Fluid Mechanics and Hydraulic Machinery Miscellaneous
 A large tank with a nozzle attached contains three immiscible, inviscid fluids as shown. Assuming that the changes in h_{1}, h_{2} and h_{3} are negligible, the instantaneous discharge velocity is

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Applying Bernoulli’s equation at exit, we get
P_{1} + gz_{1} + V_{1}² = P_{1} + gz_{2} + V_{2}² ρ_{3} 2 ρ_{3} 2
We know Z_{1} = Z_{2}, V_{1} = 0 & P_{2} = P_{atm}
Hence it reduce toP_{1} = V_{2}² ρ_{3} 2
Correct Option: A
Applying Bernoulli’s equation at exit, we get
P_{1} + gz_{1} + V_{1}² = P_{1} + gz_{2} + V_{2}² ρ_{3} 2 ρ_{3} 2
We know Z_{1} = Z_{2}, V_{1} = 0 & P_{2} = P_{atm}
Hence it reduce toP_{1} = V_{2}² ρ_{3} 2
 The difference in pressure (in N/m^{2}) across an air bubble of diameter 0.001 m immersed in water (surface tension = 0.072 N/m) is_____.

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Surface tension in a bubble = Δp.r 4 we know, P_{i} – P_{o} = 4T r Δp = 4 × 0.072 = 288 N/m^{2}. 0.01 Correct Option: B
Surface tension in a bubble = Δp.r 4 we know, P_{i} – P_{o} = 4T r Δp = 4 × 0.072 = 288 N/m^{2}. 0.01
 An inverted Utube manometer is used to measure the pressure difference between two pipes A and B, as shown in the figure. Pipe A is carrying oil (specific gravity = 0.8) and pipe B is carrying water. The densities of air and water are 1.16 kg/ m^{3} and 1000 kg/m^{3}, respectively. The pressure difference between pipes A and B is________kPa.
Acceleration due to gravity: g = 10 m/s^{2}

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P_{A} −(ρ_{oil} × g × 0.2) − (ρ_{air} × g × 0.08) + (ρ_{w} × g × 0.38) − P_{B} = 0
Correct Option: A
P_{A} −(ρ_{oil} × g × 0.2) − (ρ_{air} × g × 0.08) + (ρ_{w} × g × 0.38) − P_{B} = 0
Direction: A smooth flat plate with a sharp leading edge is placed along a gas stream flowing at U = 10 m/s. The thickness of the boundary layer at section r – s is 10 mm, the breadth of the plate is 1 m (into the paper) and the density of the gas, ρ = 1.0 kg/m^{3}. Assume that the boundary layer is thin, twodimensional, and follows a linear velocity distribution, u = U (y/δ), at the section r–s, where y is the height from plate.
 The integrated drag force (in N) on the plate, between p – s, is

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By momentum equation, we can find drag force.
Correct Option: C
By momentum equation, we can find drag force.
 The mass flow rate (in kg/s) across the section q – r is

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Mass entering from side qp = Mass leaving from side qr + Mass leaving the side rs
Correct Option: B
Mass entering from side qp = Mass leaving from side qr + Mass leaving the side rs