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Question

Pipe 1 has the radius and length of 0.2 m and 50 m respectively connected with the pipe 2 having radius and length of 0.4 m and 100 m respectively. Find the total resistance offered to the flow of water by the system of pipes, Ignoring the resistance offered by the joint.
(η is the viscosity of water)


A
8.95×104η
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B
5.5×105η
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C
4.56×105η
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D
2.86×106η
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Solution

The correct option is A 8.95×104η
Given, radius of pipe 1, r1=0.2 m
Length of pipe 1, l1=50 m
Given, radius of pipe 2, r2=0.4 m
Length of pipe 2, l2=100 m
Both pipe 1 and pipe 2 are in series.
So, total resistnace offered to the flow is given by R=R1+R2
R=8ηl1πr41+8ηl2πr42 [where, η = viscosity of water]
R=8η×50π×(0.2)4+8×η×100π×(0.4)4=8.95×104η
R=8.95×104η

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