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# MCQs on Reynolds Analogy

Temperature and velocity profiles are identical when the dimensionless Prandtl number is

a) 1

b) 2

c) 3

d) 4

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Answer: a

Explanation: They are identical when Prandtl number is unity.

eynolds analogy is given by

a) Nu x/ (Re x) (Pr x) = 5 St X = – 2 C F x

b) Nu x/ 2 (Re x) (Pr x) = 4 St X = – C F x /3

c) Nu x/ (Re x) (Pr x) = St X = – ½ C F x

d) Nu x/ (Re x) (Pr x) = 2 St X = – C F x /4

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Answer: c

Explanation: It is an excellent example of the similar nature of energy and momentum transfer.

The average drag coefficient for turbulent boundary layer flow past a thin plate is given by

C f = 0.455/ (log 10 R el) 2.58

Where R el is the Reynolds number based on plate length. A plate 50 cm wide and 5 m long is kept parallel to the flow of water with free stream velocity 3 m/s. Calculate the drag force on both sides of the plate. For water, kinematic viscosity = 0.01 stokes

a) 53.38 N

b) 63.38 N

c) 73.38 N

d) 83.38 N

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Answer: b

Explanation: Drag force = 2 C f (p U INFINITY/2) (l) (b) = 25.42 N per unit width.

Consider the above problem, estimate the value of Reynolds number

a) 0.12

b) 0.13

c) 0.14

d) 0.15

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Answer: d

Explanation: Re = l U INFINITY/v = 0.15.

During test-run, air flows at 215 m/s velocity and 25 degree Celsius temperature past a smooth thin model airfoil which can be idealized as a flat plate. If the chord length of the airfoil is 15 cm, find drag per unit width. The relevant physical properties of air are

p = 1.82 kg/m3

v = 15.53 * 10 -6 m2/s

a) 25.42 N per unit width

b) 35.42 N per unit width

c) 45.42 N per unit width

d) 55.42 N per unit width

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Answer: a

Explanation: Drag force = 2 C f (p U INFINITY/2) (l) (b) = 25.42 N per unit width.

A flat plate was positioned at zero incidence in a uniform flow stream of air. Assuming boundary layer to be turbulent over the entire plate, workout the ratio of skin-friction forces on the front and rear half part of the plate

a) 1.557

b) 1.447

c) 1.347

d) 1.247

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Answer: c

Explanation: F 1/F 2 = 0.574/1 – 0.574 = 1.347.

For a particular engine, the underside of the crankcase can be idealized as a flat plate measuring 80 cm by 20 cm. The engine runs at 80 km/hr and the crankcase is cooled by the air flowing past it at the same speed. Find loss of the heat from the crank case surface (t S = 25 degree Celsius). Assume the boundary layer to be turbulent

a) 465.04 W

b) 565.04 W

c) 665.04 W

d) 765.04 W

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Answer: b

Explanation: Heat loss by crankcase = h A d t = 565.4 W.

With respect to above problem, find the value of Nusselt number

a) 2000.89

b) 3000.89

c) 4000.89

d) 5000.89

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Answer: a

Explanation: Nusselt number = 0.036 (Re) 0.8 (Pr) 0.33 = 2000.89.

A flat plate 1 m by 1 m is placed in a wind tunnel. The velocity and temperature of free stream air are 80 m/s and 10 degree Celsius. The flow over the whole length of the plate is made turbulent by turbulizing grid placed upstream of the plate. Find the thickness of the hydrodynamic boundary layer at trailing edge of the plate

a) 19.55 mm

b) 18.55 mm

c) 17.55 mm

d) 16.55 mm

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Answer: d

Explanation: Thickness = (l) (0.371)/ (Re) 0.2 = 0.01655 m.

A flat plate 1 m by 1 m is placed in a wind tunnel. The velocity and temperature of free stream air are 80 m/s and 10 degree Celsius. The flow over the whole length of the plate is made turbulent by turbulizing grid placed upstream of the plate. Find the heat flow from the surface of the plate

a) 9424.5 W

b) 8424.5 W

c) 7424.5 W

d) 6424.5 W

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Answer: c

Explanation: Heat flow from the plate = h A d t = 7424.5 W.