15.7.4 Still ambient fluidThe initial dilution of the effluent Smalong the centreline of the jet issuing
from the port may be expressed in still water conditions in a functional
form asSmf (^0) , (15.39)
whereVpis the velocity at the exit of the port, y 0 is the depth of the port
exit below the surface and Dpis the diameter of the port. gg( (^) a 0 )/ (^0)
where (^) ais the density of the ambient fluid and 0 is the density of the
effluent. The first term in the brackets on the right-hand side of equation
(15.39) is the densimetric Froude number denoted further as FD(see also
equation (8.20)).
The spread of the buoyant jet horizontally discharged in still sur-
rounding fluid has been studied extensively and the results are presented
in the form of equation (15.39) as charts or equations. Figure 15.13
shows the graphical expression of the functional form due to Fan and
Brooks (1966). Cederwall (1968) expresses the dilution in the form of
equations as
Sm0.54FD
7/16
for 0.5FD (15.40)
y 0
Dp
y 0
DpFD
y 0
Dp
Vp
(gDp)1/2
Fig. 15.13 Centreline dilution as a function of y 0 /DpandFD