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Question

# In a laminar flow experiment, Fluid A is pumped through a straight tube and the volumetric flow rate and pressure drop per unit length are recorded. In a second straight tube having twice the internal diameter of the first one, Fluid B records the same pressure drop per unit length at the same volumetric flow rate. Assuming fully developed flow conditions in the tubes, the ratio of the dynamic viscosity of Fluid B to that of Fluid A is

A
16
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B
32
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C
64
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D
128
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Solution

## The correct option is A 16QA=πr4A(P1−P2)8μL Since, (P1−P2) is constant, and all other variables are also made constant in the second experiment. So, π(P1−P2)8μL=k(say) ∴QA=kr4A and also QB=kr4B put, rB=2rA ∴QB=k(2rA)4=16kr4A Dividing (ii) by (i) we get, QBQA=16kr4Akr4A=16

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