CIV E 530 - OPEN-CHANNEL HYDRAULICS
SPRING 2007
HOMEWORK No. 1

Given a pipe with diameter do = 1.2 m, slope S = 0.012, and Manning n = 0.015.

  1. Derive expressions for flow area A and wetted perimeter P in terms of angle θ and radius r.

  2. Calculate the discharge Qo  when the pipe is flowing full (y = do).

  3. Calculate the discharge Q  when the pipe is flowing partially full, at intervals of one-hundredth of the pipe diameter do, from y = 0.01do to y = 0.99 do.

  4. Print a table showing the following hydraulic variables at intervals of one-hundredth of the pipe diameter: y/do, y, θ (radians), θ (degrees), A, P, R, Q, and Q/Qo.

  5. Use the table to solve for the discharge Q   at y = 0.8 m.

  6. Plot y/do (in the ordinates) vs Q/Qo in item 4 (in the abscissas). Identify the relative depth y/do and maximum discharge ratio Q/Qo corresponding to the maximum discharge Q.

  7. Using GRAVITYPIPE in http://onlinecomp.sdsu.edu verify your results of items 2 and 5. Print GRAVITYPIPE output.

  8. Using GRAVITYPIPE in http://onlinecomp.sdsu.edu, verify your results of item 6, i.e., find the maximum discharge and its corresponding depth. Use 3 significant digits for y. Print GRAVITYPIPE output.

  9. Why does the maximum discharge not coincide with the maximum depth? Explain.