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Conditions for turbulence When the flow rate of water in a garden hose is measured using the bucket-and-stopwatch method, it takes 75 seconds to fill a 5-litre bucket. If the inner diameter of the hose is 15 mm and the density and viscosity of the water are approximately 1000 kg m−3 and 1.0 cP, respectively, is flow in the hose laminar or turbulent? A 5-cm-diameter wooden spoon is used to stir chicken consommé in a saucepan using a regular circular motion at a speed of 1.5 revolutions per second. At the temperature used to warm the broth, the liquid density is 970 kg m−3 and the viscosity is 0.45 cP. In this unbaffled system, turbulent flow occurs at impeller Reynolds numbers above about 105. Is flow in the saucepan likely to be turbulent?

Rheology of fermentation broth The fungus Aureobasidium pullulans is used to produce an extracellular polysaccharide by fermentation of sucrose. After a 120-hour fermentation, measurements of shear stress and shear rate are made using a rotating cylinder viscometer.

Shear stress (dyn cm−2)

Shear rate (s−1)

44.1

10.2

235.3

170

357.1

340

457.1

510

636.8

1020

a. Plot the rheogram for this fluid. b. Determine the appropriate non-Newtonian parameters. c. Estimate the apparent viscosity at shear rates of: i. 15 s−1 ii. 200 s−1