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Question 5
Water flows at the 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?


Solution

Given, speed of water flow =10m min1=1000 cm/min
 Radius of the pipe =510×2=0.25 cm
Area of the face of pipe=πr2=πr2=227×(0.25)2=0.1964 cm2
Also, given diameter of the conical vessel = 40 cm
 Radius of the conical vessel =402=20 cm
And depth of the conical vessel =13πr2h=13×227×(20)2×24=21120021=10057.14 cm3
=Required time=Volume of the conical vesselArea of thefaceofpipe×Speedofwater=10057.140.1964×10×100=51.20 min=5120100 min×60 s=51 min 12 s

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