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inconsistency in DIMENSIONAL ANALYSIS

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Sathya narayanan, modified 4 Years ago.

inconsistency in DIMENSIONAL ANALYSIS

Youngling Posts: 3 Join Date: 3/13/14 Recent Posts
Hello,
With reference to page no. 350 in D-Water Quality Technical reference manual (Version: 5.01.34078) dated 26 May 2014, i found that there seems to be inconsistency in DIMENSIONAL ANALYSIS. The term kmrd has the unit (d-1), but the product of UNITS of the terms krd, DL ,fuv , I0 and (1 - e^-epsxH)/epsxH) become UNIT LESS which is completely contradicting. Would anyone help me in giving the correct terms with proper UNITS?


Formulation

The mortality rate of coliform bacteria can be quantified with the following empirical function
of temperature, chlorinity and solar radiation (as derived from visible light):
For T > Tci:

Rmrti = kmrti x Cxi

kmrti = (kmbi + kmcli) x ktmrti^(T-20) + kmrd
kmcli = kcli x Ccl
kmrd = krd x DL x fuv x I0 x (1 - e^-epsxH)/epsxH

For T <= Tci:
Rmrti = 0:0

where:
Cx concentration of coliform bacteria species i [MPN.m-3]
DL daylength [d]
eps extinction of UV-radiation [m-1]
fuv fraction of UV-radiation as derived from visible light [-]
H water depth [m]
I0 daily solar radiation as visible light at the water surface [W.m-2]
kcl chloride related mortality constant [m3.g-1.d-1]
kmb basic mortality rate [d-1]
kmcl chloride dependent mortality rate [d-1]
kmrd radiation dependent mortality rate [d-1]
kmrt first order mortality rate [d-1]
krd radiation related mortality constant [m2.W-1.d-1]
ktmrt temperature coefficient of the mortality rate [-]
Rmrt mortality rate of coliform bacteria [MPN.m-3.d-1]
T temperature [°C]
Tc critical temperature for mortality [°C]
Ccl chloride concentration [g.m-3]
i index for coliform species, ECOLI, FCOLI, TCOLI and ENCOC


Thanks
CT
Christophe Thiange, modified 4 Years ago.

RE: inconsistency in DIMENSIONAL ANALYSIS

Jedi Knight Posts: 125 Join Date: 11/15/12 Recent Posts
Hi Sathya,

I think you can consider daylength as a fraction here, hence without units, which yields [d-1] fro kmrd.

Regards