Page 68 - Essentials of physical chemistry

30 Essentials of Physical Chemistry

TABLE 2.1
Viscosity of Water at Varied Temperatures
Temperature, 8C Viscosity Coefficient, mPa s r,kg=m 3
0.01 1791.1 999.84
10 1305.9 999.70
20 1001.6 998.21
25 890.02 997.05
30 797.22 995.65
40 653.73 992.22
50 547.52 988.03
60 466.03 983.20
70 403.55 977.76
80 354.05 971.79
90 314.17 965.31
99.606 282.75 958.63
100 12.234 0.58967

Source: Lide, D.R., CRC Handbook of Chemistry and Physics, 90th Edn.,
CRC Press, Boca Raton, FL, 2009–2010. pp. 6-1.

VISCOSITY OF BLOOD

Viscosity can be measured for blood as an auxiliary diagnostic test for diseases in which there are
abnormally high levels of proteins or to monitor the effect of blood-thinning agents as a treatment
for stroke prevention. The normal range of viscosity of human blood is from 0.99 to 1.55
centipoise and the units are in poise. Blood with viscosity higher than 4.0 centipoise (1 poise ¼ 0.1
Pa s so 0.04 poise ¼ 0.004 Pa s) is considered abnormal and may signal potential circulatory
problems. Now for health science students, it may be of interest to consider the average blood flow
in an adult human or for forensic students to know possible blood flow in a given time. One
complication is that it is known that arteries have elastic walls and flex (bulge) during the high
pressure pulse of blood flow, but we will approximate an aorta as a pipe with a fixed diameter.
Another substantial problem is that with a pulsating heartbeat, the pressure is not constant; part of
the time, there is a higher pressure pulse (beat) while between beats the pressure can be much
lower. We can solve this problem with an adjustable factor we can call a ‘‘duty factor,’’ which
represents the fraction of the time the pressure of the heartbeat pulse is high. Another interesting
consideration is that medical measurements still use the high and low pressures measured for
blood pressure with an arm cuff in the units of mmHg! Suppose we assume the duty factor is 0.1
as representing the pressure spike of the human heartbeat and then correct the duty factor to a
measured value.
Given h ¼ 0.013 poise, an aorta 6 in. long with an inner diameter of 1=4 in. and blood pressure of
140=80 using a duty cycle of 0.1, calculate the volume of blood flow in gallons=minute:

4
140 80 6 dyne 2:54 cm
p atm 1:01325 10 (0:1)

V 760 cm atm 8
2
t ¼ 8(6 in:)(2:54 cm=in:)(0:013 g=cm s)

1 gal 1 qt 60 s
:
3
4 qt 946 cm 1 min