Water is flowing at the rate of 15km/hr through a cylindrical pipe of radius 7cm into a rectangular tank which is 50m long and 44m wide. In how many hours will the water level in the tank raise by 21cm

the area of the tank is 220m^2

So, you want to have a volume of 220*.21 = 46.2 m^3

15 km/hr = 4.167 m/s
The area of the pipe is pi*.07^2 = 0.01539m^2

So, the water is flowing in at 4.167*0.01539 = 0.06414 m^3/s

46.2 m^3 / (.06414 m^3/s) = 720 s = 12 min = 0.2 hr

To find the time it takes for the water level in the tank to rise by 21cm, we need to consider the flow rate of the water and the volume of water that enters the tank.

The flow rate of water can be calculated using the formula:
Flow rate = cross-sectional area × velocity

The cross-sectional area of the cylindrical pipe can be calculated using the formula:
Area = π × radius^2

Given that the radius of the pipe is 7cm, we can calculate the cross-sectional area:

Area = π × (7cm)^2 = 154π cm^2

Since the velocity is given as 15 km/hr, it needs to be converted to cm/s:

Velocity = (15 km/hr) × (1000 m/km) × (100 cm/m) × (1 hr/3600 s) = 416.67 cm/s

Now, we can calculate the flow rate:

Flow rate = 154π cm^2 × 416.67 cm/s = 64381.17π cm^3/s

To determine the volume of water that enters the tank, we multiply the flow rate by the time:

Volume = flow rate × time

Given that the water level in the tank rises by 21 cm, we can calculate the volume using the formula:

Volume = length × width × height

Volume = 50m × 44m × 21cm = 46,200cm^3

Now, we can set up the equation:

64381.17π cm^3/s × time = 46,200 cm^3

To solve for time, we divide both sides of the equation by 64381.17π cm^3/s:

time = 46,200 cm^3 / (64381.17π cm^3/s)

Now, we can calculate the time it takes for the water level in the tank to rise by 21cm.