Fluid Mechanics and Hydraulic Machinery Miscellaneous
 Circulation is defined as line integral of tangential component of velocity about a _______ (fill in the blanks)

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In a flow field, closed contour exists.
Correct Option: C
In a flow field, closed contour exists.
 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

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1 – d, 2 – d, 3 – b
Correct Option: A
1 – d, 2 – d, 3 – b
 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

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Stream function, ψ = x² – y²
u = ∂ψ = ∂ (x^{2}  y^{2}) = 2y ∂y ∂y or V = ∂ψ = ∂ (x^{2}  y^{2}) = 2x ∂x ∂x
V = uî + vĵ at (1, 1) = 2î + 2ĵ
V = √(2)² + (2)² = 2√2Correct Option: B
Stream function, ψ = x² – y²
u = ∂ψ = ∂ (x^{2}  y^{2}) = 2y ∂y ∂y or V = ∂ψ = ∂ (x^{2}  y^{2}) = 2x ∂x ∂x
V = uî + vĵ at (1, 1) = 2î + 2ĵ
V = √(2)² + (2)² = 2√2
 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

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p_{A} = 50 cm Hg vacuum = p_{H}Correct Option: B
p_{A} = 50 cm Hg vacuum = p_{H}
 Refer to figure, the absolute pressure of gas A in the bulb is

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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}P_{A} + 170 = 760 + 50 + 20 13.6 13.6
P_{A} = 771.2 mm HgCorrect 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}P_{A} + 170 = 760 + 50 + 20 13.6 13.6
P_{A} = 771.2 mm Hg