Pressure-hole error

Pressure is measured right at the die entrance Transducers are less expensive and easier to change, allowing a better match range to material viscosity But a pressure hole error is generated (usually negligible since material flows slowly in the barrel)... 

Figure 2.13 Pressure hole error occurs in a viscoelastic fluid while it is absent in a Newtonian fluid. (Reprinted from Ref. 23 with kind permission from John Wiley Sons, Inc., New York, USA.)...

For Newtonian fluids, flie pressure measured at the bottom of the pressure hole Pm is the same as the true pressure p at the wall. For a viscoelastic fluid, on the other hand, the pressure (p + T22)m measured at the bottom of the pressure hole is always lower than the true pressure (p-t-T22) at the wall, no matter how small the hole is. This pressure difference arises because the elastic forces tend to pull the fluid away from the hole and results in the pressure hole error Ph = (p + T22)m (p + 22)- This effect is illustrated in Figure 2.13. The possible sources of error in tiie measurement have been considered by Higashitani and Lodge [73] along with a review of published data. The effect of Ph has been well substantiated for polymer solutions but the same is not the case for polymer melts with or without fillers. 

He reports that the results of Adams and Lodge (1964) and Kaye et al. (1968) seem more reasonable when corrected with eq. S.4.30 and for pressure hole errors. Olabisi and Williams also find some experimental agreement with Tanner s equations. 

In axial annular flow there is curvature across the flow streamlines, that is, curvature in the plane perpendicular to the flow direction x (see Figure 5.1.2). This is similar to the pressure hole error for flow over a parallel slot, eq.6.3.14. Both geometries measure the second normal stress difference. The pressure difference between the outer and inner cylinder gives... 

As we might expect, the pressure difference Apg is small. Furthermore, because of the curvature of the cylinder walls and the size of typical pressure transducers, pressure holes must be used (note Figure 6.4.1). When corrections are made for pressure hole errors, results for N2 are in qualitative agreement with those obtained by other methods (Lobo and Osmers, 1974 Humami, 1976). Figure 6.4.2 shows results for a 1% polyacrylamide solution. Here N2 is negative and —N2/N 0.06. This ratio is somewhat lower than the value of 0.10 of an 0.8% solution of the same polyacrylamide (Keentok et al., 1980). This discrepancy may be due to the hole pressure error, which is somewhat lower (0.251V -0.11V ) than expected by eq. 6.3.15. 

Using change of variables, it should be possible to derive an explicit expression for N similar to eq. 6.4.4. Instead Osmers and Lobo (1976) have assumed an Ellis-type equation for N, while Geiger and Winter (1978) used a numerical method to evaluate N from eq. 6.4.5. Both corrected for pressure hole errors. 

Chatmel bulge is perhaps the simplest and most direct measurement of the second nmmal stress difference. If h is positive, a convex surface N2 is negative. Since Tanner s first experiments with the tilted trough in 1970 and the discovery of the pressure hole error (Broadbent et al., 1968), nearly all studies have shown N2 to be small and negative. 

Pressure hole errors Secondary flow Instrument compliance... 

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