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ISRO 2011 Mechanical Engineering Questions, Answers and Explanation

ISRO 2011 Mechanical Engineering Questions, Answers and Explanation

9 Flow takes place at Reynolds number of 1500 in two different pipes with relative roughness of 0.001 and 0.002. The friction factor
a) Will be higher for the pipe with relative roughness of 0.001
b) Will be higher for the pipe having relative roughness of 0.002
c) Will be same in both the pipes
d) In the two pipes cannot be compared on the basis of data given.

Answer
c) Will be same in both the pipes

Explanation [Fluid Mechanics]
The friction factor f for a laminar flow (Re < 2320) in a circular pipe is given by the formula f = 64/Re. It is independent of relative roughness for the given Reynolds number

10. A liquid compressed in cylinder has a volume of 0.04 m3 at 50kg/cm2 and a volume of 0.039 m3 at 150 kg/cm2. The bulk modulus of elasticity of liquid is
a) 400 kg/cm2
b) 40 x 106 kg/cm2
c) 40 x 105 kg/cm2
d) 4000 kg/cm2

Answer
d) 4000 kg/cm2

Explanation [Fluid Mechanics]
The bulk elastic properties of a material determine how much it will compress under a given amount of external pressure. The ratio of the change in pressure to the fractional volume compression is called the bulk modulus of the material. The reciprocal of the bulk modulus is called the compressibility of the substance.
Bulk Modulus, B = ΔP/(ΔV/V)
Here ΔP = 150-50 =100 kg/cm2
ΔV = 0.04-0.039 = 0.001m3
V = 0.04m3
B = (100/(0.001/0.04)) = 100x0.04/0.001 =  4000 kg/cm2

11. A fluid jet is discharging from a 100mm nozzle and the vena contracta formed has a diameter of 90 mm. If the coefficient of velocity is 0.95, then the coefficient of discharge for the nozzle is
a) 0.7695
b) 0.81
c) 0.9025
d) 0.855

Answer
a) 0.7695

Explanation [Fluid Mechanics]
The ratio of actual velocity of the jet, at vena-contracta, to the theoretical velocity is known as coefficient of velocity.The difference between the velocities is due to friction of the orifice. The value of Coefficient of velocity varies slightly with the different shapes of the edges of the orifice. This value is very small for sharp-edged orifices. For a sharp edged orifice, the value of C\sub>v
increases with the head of water. The ratio of a actual discharge through an orifice to the theoretical discharge is known as coefficient of discharge. Coefficient of discharge = Actual discharge/Theoretical discharge
Actual discharge = Actual area x Actual velocity
Theoretical discharge = Theoretical area x Theoretical velocity
Given Coefficient of velocity = Actual velocity/Theoretical velocity = 0.95
Theoretical area = π(dtheoretical)2
Actual area = π(dactual)2/r
Coefficient of discharge = Actual discharge/Theoretical discharge
= (Actual Area x Actual velocity)/(Theoretical Area x Theoretical velocity)
= (Actual Area/Theoretical Ara) x (Actual velocity x Theoretical velocity)
= (90/100)2 x 0.95
= 0.9 x 0.9 x 0.95 = 0.7695

13 If the surface tension of water-air interface is 0.073N/m, the gauge pressure inside a rain drop of 1mm diameter will be
a) 0.146 N/m2
b) 73 N/m2
c) 146 N/m2
d) 292 N/m2

Answer
d)  292 N/m2

Explanation [Fluid Mechanics]
Gauge pressure inside a bubble = 4T/r
Gauge pressure inside a drop = 2T/r
=2 x 0.073/0.0005 = 292 N/m2

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