CIVE 413 - ENVIRONMENTAL RIVER MECHANICS Pierre Y. Julien April 2 1,2008

Sample Review Problems on River Engineering

1. Consider a large river during a flood. The main channel width is 250 m, the flow depth is 6.62 m and the flow velocity is 2.26 d s . The channel slope is 10 crnlkrn and the grain diameter is uniform 0.25 mm sand. Determine the following:

a. the Froude number b. Manning n c. the bed shear stress d, the Shields parameter e. what particle diameter is at beginning of motion f. what is the settling velocity of the bed material g. what is the shear velocity of the flow h. is most of the sediment transported as bed load or in suspension

2. Bridge piers are built on the river discussed above. The type of bridge pier considered is a square concrete bridge pier 3.5 m wide. Determine the scour depth around the structure. Also estimate the angle of repose of the material and estimate the lateral extent of the scour hole.

3. Repeat the calculations from (2) above for the case of replacing square bridge piers with a large round sheet pile caisson that is 15.2 m in diameter. Determine the scour depth and the lateral extent of the scour hole. \

4. The engineers are also considering an abutment protruding into the river. Consider a 75 m long spill-through abutment that is normal to the main flow direction. Also consider a 50 m abutment with the same orientation angle with vertical sheet pile wall at the end of the abutment. Compare the abutment scour depths for both cases.

5. The median particle size distribution of riprap is 500 mm. Determine the proper particle size distribution of the riprap if is it placed on the sand bed channel. Would a single filter be sufficient? Plot the particle size distributions and determine the particle size distribution of the filter(s).

3 s = 6 . 6 2 4 I . )

YS = 5 D 5 b ~

CIVE 413 - ENVIRONMENTAL RIVER MECHANICS Pierre Y. Julien April 18,2008

Sample Problems on Riprap Design

1. You are given the following rectangular channel with stable vertical banks.

a. Calculate the hydraulic radius for the given channel. b. If the peak flow velocity within the channel is measured to be 8 feetlsec determine

the discharge and unit discharge. c. Determine the slope if Manning n = 0.04. d. Determine the stone diameter that would stabilize the channel bed. e. What would be the gradation of the material required to stabilize the bed. f. What would be the thickness of the armor layer to stabilize the bed.

2. You design a trapezoidal channel with 20 ft base width and side slopes 1V: 3H. The channel is excavated in uniform 2 mm sand and the main flow characteristics are Q = 1000 cfs, V =' 4 mls, calculate the following in English units.

a, cross section area in ft2 b, flow depth in ft c. surface width in ft d. hydraulic radius in ft e. channel slope if n = 0.04 f. Froude number g. riprap size to stabilize the banks h. gradation of the riprap ( e.g. d20 and dloo) i. thickness of the riprap revetment in ft j. design the particle size distribution of the filter k. sketch a cross section profile of your design

3. The median particle size distribution of riprap is'200 mm. Determine the proper particle size distribution of the riprap. If the material is placed on bed material that is dz6 = 5 mm, dso =

10 mm and dso = 20-m&. Plot the particle ;ize distributions and determine the particle size distribution of the filter.