CEE 371


Fall 2009

Homework #7. Filtration


1.            Determine the effective size (d10, in mm) and the uniformity coefficient (UC) for the sand filter media characterized by the sieve analysis results presented in the following table. Include a plot of % Weight passing versus media size in your analysis.


Sieve Number (mm size opening)

% Weight Passing

14 (1.41)


16 (1.19)


18 (1.00)


20 (0.84)


25 (0.71)


30 (0.59)


35 (0.50)


40 (0.42)


45 (0.35)


50 (0.297)




2.            Consider the design of granular media filters for a water treatment plant with a design flow of 24 MGD:

a)      For a filtration hydraulic loading of 4 gpm/ft2 determine the total filter area required for filtration (in square ft). Next, select the number of parallel filters needed, and their length and width (even foot increments), if each filter is square with area between 450 and 650 square feet.

b)      Choose a dual media filter consisting of 20 inches of anthracite with an effective size (ES) of 1.1 mm over 12 inches of sand with an ES of 0.45 mm. The porosity of the anthracite layer is 0.40 and the sand porosity is 0.36. Determine the superficial filtration velocity and the pore velocities in both the anthracite and sand layers in both ft/min and m/hr units.

c)      Calculate the detention time (in minutes) through the entire depth of the filter.

d)     Calculate the clean bed head loss (in feet) for the filter using the Carmen-Kozeny equation. Assume a water temperature of 68 F and the design hydraulic loading rate. Also assume a value of 5 for the constant k in the Carmen-Kozeny equation (slides for Lecture #19). Use the media effective size for media diameter in the calculation.

e)      What is the clean bed head loss of the filtration rate was 6 gpm/ft2? What is the clean bed head loss if the water temperature is 40 F at the design loading rate?

f)       If the entire filter depth was sand of the same size as the sand used in the dual media, and the total filter media depth was also the same, what would the clean bed head loss be for the conditions of part (d)?



Assigned: 9 Nov 09

Due: 18 Nov 09