A farmer connects a pipe of internal diameter 30 cm from a canal into a cylindrical tank in her field, which is 10 m in diameter and 5 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled?
Answers
Answer:
Step-by-step explanation:
internal diameter of the pipe 20 cm = 20/100=15 cm
Internal radius=
2
diameter
=
2
1
×
5
1
=
10
1
m
Rate of flow of water=3 km/h= 3000 m/h
Let the pipe take t hours to fill up the tank
the volume of the water that flows int hours from the pipe V(t)
V(t)= Area of cross-section × speed × time
=πr
2
× speed × time
=π(
100
1
)×3000×t
V(t)=30πt
Diameter of the cylinder =10 m
the radius of the cylinder r=5 m
Depth=2 m
The volume of the tank V =πr
2
h=π(25)2=50π m
2
Now the volume of the water that flows from the pipe in t hours=volume of the tank
∴V(t)=V
∴30πt=50π
t=
30
50
hours
t=
30
50
×60
t=100 mins
∴t=100 minutes.
Volume of the cylinder = πr2h, where r and h are the radius and height of the cylinder respectively.
Therefore, the volume of water flowing through the pipe = volume of water in the cylindrical tank.
Radius of the cylindrical tank, R = 10 / 2 m = 5 m
Depth of the cylindrical tank, H = 2 m
Radius of the cylindrical pipe, r = 20/2 cm = 10/100 m = 0.1 m
Length of the water flowing through the pipe in 1 hour (60 minutes) = 3 km
Length of the water flowing through the pipe in 1 minute, h = 3 km/60 = (3 × 1000 m) /60 = 50 m
Volume of water flowing through pipe in 't' minutes = volume of water in cylindrical tank
t × πr2h = πR2H
t = R2H / r2h
= (5 m × 5 m × 2 m) / (0.1 m × 0.1 m × 50 m)
= 100
Therefore, the cylindrical tank will be filled in 100 minutes.