Water flows out through a circular pipe whose internal diameter is 2 cm. at the rate of 6 metres per second into a cylindrical tank. The radius of whose base is 60 cm. Find the rise in the level of water in 30 minutes?
Answers
Answer:
Step-by-step explanation:
The volume of the water that flows out through the circular pipe of radius 1cm, at the rate of 6 metres per second, in one second is same as the volume of a cylinder of radius 1cm and height=6 metres.
Therefore,
volume of the water that flows out through the circular pipe in 1 second=
2 3
22/7 × (1/100) × 6m
=> volume of the water that flows out through the circular pipe in 30 minutes
3
22/7 × 1/10000×6×30×60m
let the water level rise to a height of 'h' metres in 30 minutes in the cylindrical tank of base radius 60cm. Then,
Volume of the water collected in the tank in 30 minutes=
2
22/7 × (60/100) × h
Therefore,
2
22/7×(60/100)×h= 22/7×1/10000×6×30×60
=> 3m
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Given : Water flows out through a circular pipe whose internal diameter is 2 cm, at the rate of 6 m/s into a cylindrical tank and the radius of base is 60 cm.
Internal diameter of circular pipe = 2 cm
Internal radius of circular pipe ,r = 2/2 = 1 cm
r = 1 cm = 1/100 m
[1 cm = 1/100 m]
Rate of flow of water through pipe = 6 m/s
Length of pipe ,h = 6 m
Radius of base of cylindrical tank ,R = 60 cm
R = 60 cm = 60/100 m
So, volume of the water that flows through the circular pipe in 1 second = πr²h
= 22/7 × (1/100)² × 6 m³
Volume of the water that flows through the circular pipe in 30 min (30 × 60) second = 22/7 × (1/10000) × 6 × 30 × 60 m³
Let the water level rise to a height of H metres in 30 minutes in the cylindrical tank of base radius 60 cm. Then,
Volume of the water collected in the tank in 30 minutes = πR²H 22/7 × (60/100)² × H m³
The volume of water that flows out through the circular pipe of radius 1 cm at the rate of 6 m/s in 1 second is same as the volume of a cylinder of radius 1 cm and height 6 m :
22/7 × (1/10000) × 6 × 30 × 60 = 22/7 × (60/100)² × H
22/7 × (1/10000) × 6 × 30 × 60 = 22/7 × 60 × 60 × 1/10000 ×H
6 × 30 = 60 H
H = (6 × 30)/60
H = 30/10
H = 3 m
Hence, the rise in the level of water in 30 minutes is 3 m.
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