Question

Name: section is filled to top with 2. A nat tapered funnel with a fixed width rectangular cros vation). The an L. A water (i.e. the width of funnel, "a”, does not change w funnel is shown below, the drawing is not to scale and L time zero the bottom is opened and water is allowed to dr with elevation). The geometry of water is allowed to drain. (35 Points) equation for the variation of height of water in the a. Develop the differential funnel. ters b. Sol ve for the water level as a function of time in terms of the given parame Li, L2, a, and θ Top View L1

Answer 1

Given the following situation to find water remaining in the funnel as a function of time and the differential equation governing it. Let us consider that at time t water till height h remains now at t = 0, h = n and H = (L_2 - L_1)/2 tan theta volume of water remaining at time t is integral^n A dy = \r\n function of time and the di central equation governing it. Let us consider that at time t water till height h remains now t t - a, h = k and k = (L_2 - L_1)/2 tan theta volume of water remaining at time t is integral^n_a A dy = -v- = integral6h_4 (2 y cot theat_L_1) dy v = integral^n_0 2 cot y dy + L_1 integral_0 dy = [2 cot theta integral^n_0 y dy + L_1 integral^h_0 dy] a = [2 cot theta/2]_0 y^2 + L_1