Estimating the viscosity of diluted polymer solution

Question

Question 1

An open test tube at 293 K is filled at the bottom with 24.2 cm of Hg, and 11.2 cm of water is placed above the Hg. Calculate the pressure at the bottom of the test tube if the atmospheric pressure is 756 mmHg. Use a density of 13.55 g/cm3 for mercury and 0.998 g/cm3 for water. Give the answer in terms of (a) dyne/cm2, (b) psia, and (c) kPa.

Question 2

The differential manomter (shown below) is used to measure the pressure difference between two vessels. Derive the equation for the pressure difference (pA– pB) in terms of the liquid heights and densities.

Question 3

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