## Fluid Mechanics and Hydraulic Machinery Miscellaneous

#### Fluid Mechanics and Hydraulic Machinery

1. A large tank with a nozzle attached contains three immiscible, inviscid fluids as shown. Assuming that the changes in h1, h2 and h3 are negligible, the instantaneous discharge velocity is

1. Applying Bernoulli’s equation at exit, we get

 P1 + gz1 + V1² = P1 + gz2 + V2² ρ3 2 ρ3 2

We know Z1 = Z2, V1 = 0 & P2 = Patm
Hence it reduce to
 P1 = V2² ρ3 2

##### Correct Option: A

Applying Bernoulli’s equation at exit, we get

 P1 + gz1 + V1² = P1 + gz2 + V2² ρ3 2 ρ3 2

We know Z1 = Z2, V1 = 0 & P2 = Patm
Hence it reduce to
 P1 = V2² ρ3 2

1. The difference in pressure (in N/m2) across an air bubble of diameter 0.001 m immersed in water (surface tension = 0.072 N/m) is_____.

1.  Surface tension in a bubble = Δp.r 4

 we know, Pi – Po = 4T r

 Δp = 4 × 0.072 = 288 N/m2. 0.01

##### Correct Option: B

 Surface tension in a bubble = Δp.r 4

 we know, Pi – Po = 4T r

 Δp = 4 × 0.072 = 288 N/m2. 0.01

1. An inverted U-tube 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/ m3 and 1000 kg/m3, respectively. The pressure difference between pipes A and B is________kPa.
Acceleration due to gravity: g = 10 m/s2

1. PA −(ρoil × g × 0.2) − (ρair × g × 0.08) + (ρw × g × 0.38) − PB = 0

##### Correct Option: A

PA −(ρoil × g × 0.2) − (ρair × g × 0.08) + (ρw × g × 0.38) − PB = 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/m3. Assume that the boundary layer is thin, two-dimensional, and follows a linear velocity distribution, u = U (y/δ), at the section r–s, where y is the height from plate.

1. The integrated drag force (in N) on the plate, between p – s, is

1. By momentum equation, we can find drag force.

##### Correct Option: C

By momentum equation, we can find drag force.

1. The mass flow rate (in kg/s) across the section q – r is

1. Mass entering from side q-p = Mass leaving from side q-r + Mass leaving the side r-s

##### Correct Option: B

Mass entering from side q-p = Mass leaving from side q-r + Mass leaving the side r-s