Environmental Engineering FOURTH EDITION

144 ENVIRONMENTALENGINEERING

F@m 7-9. Head loss in a Mter a~ measured by a mauometQ Note
loss in a clean 6lta audiY~ is head loss in a dirty Mkr.

head

whede

L = depth of Mer,

f =frictionfactor.

D = “pipe” diameter,

v = velocity in “pip,” and

However, the “pip” or channels through the sand arc not straight and D varies,

SO we can substitute D = 4R, whae

fuea 7&/4 D

wettd-perimttea nD 4

R= - - -hydraulicJatio.

We thua have

L v2

hL= f --.

4R 2g

The velocity of &e water approaching the sand is

Q

A’ ’

va = -

and the velocity through the bed is

VP

e

v=-,

where

e = pomaity, or fraction of open spama in the sand,

Q =flowrate,&

A’ = surface -of thc sand bed.

Thc total channel volume is the porosity of the bed multiplied by the total volume,

or cV. The total solids volumc is (1 - e) times the total volume, which is also equal