The level of liquid in a cylindrical vessel is kept constant at 50 cm. It has three identical horizontal tubes, each of length 60cm, coming out at heights 5 cm, 10 cm and 15 cm. Find the length (in cm) of a single tube of the same radius as that of the three tubes, which can replace the three tubes when placed horizontally at the bottom of the cylinder.

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answer is 25.

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Detailed Solution

Let the required length be l. Volume of liquid flowing out of the single tube per second should be equal to the total volume of liquid flowing out of the three tubes.

Using Poiseuille’s formula

$V = \frac{π (hρg) r^{4}}{8 ηl}$

$We have \frac{π (50) {ρgr}^{4}}{8 ηl} = \frac{{πρgr}^{4}}{8 η (60)} (45 + 40 + 35)$

Solving, we get $l = 25 cm$

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