Strategy in the Analysis of Fluid Mechanics using Control Volumes  (continued)

 

Step

Activity

1

Identify the control volume (cv)  and control surface  (cs)

 

 

 

 

 

 

 

 

 

 

 

2

 

            

 

 

 

3.

Write vector representation of fluid velocities V1 ,  V2 , V3

and unit, outward, normal vectors   n1 , n2 , n3

 

V1 = V1 i . n1 = ˗ i,  V2 = V2(cos θ i + sin θ j,  n2 = cos θ i + sin θ j ,

V3 = V3 i , n3 =  i

 

4.

Form dot products in the equation for conservation of mass,  V • n  for the

control surfaces at stations  1,  2,  and  3.  V1 • . n1 =  - V1 ,  V2 • . n2 =  V2

 V3 • . n3 =  V3

 

 

5.

 

 

Apply:                ∂/∂t  ∫ ρ dV  +  ∫ ρ V . n dS    =  0

                                  cv              cs

  

Click here for sample calculations.

 


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