Chapter 4, Problem 44P

A conical funnel of half-angle θ = 30° drains through a small hole of diameter d = 6.25 mm. at the vertex. The speed of the liquid leaving the funnel is $V=\sqrt{2gy}$, where y is the height of the liquid free surface above the hole. The funnel initially is filled to height y₀ = 300 mm. Obtain an expression for the time, t, for the funnel to completely drain, and evaluate. Find the time to drain from 300 mm to 150 mm (a change in depth of 150 mm), and from 150 mm to completely empty (also a change in depth of 150 mm). Can you explain the discrepancy in these times? Plot the drain time t as a function diameter d for d ranging from 6.25 mm to 12.5 mm.