Page 272 - Plastics Engineering

Processing of Plastics 255
so

Also, for the element of fluid of depth, dy, at distance, y, from the centre
line (and whose velocity is V) the elemental flow rate, de, is given by

dQ = VTdy
This may be integrated to give the pressure flow, Qp

HI2
eP=2 J---.~(;-$)dy
dP
1
77 dz
0
1 dP
Q ----.TH
- 1277 dz
Referring to the element of fluid between the screw flights as shown in
Fig. 4.8, this equation may be rearranged using the following substitutions.
Assuming e is small, T = nDtan$. cos4
dL dP dP
Also, sin$ = - so - = -sin$
dz dz dL
Thus the expression for Qp becomes

nDH3 sin2@ dP
.-
QP - 12rl dL (4.7)
(c) Leakage The leakage flow may be considered as flow through a wide
slit which has a depth, 6, a length (ecos4) and a width of (nDlcos4). Since
this is a pressure flow, the derivation is similar to that described in (b). For
convenience therefore the following substitutions may be made in (4.6).

h=S
T = nD/ COS
AP
Pressure gradient = - Fig. 4.9)
(see
e cos 4
So the leakage flow, QL, is given by

n2D2d3 dP
QL = tan 4- (4.8)
1277e dL
~
A factor is often required in this equation to allow for eccentricity of the screw
in the barrel. Typically this increases the leakage flow by about 20%.