GATE CE 2022 Set 2 — Question 58
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Water Resources Engineering → Forces on Immersed Bodies → Drag Force
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Question
Two discrete spherical particles (P and Q) of equal mass density are independently released in water. Particle P and particle Q have diameters of and , respectively. Assume Stokes’ law is valid.The drag force on particle Q will be________ times the drag force on particle P. (round off to the nearest integer)
Correct answer
8 to 8
Solution
According to Stokes' Law, the drag force on a spherical particle at terminal velocity is equal to its submerged weight:Alternatively, using the drag force formula and the terminal velocity formula :In both cases, for particles of the same density in the same fluid, the drag force is proportional to the cube of the diameter:Given and , the ratio is:Thus, the drag force on particle Q is times that on particle P.
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