6. In a flow field the stream lines and equipotential lines

1. 1. are parallel

   
   
   

   2. Cut at any angle

   
   
   

   3. Are orthogonal every where in the field

   
   
   

   4. Cut orthogonal except at the stagnation points

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: D

   NA

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7. Bodies in flotation to be in stable equilibrium the necessary and sufficient condition is that the centre of gravity is located below the ____.

1. 1. Located between the metacentre.

   
   
   

   2. Located under the metacentre.

   
   
   

   3. Located below the metacentre.

   
   
   

   4. metacentre.

   
   
   

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1. View Hint View Answer Discuss in Forum

   Located below the metacentre.

   Correct Option: C

   Located below the metacentre.

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8. A hinged gate of length 5 m, inclined at 30° with the horizontal and with water mass on its left, is shown in figure below. Density of water is 1000 kg/m³. The minimum mass of the gate in kg per unit width (perpendicular to the plane of paper), required to keep it closed 5 m
   

1. 1. 5000

   
   
   

   2. 6600

   
   
   

   3. 7546

   
   
   

   4. 9623

   
   
   

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1. View Hint View Answer Discuss in Forum

   Given data
   l = 5 m
   θ = 30°
   ρ = 1000 kg/m³
   h = 2.5sin30° = 1.25m
   
   A = bl = 1 × 5 = 5 m²
   

   IG =	bl³	=	1 × (5)³	= 10.41 m4
   	12		12

   
   F = ρgAh = 1000 × 9.81 × 5 × 1.25 = 61312.5N
   

   h* = h +	IG	. sin² θ
   	Ah

   
   

   = 1.25 +	10.41	. sin² 30° = 1.67 m
   	5 × 1.25

   
   Taking moment about hinge
   

   F =	h*	= W × 2.5 × cos30°
   	sin 30°

   
   

   61312.5 ×	1.66	= Mg × 2.165
   	0.5

   
   M = 9623kg

   Correct Option: D

   Given data
   l = 5 m
   θ = 30°
   ρ = 1000 kg/m³
   h = 2.5sin30° = 1.25m
   
   A = bl = 1 × 5 = 5 m²
   

   IG =	bl³	=	1 × (5)³	= 10.41 m4
   	12		12

   
   F = ρgAh = 1000 × 9.81 × 5 × 1.25 = 61312.5N
   

   h* = h +	IG	. sin² θ
   	Ah

   
   

   = 1.25 +	10.41	. sin² 30° = 1.67 m
   	5 × 1.25

   
   Taking moment about hinge
   

   F =	h*	= W × 2.5 × cos30°
   	sin 30°

   
   

   61312.5 ×	1.66	= Mg × 2.165
   	0.5

   
   M = 9623kg

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9. Consider a frictionless, massless and leak-proof plug blocking a rectangular hole of dimensions 2R × L at the bottom of an open tank as shown in the figure. The head of the plug has the shape of a semi-cylinder of radius R. The tank is filled with a liquid of density ρup to the tip of the plug. The gravitational acceleration is g. Neglect the effect of the atmospheric pressure.
   
   The force F required to hold the plug in its position is

1. 1. 2ρR²gL		1 -	π
      			4

   
   
   

   2. 20R²gL		1 +	π
      			4

   
   
   

   3. ρR²δgL

   
   
   

   4. π/2 ρR²gL

   
   
   

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1. View Hint View Answer Discuss in Forum

   Total volume ⇒ V_total = 2R × L × R = 2 R²L ...(i)
   

   Volume : V1 =	πR2	× L....(ii)
   	2

   
   F = Weight of fluit =
   [V_total – V₁] ρg
   

   =		2R²L -	πR²L		ρg
   			2

   
   

   F = 2GρR²gL		1 -	π
   			4

   
   

   Correct Option: A

   Total volume ⇒ V_total = 2R × L × R = 2 R²L ...(i)
   

   Volume : V1 =	πR2	× L....(ii)
   	2

   
   F = Weight of fluit =
   [V_total – V₁] ρg
   

   =		2R²L -	πR²L		ρg
   			2

   
   

   F = 2GρR²gL		1 -	π
   			4

   
   

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10. A jet of water issues from a nozzle with a velocity 20 m/s and it impinges normally on a flat plate moving away from it at 10 m/s. The crosssectional area of the jet is 0.01 m², and the density of water = 1000 kg/m³. The force developed on the plate is
    

1. 1. 1000 N

   
   
   

   2. 100 N

   
   
   

   3. 10 N

   
   
   

   4. 2000 N

   
   
   

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1. View Hint View Answer Discuss in Forum

   The force developed on the plate,
   F_x = ρa(v_j - u)² = 1000 × 0.01(20 10)²
   F_x = 1000 N

   Correct Option: A

   The force developed on the plate,
   F_x = ρa(v_j - u)² = 1000 × 0.01(20 10)²
   F_x = 1000 N

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