BENG0083 – Fluid Flow and Mixing in Bioprocesses
Coursework 1
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.
|
Q (m³ s-1)
|
γ (s-1)
|
ΔP (Pa)
|
|
6.000×10-8
|
4889
|
25820
|
|
1.200×10-7
|
9778
|
36140
|
|
3.000×10-7
|
24450
|
58670
|
|
6.000×10-7
|
48890
|
82140
|
|
1.200×10-6
|
97790
|
98570
|
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
|
Elbows
|
KL
|
|
90°, flanged
|
0.3
|
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90°, threaded
|
1.5
|
|
45°, flanged
|
0.2
|
|
45°, threaded
|
0.4
|
|
|
|
|
180° return bends
|
|
|
180°, flanged
|
0.2
|
|
180°, threaded
|
1.5
|
|
|
|
|
Tees
|
|
|
Line flow, flanged
|
0.2
|
|
Line flow, threaded
|
0.9
|
|
Branch flow, flanged
|
1.0
|
|
Branch flow, threaded
|
2.0
|
|
|
|
|
Valves
|
|
|
Gate, fully open
|
0.15
|
|
Gate, ½ closed
|
2.1
|
|
Gate, ¾ closed
|
17
|
|
Ball valve, fully open
|
0.05
|
|
Ball valve, ⅓ closed
|
6
|
|
Ball valve, ⅔ closed
|
210
|
Table A.2. Equivalent roughness for new pipes
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Material
|
ε (mm)
|
|
Drawn tubing
|
0.0015
|
|
Commercial steel
|
0.046
|
|
Riveted steel
|
0.9 - 9.0
|
|
Galvanised iron
|
0.15
|
|
Cast iron
|
0.3
|
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