Answer all THREE questions

1.    A capillary rheometer is used to measure the viscosity of a fermentation broth. The capillary has an internal diameter of 0.5 mm and is 6 cm long. A pressure transducer is used to monitor the pressure drop across the capillary under different flow rates. The different flow rates tested, their corresponding shear rate and recorded pressure drop are shown in the table below.

a.  What type of flow would you expect to observe in the capillary rheometer? [6 marks]

b.   Calculate the apparent viscosity of the broth for each flow rate and determine the type of fluid. Check any assumptions made. [20 marks]

c.   Plot the rheogram and determine analytically the rheological parameters of this fluid. [16 marks]

d.   Explain which changes in the fermentation broth might have caused the rheological properties observed.  [8 marks]

2.    The space between two 0.15 m long concentric cylinders is filled with glycerin which has a viscosity of 0.95 Pa s.  The inner cylinder has a radius of 7.5 cm and the gap width between the cylinders is 2.5 mm. The outer cylinder is fixed. Assume that the velocity distribution in the gap is linear. Determine the torque and the power required to rotate the inner cylinder at  180 rpm. [25 marks]

3.    A horizontal pipe was fitted with a flow splitter (Figure 2.1), i.e. splitting the flow into two stream with the same flow rate. At point (1) the flow rate of water (p = 1000 kg m3  and µ = 0.001 Pa s) is 4 cm3  s-1 and the pressure 2 x 105  Pa. Neglecting major and minor losses determine the pressure in point (3). [25 marks]

Figure 3.1. Pipe network

Appendix to BENG0001 Coursework 1

Table A.1. Loss Coefficients for pipe components

Table A.2. Equivalent roughness for new pipes

Appendix to BENG0001 Coursework 1

Equation sheet

Rheology Equations

•    General Law of Viscosity (for Newtonian and non-Newtonian fluids)

•    Determining shear stress, shear rate and viscosity using viscometers

Fluid Flow Equations

•    Hagen-Poiseuille equation

•    Modified (or extended) Bernoulli equation

with

and

•    Carman-Kozeny equation