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Two capillary tubes of same radius r but of lengths l1 and l2 are fitted in parallel to the bottom of a vessel. The pressure head is P. What should be the length l of the single tube that can replace the two tubes, so that the rate of flow is same as before :

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a

l=l1+l2

b

l=l1l2l1+l2

c

l=1l1+1l2

d

l=1l1+l2

answer is B.

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Detailed Solution

In parallel combination P1=P2=Pand rate of flow Q=Q1+Q2πPr48ηl=πP1r48ηl1+πP2r48ηl2⇒1l=1l1+1l2⇒l=l1l2l2+l1

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Two capillary tubes of same radius r but of lengths l1 and l2 are fitted in parallel to the bottom of a vessel. The pressure head is P. What should be the length l of the single tube that can replace the two tubes, so that the rate of flow is same as before :