Question

Water is flowing at the rate of 4 km/h through a pipe of radius 7 cm into a rectangular tank with length and breadth as 25 m and 22 m, respectively. The time (in hours) in which the level of water in the tank will rise by 28 cm is \[ \text{(take } \pi = \frac{22}{7}) \]

• A. \( \frac{1}{3} \)
• B. \( \frac{1}{2} \)
• C. \( \frac{2}{3} \)
• D. \(\frac{4}{5}\)

Answer 1

The Correct Option is B

Water Flow Problem Solution

Given Data:

• Flow rate of water = 4 km/h
• Radius of pipe = 7 cm
• Length of tank = 25 m
• Breadth of tank = 22 m
• Desired rise in water level = 28 cm
• π = 22/7

Step 1: Convert all units to meters.

• Radius of the pipe = 0.07 m
• Flow rate of water = 4000 m/h
• Desired rise = 0.28 m

Step 2: Calculate the volume of water flowing per hour through the pipe:

Volume per hour = π × r² × velocity

Volume per hour = (22/7) × (0.07)² × 4000 = 61.2 m³/h

Step 3: Calculate the volume of water needed to raise the water level in the tank by 0.28 m:

Volume needed = Length × Breadth × Rise in height = 25 × 22 × 0.28 = 154 m³

Step 4: Calculate the time required:

Time = Volume needed ÷ Volume per hour

Time = 154 ÷ 61.2 ≈ 2.5 hours

Final Answer: The time required for the water level to rise by 28 cm is approximately 2.5 hours.