Question

Irrigation canals are used to move water from a source (whether it is a stream, reservoir or holding tank). A farmer connects a pipe of internal diameter 20cm from a canal into a cylindrical tank in his field, which is 10m in diameter and 2m deep. It water flows through the ppe at the rate of 6 km/h, in how much time will the tank be filled.​

Answer 1

Answer:

Good question

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Answer 2

The time taken to fill the tank is 20 min.

Given:

A farmer connects a pipe of internal diameter 20cm from a canal into a cylindrical tank in his field, which is 10m in diameter and 2m deep. It water flows through the pipe at the rate of 6 km/h.

To Find:

The time will the tank be filled?

Solution:

To find the time taken to fill the tank we will follow the following steps:

As we know,

The volume of the cylinder =

$\pi {r}^{2} h$

Here, r is the radius and h is the height.

Diameter of the tank = 10m

Radius =

$\frac{Diameter}{2} = \frac{10}{2} = 5m$

Height of tank = 2m

Diameter of pipe = 20cm = 0.1m

Radius of pipe =

$\frac{0.1}{2} = 0.05m$

Height of pipe =

$6 \frac{km}{h} = \frac{6km}{h} \times \frac{1000m}{1km} \times \frac{1h}{3600s} = 1.67m {s}^{ - 1}$

Let t be the time taken to fill the tank.

Rate of flow of liquid through pipe = volume filled in the tank

So,

$t \times \pi {(0.05)}^{2} \times 1.67 = \pi {(5)}^{2} \times 2$

$t = \frac{25 \times 2}{25 \times 1.67} \times {10}^{4} = 1198 \: sec$

1 min = 60 sec

$1198sec = \frac{1198}{60} =20min$

Henceforth, the time taken to fill the tank is 20 min.

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