Water is flowing at the rate of 15 km per hour through a pipe of diameter 14cm into a rectangular tank which is 50 m long and 44 m wide. Find the time in which the level of water in the tank will rise by 21 cm?

Question

Answer

Answer

Answer

Given data:
- Rate of flow of water through the pipe = 15 km/h
- Diameter of the pipe = 14 cm
- Length of the tank = 50 m
- Width of the tank = 44 m
- Rise in water level = 21 cm

Approach:
To find the time it takes for the water level to rise by 21 cm in the tank, we need to calculate the volume of water that enters the tank per unit time. Then, we can use the formula for volume to find the time.

Step 1: Calculate the area of the pipe:
The area of a pipe can be calculated using the formula:
Area = π * (radius)^2

Given that the diameter of the pipe is 14 cm, we can find the radius by dividing the diameter by 2:
Radius = 14 cm / 2 = 7 cm

Now, we can calculate the area of the pipe:
Area = π * (7 cm)^2

Step 2: Calculate the volume of water entering the tank per unit time:
The volume of water entering the tank per unit time can be calculated using the formula:
Volume = Area * velocity

Given that the rate of flow of water through the pipe is 15 km/h, we need to convert it to cm/s:
15 km/h = 15,000 m/h
1 m/h = 100 cm/h
15,000 m/h = 1,500,000 cm/h

Now, we can calculate the volume of water entering the tank per unit time:
Volume = Area * velocity
Volume = (π * (7 cm)^2) * (1,500,000 cm/h)

Step 3: Calculate the time taken for the water level to rise by 21 cm:
The volume of water entering the tank per unit time is equal to the volume of water needed to raise the water level by 21 cm in the tank.

The volume of water needed to raise the water level by 21 cm in the tank can be calculated using the formula:
Volume = length * width * rise

Given that the length of the tank is 50 m, the width of the tank is 44 m, and the rise in water level is 21 cm, we need to convert the dimensions to cm:
Length = 50 m * 100 cm/m = 5000 cm
Width = 44 m * 100 cm/m = 4400 cm
Rise = 21 cm

Now, we can calculate the time taken for the water level to rise by 21 cm:
Volume = length * width * rise
Volume = 5000 cm * 4400 cm * 21 cm

Finally, we can divide the volume of water entering the tank per unit time by the volume of water needed to raise the water level by 21 cm to find the time taken:
Time = (Volume of water needed) / (Volume of water entering per unit time)

Answer:
By following the above steps, you can calculate the time in which the water level in the tank will rise by 21 cm.

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