Question

Water is flowing through a horizontal pipe of diameter 20 cm. If the velocity of flow of water is $\frac{50}{\pi}$ cm s$^{-1}$, then the volume of water collected in litres in 1 minute is:

• A. 150
• B. 50
• C. 100
• D. 300

Hint:

Volume flow rate is always \(A \times v\). Keep units consistent before converting to litres.

Answer 1

The Correct Option is D

Step 1: Picture the water as a moving cylindrical column, instead of multiplying area by velocity as a flow-rate formula.
In one minute, every bit of water in the pipe moves forward by a distance equal to velocity times time. That moving stretch of water is itself a cylinder, with the same cross-section as the pipe and a length equal to how far the water travelled.
Step 2: Find the length of that cylinder.
\[ \text{length} = v \times t = \frac{50}{\pi} \times 60 = \frac{3000}{\pi} \ \text{cm} \]
Step 3: Find the cross-sectional area of the pipe.
Diameter is 20 cm, so radius $r = 10$ cm: \[ A = \pi r^2 = \pi(10)^2 = 100\pi \ \text{cm}^2 \]
Step 4: Multiply area by the cylinder's length to get the volume.
\[ V = A \times \text{length} = 100\pi \times \frac{3000}{\pi} = 100 \times 3000 = 300000 \ \text{cm}^3 \]
Step 5: Convert to litres.
\[ 300000 \ \text{cm}^3 \times \frac{1 \ \text{L}}{1000 \ \text{cm}^3} = 300 \ \text{L} \]
Final Answer:
\[ \boxed{300 \ \text{litres}} \]