Page 73 - Essentials of physical chemistry

Viscosity of Laminar Flow 35

sequence of steps in the derivation can be ‘‘learned.’’ For a few occasional chemical engineering
students in the class, the main message of Poiseuille’s law is that the flow rate through a pipe is
proportional to the fourth power of the internal radius of the pipe, a principle well worth knowing
when dealing with ‘‘plumbing.’’

PROBLEMS

2.1 Calculate the bulk volume flow of blood with viscosity 0.02 poise through a 6 inch long aorta
of inner diameter 3=8 in. due to a blood pressure of 125=80 mmHg in gallons=min assuming
that the pressure is constant (duty factor ¼ 1). Then, multiply the answer by a duty factor of
0.05 to correct for the duration of the heartbeat pulse (and the fact that we are treating the aorta
wall as rigid).
2.2 Water can be used as a standard to measure the viscosity coefficient h of an unknown liquid if
the temperature is held constant, the same volume of liquid and the same apparatus is used.
Given that h ¼ 0:010038 poise for water at 208C, calculate the viscosity of an unknown liquid
at 208C if 10 mL of distilled water took 17 s for 10 mL to flow between two marks in an
Ostwald (J-tube) viscometer and the unknown liquid took 19 s for 10 mL to flow under the
same conditions.
4
2.3 To show how the R dependence of the Poiseuille law affects flow rate, calculate the bulk flow
through a 12 in. long fire hose nozzle with an inner diameter of 2 in. delivering water with
h ¼ 0:01 ¼ 0:01 poise from a pressure of 100 psi and exiting to a pressure of 14.7 psi. Assume
there is a pump which can provide the necessary volume and give the answer in gallons=min.
2.4 Calculate the viscosity coefficient h in poise and in Pa s, if 5 gal=min flow (laminar) through a
6 in. long tube 1 in. inner diameter due to a pressure of 18 psi and exit at 14.7 psi.
2.5 Estimate the inner diameter of Lance Armstrong’s aorta assuming it is 7 in. long, his blood
pressure is 140=60 mmHg and that his heart pumps (as rumored) 9 gal=min. Use
h ¼ 0:02 ¼ 0:02 poise and integrated pulse factor ¼ 0.05.

REFERENCES
1. Neuenschwander, D. E., Albert Einstein’s Dissertation, http:==www.sigmapisigma.org=radiations=2005=
ecp_spring05.pdf
2. Pfitzner, J., Poiseuille and his law. Anaesthesia 31, 273 (1976).
3. Einstein, A., Eine neue Bestimmung der Moleküldimensionen. Ann. Phys., 19, 289 (1906).
4. Einstein, A., Berichtigung zu meiner Arbeit: Eine neue Bestimmung der Moleküldimensionen. Ann.
Phys., 34, 591 (1911).
5. Castellan, G. W., Physical Chemistry, 3rd Edn., Addison-Wesley, London, 1983, p. 942.
6. Lide, D. R., CRC Handbook of Chemistry and Physics, 90th Edn., CRC Press, Boca Raton, FL,
2009–2010, pp. 6-1.
7. Mark, H. and A. V. Tobolsky, Physical Chemistry of High Polymeric Systems, Interscience, New York,
1950, p. 290.
8. Staudinger, H. and R. Nodzu, Über hochpolymere Verbindungen, 36. Mitteil.: Viscositäts-Untersuchungen
an Paraffin-Lösungen. Berichte 63, 721 (1930).
9. Shoemaker, D. P., C. W. Garland, and J. W. Nibler, Experiments in Physical Chemistry, 6th Edn., The
McGraw Hill Book Co., Inc., New York, 1996.