Q19 of 31 Page 1

Water is flowing at the rate of 0.7 m/sec through a circular pipe whose internal diameter is 2 cm into a cylindrical tank, the radius of whose base is 40 cm. Determine the increase in the level of water in half hour.

Let the increase in level of water in cylindrical tank be ‘h’ cm.


Given


Diameter of circular pipe = 2 cm


⇒ Radius of circular pipe, r1 = 1 cm [∵ diameter = 2 × radius]


Rate of flow = 0.7 m/sec


Height of Water flowed in half hour(1800 seconds) = 1800 × 0.7


= 1260 m = 126000 cm


Base radius of cylindrical tank, r2 = 40 cm


Formula


Volume of circular cylinder = πr2h


Where, r is base radius and h is the height of cylinder


Now,


Water flowed from pipe in half hour = Volume of cylindrical tank with height h


⇒ Volume of pipe with height 126000 cm = Volume of cylindrical tank with height h


⇒ πr12(126000) = πr22h


⇒ 126000 = (40)2h


⇒ 16h = 1260


⇒ h = 78.75 cm


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