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Q45

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type=MCQ · page=22–23 · marks=2 · content_conf=0.7999999999999999 · math_conf=0.79

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file: GATE CH 2020 (with Solutions).pdf

pages: 22–23

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Consider steady, laminar, fully developed flow of an incompressible Newtonian fluid through two horizontal straight pipes, I and II, of circular cross section. The volumetric flow rates in both the pipes are the same. The diameter of pipe II is twice the diameter of pipe I, i.e.,

d_{ii} = 2d_1. /text{The} /text{ratio} /text{of} /text{the} /text{shear} /text{stress} /text{at} /text{the} /text{wall} /text{of} /text{pipe} I /text{to}

the shear stress at the wall of pipe II is

Options

A.
0.5
B.
2
C.
4
D.
8

Answer

Solution

.

.

.

∂p = /frac{32/mu{}uL}{D^2} = /text{For} /text{const} Q

∂p = /frac{32/mu{}QL}{A.DL} = /frac{32/mu{}QL}{(/frac{/\pi{}{}}{4} /times D^4)}

∂p ∝ /frac{1}{D^4}

.

.

()^3

.

.

Hence, the correct option is (D).

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Source PDF: GATE CH 2020 (with Solutions).pdf

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