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doubts on the formula of near-bed concentration in volume

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Old   April 25, 2012, 22:35
Question doubts on the formula of near-bed concentration in volume
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Hui Guo
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These days I had some doubts on the formula of near-bed concentration in volume which's published in the following paper:

Zhixian Cao. Equilibrium near-bed concentration of suspended sediment [J]. Journal of Hydraulic Engineering, 1999, 125 (12): 1270~1278.

the series of formulae are in the attachments.
For convenience, the key formulae are listed additionally:

qb=5p(sgd^3)^(1/2)(θ^1/2-0.7θc^1/2) ! Engelund(1976) formula for calculation of bedload tranport rate in volume(m^3/ms)
p=[1+[πμ/[6(θ-θc)]]^4]^(-1/4) ! the probability of sediment entrainment
qs=qt-qb ! suspended load transport equals to the total load transport rate minus qb
Ca=qs/I ! Ca---near-bed concentration; I---shape integration
I's expression is complex, so you can see it in the attachments.

Question: As I noticed, the author equated the near-bed concentration Ca to qs/I, in which qs denotes the suspended load transport rate in volume(m^3/ms),and I is the shpae integration, which is nondimensional. So I wonder if the unit of Ca is wrong according to the formula: Ca=qs/I since Ca has the unit kg/m^3 (in mass) or m^3/m^3 (in volume)?

Who can help me?
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Old   April 27, 2012, 02:28
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The background for these formulas are listed in the attachments. Actually, these formulas are important for simulation of sediment transport, so it's necessary to fully understand their meanings and application background.
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