Symbols

a Coefficient in head loss equation for deposited materials

A Cross-sectional area of flow (i.e., superficial area times the porosity; bounding surface area of control mass and control volume)

A5 Surface area of grains in filter b Exponent in head loss equation for deposited materials c Concentration of solids introduced into bed d Diameter of spherical particle dp Sieve diameter f Fraction of total cycle time tc spent in actual filtration fp Friction factor g Acceleration due to gravity hd Head loss due to deposited materials hL Head loss across filter hLb Backwashing head loss hLo Head loss across clean bed

K Proportionality constant for the inertial force

K5 Proportionality constant for the shear force l Length of bed le Expanded bed depth

Lf Filter yield m Rate of mass inflow into bed mc Mass of cake per unit volume of filtrate

M Control mass n Unit normal vector

le

Expanded bed porosity

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