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From a mineral oil is known: η1 = 0.300 Pas (at p1 = 0.1 MPa = 1 bar), and η2 = 2.22 Pas

(at p2 = 100 MPa = 1000 bar). Desired is the viscosity value η3 at p3 = 75 MPa (= 750 bar).

1 Here is selected: pref = p1 = 0.1 MPa

2 ap is calculated for p2 (as ap2): ap2 = η2 (p2) / η1 (pref) = 2.22 Pas / 0.300 Pas = 7.40

3 αp is calculated, with Δp = Δp21 = p2 – pref:ln (ap) = αp ⋅ Δp, and thus: αp = ln (ap) / Δpαp = ln (7.40) / (100 – 0.1) MPa = 2.00 / 99.9 MPa = 0.02 MPa-1 (= 20 ⋅ 10-3 MPa-1)

4 ap is calculated for p3 (as ap3), with Δp = Δp31 = p3 – pref:ap3 = exp (αp ⋅ Δp31) = exp [0.02 MPa-1 ⋅ (75 - 0.1) MPa] = e1.5 = 4.48

5 Result: η3 (p3) = ap3 ⋅ η1 (pref) = 4.48 ⋅ 0.300 Pas = 1.34 Pas

Table 3.6: Pressure-dependent viscosity values, see the example of Chapter 3.6
p [MPa]	0.1	1	10	25	50	75	100
η [Pas]	0.300	0.306	0.366	0.495	0.813	1.34	2.22

The already mentioned and some further pressure-dependent viscosity values are presented in Table 3.6.