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Question

# Two capillary tubes A and B are arranged in parallel. A liquid flows through these capillary tubes under the same pressure head. Both the tubes have the same length. The radii of A and B are r and r2 respectively. If the rate of flow of liquid through A is 8 cm3/s, then the rate of flow through the combination of A and B is:

A
8.0 cm3/s
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B
8.5 cm3/s
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C
12.75 cm3/s
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D
16 cm3/s
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Solution

## The correct option is B 8.5 cm3/sFrom Poiseuille equation, flow rate is given by:Φ=πR4ΔP8ηLGiven, ΔP and L are same for both.Hence, Φ∝R4R2=r/2=R1/2⟹Φ2=Φ1/16=8/16=0.5 cm3/sPipes are in parallel, hence total flow rate is sum of the two flow rates.Φ=Φ1+Φ2=8.5 cm3/s

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