Water flows into a rain gutter on a house as shown in Fig. P5.12 and in Video V10.7 at a...

Water flows into a rain gutter on a house as shown in Fig. P5.12 and in Video V10.7 at a rate of 0.0040 ft³/s per foot of length of the gutter. At the beginning of the gutter (x = 0), the water depth is zero. (a) If the water flows with a velocity of 1.0 ft/s throughout the entire gutter, determine an equation for the water depth, h, as a function of location, x. (b) At what location will the gutter overflow?