56. At two points 1 and 2 in a pipeline, the velocities are V and 2V, respectively. Both the points are at the same elevation. The fluid density is ρ. The flow can be assumed to be in compressible, inviscid, steady and irrotational. The difference in pressures P₁ and P₂ at points 1 and 2 is
    

1. 1. 0.5 ρV²

   
   
   

   2. 1.5 ρV²

   
   
   

   3. 2 ρV²

   
   
   

   4. 3 ρV²

   
   
   

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1. View Hint View Answer Discuss in Forum

   Bernoullis equation,
   

   	P1	+	V2	=	P2	+	(2V)2	=	P2	+	4V2
   	ρg		2g		ρg		2g		ρg		ρg

   
   

   	P1 - P2	=	3V2
   	ρg		2g

   
   ∴ P₁ - P₂ = P × 1.5 V² = 1.5 ρV².

   Correct Option: B

   Bernoullis equation,
   

   	P1	+	V2	=	P2	+	(2V)2	=	P2	+	4V2
   	ρg		2g		ρg		2g		ρg		ρg

   
   

   	P1 - P2	=	3V2
   	ρg		2g

   
   ∴ P₁ - P₂ = P × 1.5 V² = 1.5 ρV².

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57. A horizontal water jet with a velocity of 10 m/s and cross sectional area of 10 mm² strikes a flat plate held normal to the flow direction. The density of water is 1000 kg/m³. The total force on the plate due to the jet is
    

1. 1. 100 N
      

   
   
   

   2. 10 N
      

   
   
   

   3. 1 N
      

   
   
   

   4. 0.1 N

   
   
   

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1. View Hint View Answer Discuss in Forum

   F = ρaV. (V – O) = ρaV²
   = 1000 × 10 × (10^–3)² × 10² = 1N.

   Correct Option: C

   F = ρaV. (V – O) = ρaV²
   = 1000 × 10 × (10^–3)² × 10² = 1N.

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58. At 1 : 50 scale model of a spillway is to be tested in the laboratory. The discharge in the prototype is 1000 M³ /s. The discharge to be maintained in the model test is
    

1. 1. 0.057 m³ /s
      

   
   
   

   2. 0.08 m² /s
      

   
   
   

   3. 0.57 m³ /s
      

   
   
   

   4. 5.7 m³ /s

   
   
   

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1. View Hint View Answer Discuss in Forum

   Froude’s law,
   

   	Vm	=	Vp
   	√g ym		√g yp

   
   ∴ V ∝ √y_m
   i.e. V_r ∝ √L_r
   Q_r = A_rV₂ = L_r² × √L_r
   = (L_r)^{5 / 2}
   

   Qm	= (Lr)5 / 2 =		1		5 / 2
   Qp			50

   
   

   ∴ Qm =		1		2 / 3	× 1000 = 0.057 m3 / s
   		50

   
   

   Correct Option: A

   Froude’s law,
   

   	Vm	=	Vp
   	√g ym		√g yp

   
   ∴ V ∝ √y_m
   i.e. V_r ∝ √L_r
   Q_r = A_rV₂ = L_r² × √L_r
   = (L_r)^{5 / 2}
   

   Qm	= (Lr)5 / 2 =		1		5 / 2
   Qp			50

   
   

   ∴ Qm =		1		2 / 3	× 1000 = 0.057 m3 / s
   		50

   
   

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59. Flow rate of a fluid (density = 1000 kg/m³) in a small diameter tube is 800 mm³ /s. The length and the diameter of the tube are 2 m and 0.5 mm, respectively. The pressure drop in 2 m length is equal to 2.0 MPa. The viscosity of the fluid is
    

1. 1. 0.025 N.s/m²

   
   
   

   2. 0.012 N.s/m²

   
   
   

   3. 0.00192 N.s/m²

   
   
   

   4. 0.00102 N.s/m²

   
   
   

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1. View Hint View Answer Discuss in Forum

   hf =	flv2	, f =	64	=	64
   	2gD		Re		ρv (d /μ)

   
   

   ∴ hf =	64μ	×	lv2
   	ρVd		2gD

   
   

   =	32 LVμ
   	PgD2

   
   

   V =	Q	=	Q	=	800
   	A		(π /4)d2		(π /4)(0.5)2

   
   = 4.07 m /s
   

   ∴ hf =	32 × 2 × 4.072 × μ
   	1000 × 9.81 × (0.5 × 103)2

   
   ∴ μ = 0.00192 N³ / m²

   Correct Option: C

   hf =	flv2	, f =	64	=	64
   	2gD		Re		ρv (d /μ)

   
   

   ∴ hf =	64μ	×	lv2
   	ρVd		2gD

   
   

   =	32 LVμ
   	PgD2

   
   

   V =	Q	=	Q	=	800
   	A		(π /4)d2		(π /4)(0.5)2

   
   = 4.07 m /s
   

   ∴ hf =	32 × 2 × 4.072 × μ
   	1000 × 9.81 × (0.5 × 103)2

   
   ∴ μ = 0.00192 N³ / m²

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60. A stable channel is to be designed for a discharge of Q m³ /s with silt factor f as per Lacey’s method. The mean flow velocity (m/s) in the channel is obtained by

1. 1. 		Qf2		1 / 6
      		140

   
   
   

   2. 		Qf		1 / 3
      		140

   
   
   

   3. 		Q2 f2		1 / 6
      		140

   
   
   

   4. 0.48		Q		1 / 3
      		f

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: A

   NA

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