WATER IS FLOWING AT THE RATE OF 5 KM/hr THROUGH A PIPE OF DIAMETER 14 cm INTO A RECTANGULAR TANK WHICH IS 50 m LONG AND 40 m WIDE. DETERMINE THE TIME IN WHICH THE LEVEL OF WATER IN THE TANK WILL RISE BY 7 cm.
Answers
Given that the water is flowing at the rate of 5 km/hr through a pipe of diameter 14 cm into a rectangular tank which is 50 m long and 44m wide.
Let the level of the water in the tank rise by 7 cm in x hours.
Again the water is flowing at the rate of 5 km/hr
So, the length of the water in x hours = 5x km = 5x * 1000 = 5000x m
Here, the water forms a cylinder having radius r = 14/2 = 7 cm = 7/100 m
and length h = 5000x m
Now, the volume of the water flowing through the cylindrical pipe in x hours = πr2 h = (22/7)*(7/100)2 *5000x
= (22*7*7*5000x)/(7*100*100)
= (22*7*5x)/10
= (22*7*x)
= 11*7*x
= 77x
Now, volume of the water that falls into the tank in x hours
= (50*44*7)/100
= (44*7)/2 = 22*7 = 154
Now, volume of the water flowing through the cylinder pipe in x hours = volume of the water that falls in the tank in x hours
=> 77x = 154
=> x = 154/77
=> x = 2
So, the level of water in the tank will rise by 7 cm in 2 hours.