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Water is flowing at a rate of 15 km/hr through a cylindrical pipe with a diameter of 14 cm into a cuboidal pond that is 50 m long and 44 m wide.

In what time does the water level in the pond rise by 21 cm?

a) 2 hours
b) 3 hours
c) 4 hours
d) 5 hours

Answer :

Final answer:

To calculate the time it will take to fill a pond, we first calculate the volume that the water will occupy, then the pipe's cross-sectional area to determine the flow rate, and then use the flow rate to find the time required. The time taken is approximately 2 hours.

Explanation:

The question at hand involves the concept of fluid dynamics under the category of Mathematics. To solve it, we need to calculate the volume of water required to raise the level in the pond by 21 cm, and then find out how long it would take for the cylindrical pipe to deliver this volume at the given flow rate.

First, we calculate the volume of the pond that will be filled:

Volume = pond length × pond width × water level rise
Volume = 50 m × 44 m × 0.21 m
Volume = 462 m³

Next, we calculate the cross-sectional area of the pipe:

Area = π × (diameter/2)^2
Area = π × (0.14 m / 2)^2
Area = 0.0154 m³

Now, we find the flow rate in m³/s:

Flow rate = velocity × area
Flow rate = 15 km/h × (1000 m/km) / (3600 s/h) × 0.0154 m³
Flow rate = 0.06426 m³/s

Finally, we determine the time it takes to fill the required volume:

Time = Volume / Flow rate
Time = 462 m³ / 0.06426 m³/s
Time = 7189.88 s
Time = 1.997 hours

Therefore, the closest answer to how long it takes to raise the water level by 21 cm is 2 hours (Option a).

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