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 1000 cubic feet/second is flowing through the channel?

To solve this problem, use Manning's equation: uploaded image 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 X width / (2.0 X depth + width)

To solve this problem ,design a problem 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 percent 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 5.000 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:1000.0000cfs Difference:-17.7784 Error:-1.7778 percent Enter guess>6.8

Can you answer the question in MATLAB format. Using a while loop and fprintf

also,

% *****CONSTANTS*****

% *****COMPUTE*****

% compute flow for half the channel depth

% *****OUTPUT*****

% print flow for half the channel depth

% print headers for water depth guesses and output

% get guesses and compute flow until flow rate is within .1% of target flow

% get water depth % compute flow rate

% print current information