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Q.

A vessel has water to a height of 40 cm. It has three horizontal tubes of same diameter each of length 15 cm coming out at heights 10 cm, 15 cm, 20 cm. The length of a single tube of same diameter as that of the three tubes which can replace them when placed horizontally at the bottom of the vessel is :

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a

45 cm

b

5 cm

c

8 cm

d

16 cm

answer is C.

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Detailed Solution

h is total height of water. h₁, h₂ h₃ are the heights at which tubes are fitted
$\begin{array}{l} Q_{1} = \frac{π (h - h_{1}) {dgr}^{4}}{8 ηl}; Q_{2} = \frac{π (h - h_{2}) {dgr}^{4}}{8 ηl} \\ Q_{3} = \frac{π (h - h_{3}) {dgr}^{4}}{8 η 1} and Q = Q_{1} + Q_{2} + Q_{3} \end{array}$
$with Q = \frac{π {hdgr}^{4}}{8 η 1}; \frac{h}{l} = \frac{h_{1}}{l_{1}} + \frac{h_{2}}{l_{2}} + \frac{h_{3}}{l_{3}}$

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