water is flowing at the rate of 15km/hr through a pipe of diameter 14 cm into a rectangular tank which is 50m long and 44m wide . find the time in which the level of water in the tank will rise by 21 cm
For the pipe...
Speed = 15 km/hr = 1500000 cm/hr = 1500000/60 cm/min = 2500 cm/ min
radius = 7cm
Volume of water that flows through the pipe per minute...
=> pi * r2 * h = 49 * 2500 * pi = 122500 pi cm2
For the tank.....
volume = 4400 * 5000 * 21 cm2 = 462000000 cm2
Now, Time = distance/speed
=4620000 * 7/ 122500 * 22 = 1200 min = 20 hrs
cm2
Now, Time = distance/speed
= 4620000 * 7/ 122500 * 22 = 1200 min = 20 hrs
- -21
Let the level of water in the pond rises by 21 cm in t hours.
Speed of water = 15 km/hr
Volume of water flowing out of the pipe in 1 hour
= π r 2 h
= 231 m3
∴ Volume of water flowing out of the pipe in t hours = 231 t m3.
Volume of water in the cuboidal pond
= 462 m3
Volume of water flowing out of the pipe in t hours = Volume of water in the cuboidal pond
∴ 231 t = 462
Thus, the water in the pond rise by 21 cm in 2 hours.
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- -9
Let the level of water in the pond rises by 21 cm in t hours.
Speed of water = 15 km/hr
Diameter of the pipe = 14/100 m
Radius of the pipe (r) = 7/100 m
Volume of water flowing out of the pipe in 1 hour
= π r 2 h
= (22/7) x (7/100) x (7/100) x 15000
= 231 m3
Volume of water flowing out of the pipe in t hours = 231 t m3.
Volume of water in the cuboidal pond
= 50 x 44 x (21/100)
= 462 m3
Volume of water flowing out of the pipe in t hours = Volume of water in the cuboidal pond
So, 231 t = 462
t = 2
Thus, the required time is 2 hours.
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- -2
Therefore radius of cylinder, r = 7 cm
Volume of cylinder = πr2h cubic units
Volume of water flowing through the cylindrical pipe in 1 hour at the rate of 15km/hr
= (22/7) x (7/100) x (7/100) x 15000 = 231 cu m
We know that volume of cuboid = lbh cubic units
Therefore volume of water in the tank = 54 x 44 x (21/100) = 462 cu m
Time taken = (462/231) = 2 hours
- 19
r= 7/100 m
Let time taken be T.....
volume= πr2h= 22/7 x 7/100 x 7/100 x 15000 x T
Cuboidal Tank- L=50m
B= 44m
H= 21/100
Volume= LBH= 50 x 44 x 21/100
Volume of pipe x time = volume of cuboidal tank
22/7 x 7/100 x 7/100 x 15000 x T= 50 x 44 x 21/100
T = 44/22
=2 hours
- 20
Thanks
Regards
In cylinder,
r=7cm=0.7m l=15km b=15000m
In tank,
l=50m b=44m h=0.21m
Volume of water in tank= length x breadth x height =50 x 44 x 0.21 =462m³
Height of cylindrical pipe=Volume / πr² =462/(0.07)²(22/7) =462/0.0154 =30000m
Time = 30000/15000 = 2 hours
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