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Processing of Plastics 317

Pressure
Drofile \

+

Fig. 4.58 Melt flow between calender rolls

If this equation is integrated and the value of x from (4.38) substituted then
the maximum pressure may be obtained as

P,, = -
HO
(4.40)
J(H - How
where w= (4.41)
H
Example 4.9 A calender having rolls of diameter 0.4 m produces plastic
sheet 2 m wide at the rate of 1300 kghour. If the nip between rolls is 10 mm
and the exit velocity of the sheet is 0.01 m/s estimate the position and magni-
tude of the maximum pressure. The density of the material is 1400 kg/m3 and
its viscosity is 104 Ns/m2.
Solution Flow rate, Q = 1300 kg/hour = 0.258 x m3/s
but Q = HWVd where W = width of sheet
0.258 x
so H= = 12.9 mm
2 x 0.01
The distance upstream of the nip at which the pressure is a maximum is
given by equation (4.38)

x = d(12.9 - 10)200 = 24.08 ~III
Also from (4.37)
3 x 104 x 0.01
Pmax = {(2 x 1.865) - 0.13[1.865 + (4.45)(0.494)1)
io x 10-3
= 96 kNim2