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Question

What will be the total resistance offered to the flow of water by the system of pipe 1, pipe 2, pipe 3 and pipe ignoring the joints? If all the pipes are of length 3 m and radius 2 m and 'η' is viscosity of water. (Assume π=3)


A
1.25η
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B
3η
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C
4.5η
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D
9η
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Solution

The correct option is A 1.25η
Given, radius and length of the pipes are r=0.6 m and l=3 m.
Divide the four pipes into three section as show in figure.


Section 1:
Resistance offered to flow of water by pipe 1.
R1=8ηlπr4
Section 2:
Pipe 2 and pipe 3 are in parallel connection. Resistance offered to flow of water by pipe 2 and pipe 3 is given by (R2) 1R2=1R+1R[where R=8ηlπr4]
1R2=2R
R2=R2=8ηl2×πr4
Section 3:
Resistance offered by the pipe 4 to the flow of water (R4)
R4=8ηlπr4
Total Resistance offered by the pipe 1, pipe 2, pipe 3 and pipe 4 are
R=R1+R2+R4
R=8ηlπr4+8ηl2πr4+8ηlπr4
R=20ηlπr4=20η×33×(2)4=1.25η

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