CIV E 530 - OPEN-CHANNEL HYDRAULICS
SPRING 2006
HOMEWORK No. 1

Given a pipe with diameter do = 1.53 m, slope S = 0.015, and Manning n = 0.013.

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

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

  3. Calculate the discharge Qo  when the pipe is flowing full.

  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 = 1.0 m.

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

  7. Using GRAVITYPIPE in http://onlinecomp.sdsu.edu verify your results of items 3 and 5.

  8. Using GRAVITYPIPE in http://onlinecomp.sdsu.edu, verify your results of item 4, i.e., find the maximum discharge and its corresponding depth.

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