Page 429 - Civil Engineering Formulas

HYDRAULICS AND WATERWORKS FORMULAS 355

where Q discharge, cfs
H head, ft
L length, ft
C a coefficient that depends on the character of the material
1
Substituting for Q, the value A [Eq. 12.200] becomes
v
H
L C 1 (12.201)
V
For each class of foundation material, homogeneity being assumed, there is a
definite maximum velocity Vn, at which the water can emerge below the dam
without carrying away foundation material and causing the failure of the structure.
This value of V may be combined with C to form a new coefficient C 2 C 1 V n .
1
n
Substituting C in Eq. (12.201) for C /V, there results
1
2
L n C 2 H (12.202)
where L minimum safe length of travel path
n
C a coefficient depending upon the foundation material
2
One way to avoid the possibility of a dam being carried away by the flow of
water under it is shown in Fig. 12.31. From the flow net diagram and Darcy’s
law of flow through soils, the approximate uplift pressures and percolation
velocities can be computed.
If the number of equipotential divisions N in Fig.12.31 is 18, and the num-
1
ber of flow channels N bounded by flow lines is 5, then
2
N 1
Hydraulic gradient per unit head i (12.203)
N 2
For a soil of permeability k, void ratio e, and specific gravity s, the flow
under a head H is
N 1
Q kH (12.204)
N 2
At a point a (Fig.12.31) at a depth D, below the surface, a saturated founda-
tion and flow path L being assumed, the total pressure is calculated as follows:
Let P total stress per unit area
P effective stress per unit area
e
P neutral stress per unit area
n
specific gravity of water
w
s e

Then p D w (12.205)
1 e
D
p n D w H w (12.206)
L