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?
Given, speed of water flow =10m min−1=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