VELOCITY OF EFFLUX FROM SLÜICES.
239
or,
V = Jigh.
(37)
In the case of a liquid whose motion is impeded by friction, the rate of
flow is naturally less. The amount of reduction may be expressed by a
fractional coefficient, attached to the preceding equation, denoting the
proportion of head expended in overcoming the frictional résistance.
Thus, the total head may be considered as divided into two portions,
only one of which is available for producing velocity—
whence
/ 29/1
^ V^F..............................(38)
The laws of fluid friction, which it will be useful to state at this point,
differ materially from those relating to the surface-contact of solid bodies.
They are as follows :—
1. The friction is independent of the head, or pressure.
2. It varies directly as the area of the surface exposed to action.
3, It varies directly (or very
nearly so) as the square of the
velocity. This, however, is only liter- ErZ~r~E
ally true so long as the rate of flow ^^Hr^ æ ’rz^s^ï?
is sufficient to prevent the adherence z7ùj-£?-£ ~—
of water to the surface in question.
Now, let us consider the case of
,i c 1 Fig. 171.
a horizontal culvert of length, æ
(fig. 171), and sectional area, a, in which water is running full. Agree-
ably to the foregoing laws, we may express the amount of surface
friction as
S = f.p.x.v2,
where 7 is a coefficient to be determined later, and p is the perimeter of
fluid section.
Now, assume the surface friction to be just counteracted by the differ-
ence of pressure upon the two faces of the length, æ. That is—
(171 - QÙa = f■p-x.v2.
But this resultant pressure, (^ — q^ a, is due to a difference in head
on each side of the culvert. Hence, we may substitute for it the expres-
sion for the pressure of the differential head—viz., w h1 a, in which w is
the weight of a eubic foot of water. At the same time, let R = and the
P
equation becomes
æ v2
’ R'w’