CIV E 530 - OPEN-CHANNEL HYDRAULICS
SPRING 2008
HOMEWORK No. 5

  1. Prove that the Darcy-Weisbach friction factor is related to Manning's n by the following relation:

    fD = 8gn2 / (K2 R1/3)

    in which fD = Darcy-Weisbach friction factor, g = gravitational acceleration, R = hydraulic radius, and K = constant specific for the system of units, equal to 1 in SI units and 1.486 in U.S. Customary Units. Express the relation in SI and U.S. Customary units.

  2. Use ONLINE CHANNEL 01 to calculate normal depth, velocity, and Froude number for the following cases:

    • Q = 100 m3/s, b = 10 m, z = 2, So = 0.0005, n = 0.025
    • Q = 200 cfs, b = 20 ft, z = 1, So = 0.001, n = 0.030
    • Q = 250 m3/s, b = 15 m, z = 1, So = 0.0008, n = 0.035
    • Q = 350 cfs, b = 25 ft, z = 3, So = 0.005, n = 0.035

  3. A recent flood on Clearwater Creek has left observable water marks on a certain river reach. To estimate the flood magnitude, hydraulic data has been measured at two cross sections A and B, a distance of 2,350 ft apart. The reach fall between the cross sections is 12.3 ft and the average Manning's n is 0.035. The upstream flow area, wetted perimeter, and α coefficient are 600 ft2, 55 ft, and 1.17; the downstream flow area, wetted perimeter, and α coefficient are 720 ft2, 52 ft, and 1.12. Use SLOPE AREA to calculate the flood discharge.

  4. Calculate the unit-width discharge in an overland flow plane, under laminar flow, with mean depth of 3 cm and slope of 0.0015. Assume water temperature T = 15 oC.