A diluted polymer solution with a density of 1130 kg/m3 was extruded through a capillary tube of 3.5 mm internal diameter and 1 m long. The following results were obtained at 25°C. [Please submit the hand calculations illustrating all necessary steps. Whist, the use of MS Excel is strongly encouraged to assist your understanding further since it is an assignment, the Excel submission is optional.]

Pressure Drop (kPa)                                                                                          Volumetric Flow Rate(m³/s)

1.5 x 10³                                                                                                                          1.0 x 10^-5

2.2 x 10³                                                                                                                          2.7 x 10^-5

5.2 x 10³                                                                                                                          1.05 x 10^-4

1.0 x 10⁴                                                                                                                          3.0 x 10^-4

2.0 x 10⁴                                                                                                                          9.0 x 10^-4

5.0 x 10⁴                                                                                                                          3.5 x 10^-3

(a) Establish the nature of the fluid behaviour with supporting explanation.

(b) Determine the flow parameters of the fluid and hence propose a fluid rheological model in terms of shear stress (τ_w) as a function of wall shear rate -(du/dr)_w.

(c) Estimate the viscosity of this diluted polymer solution when the wall shear rate is at 1.50 x 10⁵ s^-1.