3) A problem on SPM profiles (40 pts): Consider a flow 12m deep with U- of 0.05 m/s and zo =

10 mm and Zref = 0.1 m (Zref is the location where the reference value of C is measured). A deep,

rapidly flowing river like this would like have a continuum of sediment sizes that would have to

be very simply "binned" for any sediment transport calculation. We will consider only three

"size classes" (as they are called): silt d₁ = 25 µm, fine sand d₂ = 250 µm, and coarse sand d3 =

1000 μm (assume Corey shape factor =0.7), and information of the sort that one might be able

obtain in a real system.

(a) Find Ws, Ws/U., and the Rouse number P for each size class; 10 pts.

(b) Assume that a log-layer velocity profile is adequate to describe the flow. What is that veloc-

ity profile? 5 pts

(c) What is the corresponding parabolic eddy diffusivity profile? 5 pts

(d) Using the Rouse solution for the SPM profile in class notes (the solution applicable in a log-

boundary layer), calculate for each size class the ratios: (Clz=10m/C|z=zref), (C|z= 1m/C|z=zref), and

(C|z=0.5m/C|z=zref). If Clz- zref is the same for each of the three size classes, where do you expect

the bulk of the sediment transport to occur for each size class? You don't need to know an actual

value of Cz=zref to answer the question. But when working with observations, you want to have

data (z= zref) as close to the bed as possible, to get good results. Otherwise, you'll miss the

larger sizes; 20 pts

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