Page 271 - Plastics Engineering

254 Processing of Plastics

Pitch =KO ton @ Axial velocity, VO
-!el--
qXN

Element ot fluid

Fig. 4.8 Details of extruder screw

(b) Pressure flow: Consider the element of fluid shown in Fig. 4.7(b). The
forces are

F2 = P-dydX

F3 = ty dzdx
where P is pressure and dt is the shear stress acting on the element. For steady
flow these forces are in equilibrium so they may be equated as follows:
F1 = F2 + 2F3

which reduces to
dP
Y z = tY (4.4)

Now for a Newtonian fluid, the shear stress, ty, is related to the viscosity, r,~,
and the shear rate, 9, by the equation
. dV
ty = vy = r)-
dY
Using this in equation (4.4)
dP dV
Yx = tlby

Integrating
V