Water flows at 15 km/h through a pipe of diameter 14 cm into a cuboidal pond \(50\,\text{m}\times44\,\text{m}\). In what time will the water level rise by 21 cm?
2 hours
Step 1: Volume of water required to raise the pond level
The pond is a cuboid of length \(50\,m\), breadth \(44\,m\), and the required rise in water level is \(21\,cm = 0.21\,m\).
So, volume required = \(50 \times 44 \times 0.21 = 462\,m^3\).
Step 2: Volume of water flowing from the pipe in 1 hour
Diameter of pipe = \(14\,cm = 0.14\,m\). Radius = \(0.07\,m\).
Cross-sectional area of pipe = \(\pi r^2 = 3.1416 \times (0.07)^2 \approx 0.0154\,m^2\).
Speed of water = \(15\,km/h = 15000\,m/h\).
Discharge per hour = area × speed = \(0.0154 \times 15000 \approx 231\,m^3/h\).
Step 3: Time taken to fill required volume
We need \(462\,m^3\) and in 1 hour \(231\,m^3\) flows in.
So, time = \(462 / 231 = 2\,h\).
Final Answer: The water level will rise by 21 cm in 2 hours.