CIVIL ENGINEERING FORMULAS

HYDRAULICS AND WATERWORKS FORMULAS 355

where Qdischarge, cfs
Hhead, ft
Llength, ft
C 1 a coefficient that depends on the character of the material
Substituting for Q, the value Av[Eq. 12.200] becomes

(12.201)

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 Vnmay be combined with C 1 to form a new coefficient
SubstitutingC 2 in Eq. (12.201) for C 1 /V, there results
(12.202)

whereLnminimum safe length of travel path
C 2 a coefficient depending upon the foundation material

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 1 in Fig.12.31 is 18, and the num-
ber of flow channels N 2 bounded by flow lines is 5, then

Hydraulic gradient per unit head (12.203)

For a soil of permeability k, void ratio e, and specific gravity s, the flow
under a head His

(12.204)

At a point a(Fig.12.31) at a depth D, below the surface, a saturated founda-
tion and flow path Lbeing assumed, the total pressure is calculated as follows:

LetPtotal stress per unit area

Peeffective stress per unit area

Pnneutral stress per unit area

specific gravity of water

Then (12.205)

pnDw (12.206)

D

L

Hw

pD

se

1 e

w

w

QkH

N 1

N 2

i

N 1

N 2

LnC 2 H

C 2 C 1 Vn.

LC 1

H

V