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Fluid Mechanics and Hydraulic Machinery Miscellaneous

Fluid Mechanics and Hydraulic Machinery

  1. A solid block of 2.0 kg mass slides steadily at a velocity Valong a vertical wall as shown in the figure below. A thin oil film of thickness h = 0.15 mm provides lubrication between the block and the wall. The surface area of the face of the block in contact with the oil film is 0.04 m². The velocity distribution within the oil film gap is linear as shown in the figure. Take dynamic viscosity of oil as 7 × 10-3 Pa-s and acceleration due to gravity as 10 m/s². Neglect weight of the oil. The terminal velocity V (in m/s) of the block is __________(correct to one decimal place).
    1. 10.714 m/s
    2. 11.714 m/s
    3. 30.714 m/s
    4. 12.714 m/s
Correct Option: A


Terminal velocity is a constant velocity i.e. the net acceleration is zero.
So, ΣFnet = ma
mg – τA = 0
τA = mg

μ
V
A = mg
h

7 × 10-3 ×
V
× 0.04 = 2 × 10
0.15 × 10-3

V = 10.714 m/s



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