Question

water is flowing at the rate of 25 km/h through a pipe of diameter 22 cm into a cuboidal pond which is 60 m long and 54 m wide. in what time will the level of water in pond rise by 50 cm?

Answer 1

The water level in the pond will rise by 50 cm in approximately 7.50 seconds.

Step-by-step explanation:

To find the time it takes for the water level in the pond to rise by 50 cm, we can use the equation:

Volume of water = Area of the pipe x Velocity of water

First, we need to calculate the area of the pipe:

Area = π x (radius)^2 = π x (diameter/2)^2

Area = π x (22 cm/2)^2

Area = π x 11 cm^2

Next, we convert the velocity from km/h to cm/s:

Velocity = 25 km/h x 100000 cm/km / 3600 s/h

Velocity ≈ 694 cm/s

Now, we can substitute these values into the equation:

Volume of water = π x 11 cm^2 x 694 cm/s

Volume of water = 255958 cm^3

To find the time, we divide the volume of water by the cross-sectional area of the pond:

Time = Volume of water / (Length x Width)

Time = 255958 cm^3 / (60 m x 100 cm/m x 54 m x 100 cm/m)

Time ≈ 7.50 seconds

Therefore, it will take approximately 7.50 seconds for the water level in the pond to rise by 50 cm.