Water and Wastewater Treatment and Management · Water Treatment · 2 marks · Numerical answer
Water filters at .002 m/s through .67 m of uniform .4 mm spherical sand, SG2.65,porosity .35. Water density998.2 kg/m³,viscosity .001002 Pa s. Use f=1.75+150(1−η)/Re and the stated Carman–Kozeny/Ergun form to find head loss in m, to three decimals.
$Re=\rho vd/\mu=.7970$,giving $f=1.75+150(.65)/Re\approx124.1$. With this friction-factor convention,$h=f(L/d)(v^2/g)(1-\eta)/\eta^3$. Substitution yields **1.285 m**. There is no extra factor1/2 in this Ergun convention. Grain SG would matter for fluidization, but does not enter the fixed-bed loss formula.
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