation to derive the equation of conservation of mass for a control volume

Transcribed Image Text:

ΣF = ma = m dv dt dt (mv) sys