Water is flowing at the rate of 2.52 km/he through a cylindrical pipe into a cylindrical tank , the radius of whose base is 40cm. If the increase in level of water in the tank in half an hour is 3.15 m, find the diameter of the pipe .
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Given :-
• Water is flowing @ 2.52km/hr through a cylindrical pipe into a cylindrical tank.
• Radius of base = 40cm
• level of increase of water in half an hour = 3.15m
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To Find :-
• Internal diameter of the pipe
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Let the internal radius of the pipe be r
Lenth of water flowing through the pipe in 1 hour ,
h = 2.52km = 2520m
Length of water flowing through the pipe in 1 hour,
= πr²h = ( π × r² × 2520 ) m³
Volume of water flowing through the pipe in half an hour,
= ( 1/2 × πr² × 2520 ) m³ = (1260πr²) m³
Radius of the cylindrical tank, R = 40cm = 2/5m
Increase in level of water, H = 3.15m
Volume of water filled in tank
=πR²H = (π × 2/5 × 2/5 × 315/100)m³ = (63π125)m³
Now , volume of water flown in half an hour = volume of water filled in the tank
= = > 1260πr² = 63π/125
= = > r² = 63/(125×1260)
= = > r² = 1/2500
= = > r = √(1/2500)
= = > r = 1/50m = ( 1/50 × 100 )cm = 2cm
Hence, the internal diameter of the pipe is (2×2)cm = 4cm
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