166. Circulation is defined as line integral of tangential component of velocity about a _______ (fill in the blanks)

1. 1. In a flow field

   
   
   

   2. closed contour exists.

   
   
   

   3. A and B

   
   
   

   4. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   In a flow field, closed contour exists.

   Correct Option: C

   In a flow field, closed contour exists.

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167. Shown below are three pipe sections through which water flows as shown. Option a to d below pertain to the direction of the net force on the pipe section due to the flow of water.
     45° to both +ve x and +ve y axes
     45° to both -ve x and +ve y axes
     45° to both +ve x and -ve y axes
     45° to both -ve x and -ve y axes
     State which of the options indicate the correct direction of force for pipe 1, pipe 2 and pipe 3
     
     

1. 1. 1 – d, 2 – d, 3 – b

   
   
   

   2. 1 – d, 2 – a, 3 – c

   
   
   

   3. 1 – d, 2 – c, 3 – b

   
   
   

   4. 1 – c, 2 – a, 3 – b

   
   
   

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1. View Hint View Answer Discuss in Forum

   1 – d, 2 – d, 3 – b

   Correct Option: A

   1 – d, 2 – d, 3 – b

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168. The stream function in a two dimensional flow field is given by ψ = x² – y² The magnitude of the velocity at point (1, 1) is
     

1. 1. 2
      

   
   
   

   2. 2√2
      

   
   
   

   3. 4
      

   
   
   

   4. 8

   
   
   

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1. View Hint View Answer Discuss in Forum

   Stream function, ψ = x² – y²
   

   u =	-∂ψ	=	-∂	(x2 - y2) = 2y
   	∂y		∂y

   
   

   or V =	-∂ψ	=	∂	(x2 - y2) = 2x
   	∂x		∂x

   
   V = uî + vĵ at (1, 1) = 2î + 2ĵ
   V = √(2)² + (2)² = 2√2

   Correct Option: B

   Stream function, ψ = x² – y²
   

   u =	-∂ψ	=	-∂	(x2 - y2) = 2y
   	∂y		∂y

   
   

   or V =	-∂ψ	=	∂	(x2 - y2) = 2x
   	∂x		∂x

   
   V = uî + vĵ at (1, 1) = 2î + 2ĵ
   V = √(2)² + (2)² = 2√2

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169. In given figure, if the pressure of gas in bulb A is 50 cm Hg vacuum and p_atm = 76 cm Hg, then height of column H is equal to
     
     

1. 1. 26 cm
      

   
   
   

   2. 50 cm
      

   
   
   

   3. 76 cm
      

   
   
   

   4. 126 cm

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   p_A = 50 cm Hg vacuum = p_H

   Correct Option: B

   
   p_A = 50 cm Hg vacuum = p_H

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170. Refer to figure, the absolute pressure of gas A in the bulb is
     
     

1. 1. 771.2 mm Hg
      

   
   
   

   2. 752.65 mm Hg
      

   
   
   

   3. 767.35 mm Hg
      

   
   
   

   4. 748.8 mm Hg

   
   
   

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1. View Hint View Answer Discuss in Forum

   P_atm = 760 mm Hg
   
   Let P_A be the absolute pressure at 'A'
   Pressure at D = Pressure at E
   or P_A + P_CD = P_atm + P_AF + P_FE
   

   PA +	170	= 760 +	50	+ 20
   	13.6		13.6

   
   P_A = 771.2 mm Hg

   Correct Option: A

   P_atm = 760 mm Hg
   
   Let P_A be the absolute pressure at 'A'
   Pressure at D = Pressure at E
   or P_A + P_CD = P_atm + P_AF + P_FE
   

   PA +	170	= 760 +	50	+ 20
   	13.6		13.6

   
   P_A = 771.2 mm Hg

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