Modern Engineering Thermodynamics

712 CHAPTER 17: Thermodynamics of Biological Systems
WHAT ABOUT BIRDS?
The pulse to breathing rate ratio is about 9.0 for all birds (regardless of their size) because birds have a continuous flow of
air in only one direction through their lungs, in contrast to the two-way in-out breathing of mammals. The unidirectional
air flow in birds is also countercurrent (in the opposite direction to) the blood flow in the lungs, thus improving the efficiency
of gas exchange.
itself is proportional to L 3 . Therefore, the ratio of blood flow rate to heart volume varies with L 2 /L 3 = L −1 ,and
consequently, the heart pulse rate also varies with L –1 . For mammals, the heart pulse rate has been correlated
with body mass according to
where the body mass m is in kilograms.
Heart pulse rate ðin beats per minuteÞ = 241ðm −0:25 Þ = 241
m 1/4 (17.18)
The same argument can be made for the respiratory system. The ratio of the gas transport rate through the lung
wall to the lung volume also varies with L –1 , and the breathing rate is also proportional to L –1 . Experimentally,
we find that the ratio of pulse rate to breathing rate is constant at about 4.5 in all mammals regardless of their
size. The breathing rate for mammals has been correlated with body mass as
Breathing rate ðin breaths per minuteÞ = 54:0ðm −0:25 Þ = 54:0
(17.19)
m 1/4
where the body mass m is in kilograms.
EXAMPLE 17.7
As a famous biomedical engineer, you are challenged on your medical exam to determine the heart rate and respiratory rate
of a 0.0300 kg mouse, a 70.0 kg human, and a 4000. kg elephant.
Solution
The heartbeat rate for mammals in beats per minute is given by Eq. (17.18) as
so the heartbeat rates of the mouse, human, and elephant are
Heartbeat rate = 241ðm −0:25 Þ Beats/min
ðHeartbeat rateÞ mouse = 241ð0:0300 −0:25 Þ = 579: Beats/min
ðHeartbeat rateÞ human = 241ð70:0 −0:25 Þ = 83:3 Beats/min
ðHeartbeat rateÞ elephant = 241ð4000: −0:25 Þ = 30:3 Beats/min
The respiratory rate of mammals in breaths per minute is given by Eq. (17.19) as
So the breathing rates of the mouse, human, and elephant are
Respiratory ðbreathingÞ rate = 54:0ðm −0:25 Þ Breaths/min
ðBreathing rateÞ mouse = 54:0ð0:0300 −0:25 Þ = 130: Breaths/min
ðBreathing rateÞ human = 54:0ð70:0 −0:25 Þ = 18:7 Breaths/min
ðBreathing rateÞ elephant
= 54:0ð4000: −0:25 Þ = 6:79 Breaths/min
Exercises
19. Determine the heatbeat rate of a 2.80 kg house cat. Answer: 186 beats/min.
20. Determine the breathing rate of a 700. kg racehorse. Answer: 10.5 breaths/min.
21. Since whales are mammals, determine the heart rate of a 136,000 kg (150. ton) blue whale. Answer: 12.6 beats/min.
Because plants lack mobility, their size criteria are generally simpler than those for animals. The main strength
concerns in plants center on the buckling of their central trunk and excessive deflections of their cantilevered
limbs. Consider a circular cylinder of height h and diameter d. Then, for slender cylinders ðh/d > 25Þ the critical
height for a cylinder buckling under its own weight can be shown to be
h critical = 0:85 E 1/3d
2/3
γ
(17.20)