Water flows at the rate of 10 metres per minute through a cylindrical pipe 5 mm in diameter.How long would it take to fill a conical vessel whose diameter at the surface is 40 cm and depth 24cm ?

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Solution

Radius of the pipe = 5/2 mm = 5/2 x 1/10 cm = 1/4 cm

Speed of water = 10 m/min = 1000 cm/min

Volume of water that flows in 1 minute = Π r² h = 22/7 x 1/4 x 1/4 x 1000 = 1375/7 cm³

Radius of conical vessel = 40/2 = 20 cm; Depth = 24 cm

Therefore, Capacity of the vessel = 1/3 x Π r² h

= 1/3 x 22/7 x 20 x 20 x 24 = 70400/7 cm³

Therefore, Time required to fill the vessel = capacity of the vessel / volume of water flowing per minute

= 70400/7 / 1375/7 = 70400/7 x 7/1375 = 256/5 minutes = 51 min 12 sec

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