1.A 50 meter wide rectangular channel is carrying a flow of 250 m3/s at a flow depth of 5 meters. To produce critical flow in this channel, determine

a.) the height of the step in the channel botom if the width remains constant.

b.) the reduction in the channel width if the channel-bottom level remains unchanged.

c.) a combination of the width reduction and the bottom step.

2.A bicyclist leaves from her home at 9am and rides to a beach 40 miles away. Because of a breeze off the ocean, the temperature at the beach remains 60 degrees F throughout the day. At the cyclist's home the temperature increases linearly with time, going from 60 degrees F at 9am to 80 degrees F by 1pm. The temperature is assumed to vary linearly as a function of position between the cyclist's home and the beach. Determine the rate of change of temperature observed by the cyclist for the following conditions: a) as she pedals 10 mph through at town 10 mi from her home at 10am; b) as she eats lunch at a rest stop 30 mi from her home at noon; c) as she arrives enthusiastically at the beach at 1pm, pedaling 20 mph.