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:
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:
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Volume flow rate is always \(A \times v\). Keep units consistent before converting to litres.
Updated On: Jul 18, 2026
- 150
- 50
- 100
- 300
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The Correct Option is D
Solution and Explanation
Step 1: Understanding volume flow rate concept.
The volume of water flowing per second is given by: \[ Q = A \cdot v \] where \(A\) is cross-sectional area of pipe and \(v\) is velocity of flow. This gives volumetric discharge in cm$^3$/s.
Step 2: Calculate cross-sectional area of pipe.
Diameter = 20 cm, so radius: \[ r = 10 \, \text{cm} \] Area: \[ A = \pi r^2 = \pi \times 10^2 = 100\pi \, \text{cm}^2 \]
Step 3: Multiply area with velocity.
Given velocity: \[ v = \frac{50}{\pi} \, \text{cm/s} \] So flow rate: \[ Q = 100\pi \times \frac{50}{\pi} = 5000 \, \text{cm}^3/\text{s} \]
Step 4: Convert into volume per minute.
\[ Q_{1\,min} = 5000 \times 60 = 300000 \, \text{cm}^3 \]
Step 5: Convert cm$^3$ to litres.
\[ 1000 \, \text{cm}^3 = 1 \, \text{litre} \] \[ 300000 \, \text{cm}^3 = 300 \, \text{litres} \]
Step 6: Final conclusion.
\[ \boxed{300 \, \text{litres}} \]
The volume of water flowing per second is given by: \[ Q = A \cdot v \] where \(A\) is cross-sectional area of pipe and \(v\) is velocity of flow. This gives volumetric discharge in cm$^3$/s.
Step 2: Calculate cross-sectional area of pipe.
Diameter = 20 cm, so radius: \[ r = 10 \, \text{cm} \] Area: \[ A = \pi r^2 = \pi \times 10^2 = 100\pi \, \text{cm}^2 \]
Step 3: Multiply area with velocity.
Given velocity: \[ v = \frac{50}{\pi} \, \text{cm/s} \] So flow rate: \[ Q = 100\pi \times \frac{50}{\pi} = 5000 \, \text{cm}^3/\text{s} \]
Step 4: Convert into volume per minute.
\[ Q_{1\,min} = 5000 \times 60 = 300000 \, \text{cm}^3 \]
Step 5: Convert cm$^3$ to litres.
\[ 1000 \, \text{cm}^3 = 1 \, \text{litre} \] \[ 300000 \, \text{cm}^3 = 300 \, \text{litres} \]
Step 6: Final conclusion.
\[ \boxed{300 \, \text{litres}} \]
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