Reference no: EM132715837

Question: A concrete channel to bring water to Crystal Lake is being designed. It will have vertical walls and be 15 feet wide. It will be 10 feet deep, have a slope of .0015 feet/foot, and a roughness coefficient of .014. How deep will the water be when 1,000 cubic feet per second is flowing through the channel?

To solve this problem, we can use Manning's equation
Q = 1.486
N
AR2>3
S1>2

where Q is the flow of water (cubic feet per second), N is the roughness coefficient (unitless), A is the area (square feet), S is the slope (feet/foot), and R is the hydraulic radius (feet). The hydraulic radius is the cross-sectional area divided by the wetted perimeter. For square channels like the one in this example,
Hydraulic radius = depth * width>(2.0 * depth + width)

To solve this problem, design a program that allows the user to guess a depth and then calculates the corresponding flow. If the flow is too little, the user should guess a depth a little higher; if the flow is too high, the user should guess a depth a little lower. The guessing is repeated until the computed flow is within 0.1% of the flow desired.

To help the user make an initial guess, the program should display the flow for half the channel depth. Note the example run: At a depth of 5.0000 feet, the flow is 641.3255 cubic feet per second. Enter your initial guess for the channel depth when the flow is 1000.0000 cubic feet per second
Enter guess> 6.0
Depth: 6.0000 Flow: 825.5906 cfs Target: 1000.0000 cfs
Difference: 174.4094 Error: 17.4409 percent
Enter guess> 7.0
Depth: 7.0000 Flow: 1017.7784 cfs Target: 1000.0000 cfs
Difference: -17.7784 Error: -1.7778 percent
Enter guess> 6.8