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 64381.17Ï€ cm^3/s:
time = 46,200 cm^3 / (64381.17Ï€ cm^3/s)
Now, we can calculate the time it takes for the water level in the tank to rise by 21cm.