Solutions Manual Fundamental Mechanics of Fluids 4th Edition by I. G. Currie

Solutions Manual
Fundamental Mechanics of Fluids 4th Edition

By
I. G. Currie

( All Chapters Included - 100% Verified Solutions )




1

, BASIC CONSERVATION LAWS


Problem 1.1




Inflow through x = constant:  u y z

Outflow through x   x = constant:  u y z  (  u  y  z)  x 
x

Net inflow through x = constant surfaces:  ( u ) x y  z 
x

Net inflow through y = constant surfaces:  ( v ) x y  z 
y

Net inflow through z = constant surfaces:  ( w) x y  z 
z
But the rate at which the mass is accumulating inside the control volume is:

(   x  y  z)
t
Then the equation of mass conservation becomes:

    
 x  y  z    ( u )  (  v)  (  w)   x  y  z 
t  x y z 

Taking the limits as the quantities  x,  y and  z become vanishingly small, we get:


   
 ( u)  (  v)  (  w)  0
t x y z




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,BASIC CONSERVATION LAWS


Problem 1.2




Inflow through R = constant:  u R R   z

Outflow through R   R = constant:  u R R   z  (  u R R   z )  R 
R

Net inflow through R = constant surfaces:  (  R u R )  R   z 
R

Net inflow through  = constant surfaces:  (  u )  R   z 


Net inflow through z = constant surfaces:  (  u z ) R  R   z 
z
But the rate at which the mass is accumulating inside the control volume is:

(  R  R   z )
t
Then the equation of mass conservation becomes:

    
R  R   z    (  Ru R )  (  u  )  R (  u z )   R   z 
t  R  z 

Taking the limits as the quantities  R,  and  z become vanishingly small, we get:

 1  1  
 ( R u R )  (  u )  (  u z )  0
t R R R  z




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, BASIC CONSERVATION LAWS


Problem 1.3




Inflow through r = constant:  u r r 2 sin   
Outflow through r   r = constant:  u r r 2 sin   

 (  r 2u r sin    )  r 
r

Net inflow through r = constant surfaces: (  r 2u r )sin   r   
r

Net inflow through  = constant surfaces:  (  u sin  ) r  r   


Net inflow through  = constant surfaces:  (  u  ) r  r   

But the rate at which the mass is accumulating inside the control volume is:

(  r 2 sin   r   )
t
Then the equation of mass conservation becomes:

 2    
r sin   r      (  r 2u r ) sin   r (  u  sin  )  r (  u  )   r   
t  r   

Taking the limits as the quantities  r,  and  become vanishingly small, we get:


 1  1  1 
 2 (  r 2u r )  (  u  sin  )  (  u )  0
t r r r sin   r sin  




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