Water is poured into a funnel at a constant rate S = 1 kg/s. It has a top radius rt = 1 m and a bottom radius rb = 0.01 m. The top and bottom levels are separated by a distance of 5 m. Assume that, at each level in the funnel, the downward vertical velocity w is constant. The funnel is constructed so that w increases linearly with depth z below the top, so that that dw/dz is constant. Assume z = 0 at the top radius. Assume the fluid in the funnel is at steady state. Write down an expression for the vertical velocity w(z) in terms of the constant S, the funnel radius r(z), and the density of water rhow (also constant). Pay attention to units. You can use rhow = 1000 kg/m3.
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