146. Match the following pairs:
     

     Equation	Physical Interpretation
     P. ∇ × v̄ = 0	I. Incompressible continuity equation
     Q. ∇ . v̄ = 0	II. Steady flow
     R. ∆v̄/∆t = 0	III. Irrotational flow
     S. δv̄/δt = 0	IV. Zero acceleration of fluid particle

1. 1. P-IV, Q-I, R-II, S-III

   
   
   

   2. P-IV, Q-III, FRS-II

   
   
   

   3. P-III, Q-I, R-IV, S-II

   
   
   

   4. P-III, Q-I, R-II, S-IV

   
   
   

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1. View Hint View Answer Discuss in Forum

   P-III, Q-I, R-IV, S-II

   Correct Option: C

   P-III, Q-I, R-IV, S-II

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147. For an in-compressible flow field, V, which one of the following conditions must be satisfied?

1. 1. ∇ . V̄ = 0

   
   
   

   2. ∇ × V̄ = 0

   
   
   

   3. (V̄.∇) V̄ = 0

   
   
   

   4. 	δV̄	(V̄.∇) V̄ = 0
      	δt

   
   
   

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1. View Hint View Answer Discuss in Forum

   In compressible flow condition
   ∇.v̄ = 0

   Correct Option: A

   In compressible flow condition
   ∇.v̄ = 0

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148. For the continuity equation given by∆ . V̄ = 0 to be valid, where V̄ is the velocity vector, which one of the following is a necessary condition?

1. 1. Steady flow

   
   
   

   2. Irrotational flow

   
   
   

   3. Inviscid flow

   
   
   

   4. Incompressible flow

   
   
   

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1. View Hint View Answer Discuss in Forum

   The basic equation of continuity for fluid flow is given by
   

   	ρu		ρv		ρw		ρ
   	u		y		z		t

   
   Now if ρ remains constant, then only we can write
   ∇.v̄ = 0
   

   i.e.	δu	+	δv	+	δw	= 0
   	δx		δy		δz

   
   hence incompressible flow

   Correct Option: D

   The basic equation of continuity for fluid flow is given by
   

   	ρu		ρv		ρw		ρ
   	u		y		z		t

   
   Now if ρ remains constant, then only we can write
   ∇.v̄ = 0
   

   i.e.	δu	+	δv	+	δw	= 0
   	δx		δy		δz

   
   hence incompressible flow

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149. Which combination of the following statements about steady incompressible forced vortex flow is correct?
     P: Shear stress is zero at all points in the flow.
     Q: Vorticity is zero at all points in the flow.
     R: Velocity is directly proportional to the radius from the centre of the vortex.
     S: Total mechanical energy per unit mass is constant in the entire flow field.
     Select the correct answer using the codes given below:

1. 1. P and Q

   
   
   

   2. R and S

   
   
   

   3. P and R

   
   
   

   4. P and S

   
   
   

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1. View Hint View Answer Discuss in Forum

   Clearly zero shear stress and vortex.

   Correct Option: B

   Clearly zero shear stress and vortex.

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150. The 2-D flow with, velocity
     V̄ = (x + 2y + 2) î + (4 – y) ĵ is

1. 1. Compressible and irrotational

   
   
   

   2. Compressible and not irrotational

   
   
   

   3. In compressible and irrotational

   
   
   

   4. In compressible and not irrotational

   
   
   

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1. View Hint View Answer Discuss in Forum

   v̄ = (x + 2y +2)î + (4 - y)ĵ
   u =x + 2y + 2, v = 4 – y
   

   ∴	δv	= 1,	δv	= - 1
   	δx		δy

   
   

   ∴	δv	+ 1,	δv	= 0
   	δx		δy

   
   hence in compressible.
   

   Again, ω =	1			δv	-	δv
   	2			δx		δy

   
   

   =	1	(0 - 2) = - 1.
   	2

   
   hence not irrotational.

   Correct Option: D

   v̄ = (x + 2y +2)î + (4 - y)ĵ
   u =x + 2y + 2, v = 4 – y
   

   ∴	δv	= 1,	δv	= - 1
   	δx		δy

   
   

   ∴	δv	+ 1,	δv	= 0
   	δx		δy

   
   hence in compressible.
   

   Again, ω =	1			δv	-	δv
   	2			δx		δy

   
   

   =	1	(0 - 2) = - 1.
   	2

   
   hence not irrotational.

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