Four pipes each of 5 cm in diameter are to be replaced by a single pipe discharging the same quantity of water. If the speed of water remains same in both the cases, then the diameter (in cm) of the single pipe is:

5 cm

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6 cm

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10 cm

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12 cm

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Solution

The correct option is A 5 cm
Given, diameter = 5 cm
$\Rightarrow$ radius r =2.5 cm

According to the question,
the sum of the cross sectional area of the four pipes should be equal to the cross sectional area of the new pipe.
Let R be the new radius.
Hence,
$4 \times π \times (2.5)^{2} = π \times (R)^{2}$
$\Rightarrow R = 5 c m$

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Four pipes each of 5 cm in diameter are to be replaced by a single pipe discharging the same quantity of water. If the speed of water remains same in both the cases, then the diameter (in cm) of the single pipe is:

The correct option is A 5 cmGiven, diameter = 5 cm ⇒ radius r =2.5 cm According to the question, the sum of the cross sectional area of the four pipes should be equal to the cross sectional area of the new pipe. Let R be the new radius. Hence, 4×π×(2.5)2=π×(R)2 ⇒R=5cm