1. Graded Problem

Rainwater is flowing at a steady rate down a street having an incline of 30° with the horizontal. A scrap of paper on the surface of the water moves at a rate of U= 1 ft/s. The street is 20 ft wide, and the water depth is h = 0.5 in. Estimate the flow rate of rainwater for the following water velocity profiles. The y-coordinate is normal to the solid surface, with y = 0 is at the solid surface, and y = hat the free surface of the flow. \text { a) } u=U \text {; } \text { b) } u=\frac{U y}{h} \text {; } u=U\left(2\frac{y}{h}-\frac{y^2}{h^2}\right)