Question

How to convert from system analysis to control volume analysis?

please short and simple answer for memorization please no handwritten i wish to get answer as soon as possible

Answer 1

The Reynolds Transport Theorem provides a way to transfer equations for conservation of mass, momentum, and energy from system analysis to the volume analysis.

Let B = extensive property related to fluid flow (mass, momentum, energy etc) &

b = intensive property( linear momentum per unit mass, energy per unit mass etc).

Then Reynolds transport theorem is

              dB/dt |_sys = ∂/∂t ∫ ρb dV + ∫ ρb V . n dS      

                                         cv              cs

                  cv = control volume,    cs = control surface

where

          ρ       = the mass density of the fluid

        ∂/∂t      =   the time rate of change

         dV      =   the element of volume within the control volume

         V        =   the fluid velocity crossing the control surface

         n         =   the unit outward normal to the control surface

     V . n     =   the normal component of velocity crossing the control surface (dot product)

       dS         =    the element of area on the control surface

and

∂/∂t ∫ ρb dV = the time rate of change of B within the control volume
       cv

∫ ρb V . n dS = the flux of B across the control surface

cs