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Question

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

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Solution

Given: Speed of water flow =10 m/minute=1000 cm/minute

Radius of the pipe =52 mm=2.510 cm=0.25 cm

Area of the face (Circular in shape) of pipe =πr2=227×(0.25)2 cm2

Diameter of the conical vessel =40 cm

So, radius of the conical vessel, r=20 cm

And, Depth of conical vessel, h=24 cm

Volume of the Conical vessel =13πr2h

=13×227×202×24 cm3

Now, Required time to fill the conical vessel

=Volume of the vesselArea of the circular face of pipe×Speed of water

=13×227×202×24227×(0.25)2×1000

=20×20×80.25×0.25×1000

=20×20×82.5×25

=4×4×82.5×1

=4×4×8×1025

=4×4×8×25

=51.20 minute

=51 minute and 12 second [ 0.20 minute=0.20×60=12 second]


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