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A cylindrical pipe has an inner diameter of 7 cm and water flows through it at 192.5 liters per minute. Find the rate of flow in kilometers per hour.

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4 km / hr

2 km / hr

5 km / hr

3 km / hr

answer is D.

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Detailed Solution

Given,
A cylindrical pipe of diameter d= 7 cm.
Radius of the pipe is,

r = \frac{7}{2} cm

r = 3.5 cm

Here, 192.5 liters of water flow every minute.
So,
Water flow rate in one hour

= (192.50 \times 60) litres

= (192.50 \times 60 \times 1000) {cm}^{3}

(since 1 liter = 1000 cm3)
This is equal to the volume of cylinder,

V = (192.50 \times 60 \times 1000) {cm}^{3}

Suppose water column's hourly height = h cm.
We know that,
Volume of cylinder

= π r^{2} h

V = (\frac{22}{7} \times (3.5)^{2} \times h) {cm}^{3}

…….. (ii)

192.50 \times 60 \times 1000 = \frac{22}{7} \times (3.5)^{2} \times h

h = \frac{192.50 \times 60 \times 1000 \times 7}{22 \times 3.5 \times 3.5} cm

h = 3 km / hr

Hence, the rate of flow in 3 kilometers per hour.
So, the correct option is 4.

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