Mr. Morison made use of Mr. Hazen’s filtration formula for estimating
the rate and quantity of seepage through the permeable strata below the
dam. This formula is:
h t + 10°
V = cd² –– ––––––
l 60
where
V = rate of flow in meters per day through the whole section.
c = constant varying from 450 to 1,200,
according to cleanness of the sand.
d = “effective size” of sand in mm.
h = head in feet.
l = length or distance water must pass.
t = temperature of the water (Fahr.)
This formula should be used only when the _effective sizes_ of sands
are from 0.10 to 3.0 mm. and with _uniformity coefficients_ below
5.0[5].
Mr. Morison used the following values: c = 1,000; d = 1.0 mm.; h = 90
ft.; l = 2,500 ft.; t = 90°; for the solution of this problem, and
obtained a velocity of 0.002 ft. per sec. The bed of sand and gravel
was assumed to have a sectional area of 20,000 sq. ft. for 2,500 ft. in
length. This gives a seepage of 40 cu. ft. per sec.
It is believed that the above rate of 0.002 ft. per sec., equivalent to
1⅜ ins. per minute, or 7 ft. per hour, is not sufficient to move any of
the material. The velocity of water percolating through sand is found
to vary directly as the head and inversely as the distance.
The value of “c” in the formula is larger for sands of filters
favorable for flow, and smaller for compacted materials and dams.
Mr. Morison thought it might be nearer the actual conditions to assume
d = 0.50 mm.; c = 500; and l = 5,000 ft.; in which case the seepage
would only amount to 2.5 ft. per sec. In this last assumption the
“effective size” of sand grains is 2½ times that classed as “permeable
material” at the North Dike of the Wachusett Reservoir.
Prof. Philipp Forchheimer, of Gratz, Austria, recommends the use of the
formula,
h
––– = a√ + b√²
l
for the percolation through soils between loam and loamy sand.
Sellheim, Masoni, Smreker, Kröber and other authorities on filtration
use still other formulas, to which the reader and student is referred
for further research.
Public-domain text, read in full here on John Shaqi.
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