1. Using the table below to compile data for the literature or on-line sources and then compute the Reynolds number value for each species and its associated activity. Then decide on the flow regime based on the magnitude of the Reynolds number ( > 10,000 = turbulent,
Table 1: Table of Reynold’s numbers for different flow situation in biological systems
Activity and species
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characteristic length (length of the animal diameter of the tube in m or mm)
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characteristic velocity How fast is the anima l of fluid moving usually in m/s or mm/s)
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kinematic viscosity of the fluid (m2/s)a
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Reynolds number
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Flow (Turbulent, Laminar or In between)
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Filter feeding barnacle
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Swimming blue fin tuna
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Flying mosquito
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Flying king eider duck
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Human spermatozoa
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Blood in the aorta of a mouse
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a
The kinematic viscosity depends on the type of fluid (air, water, salt water, seamen ) and its temperature.
Problem1
The kinematic viscosity depends on the type of fluid(air,water,salt water,seamen)and its temperature.
Example Blue whale
Length (m) 30m body length could use tail length 4m maybe
Velocity (m/s) 20 km/h = 5.5 m/s
Kinematic Viscosity for sea water at a proper temperature (m^2/s) 0.000000138
https://www.engineeringtoolbox.com/water-dynamic-kinematic-viscosity-d_596.html
Re = (30 m * 5.5 m/s)/ 0.000000138 = 127 x10^6
Grasshopper flying
Length (m) body length is about 2 cm = 0.02 m
Velocity (m/s) 5 m/s
Kinematic Viscosity (m^2/s) 15 x 10^-6
Re 16,700
Kinematic Viscosity (m^2/s) can be found here
https://pdfs.semanticscholar.org/483d/1829c6f6599b66f6ce2478ad6b7bebce0608.pdf
2. Below is a table with data from the circulation system of a dog (Schmidt-Nielsen 5th addition p. 105 Table 3.5 Vessel geometry from Burton 1972 based on dog mesentery tissue). Calculate the diameter of the vessels in cm. The vessels are circular in section, calculate the total area and compare that with what is in the table. Then calculate the total and cumulative (add each stage up) volumes. % volume is just the total Compare your results with the measured volumes in the table and comment. I think you should be able to cut and paste this table in a spreadsheet for easy calculation.
Vessel Type
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diameter (mm)
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diameter (cm)
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Number of Vessels
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Total area of all Vessels (cm2)
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Calculated total area (no. x area per vessel) (cm2)
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Approx. length of each vessel (cm)
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Calculated Total Volume = tot. Area x length (cm3)
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Cumulative total volume (cm3)
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Measured Volume (cm3)
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% total volume
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From Melbin and Noordergraaf (ml)
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% total volume
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aorta
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10
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1
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0.8
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40
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100
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large arteries
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3
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40
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3
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20
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300
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arterial branches
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1
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2400
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5
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5
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arterioles
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0.02
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40000000
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125
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0.2
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sum of arteries
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190
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50
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capillaries
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0.008
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1.2E+09
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600
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0.1
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sum capillaries
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60
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250
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venules
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0.03
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80000000
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570
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0.2
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300
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veins
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2
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2400
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30
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5
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2200
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large veins
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6
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40
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11
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20
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vena cava
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12.5
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1
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1.2
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40
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sum of venous
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680
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300
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total of all
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930
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3. Using Bishop’s paper (Bishop, C.M., 1997. Heart mass and the maximum cardiac output of birds and mammals: implications for estimating the maximum aerobic power input of flying animals.Philosophical Transactions of the Royal Society B: Biological Sciences,352(1352), pp.447-456.) on scaling of heart function, using the graphs and the equations estimate the aerobic capacity of a 100 g bird by his two methods (see methods on pg. 450). In figure 4 Bishop compares mean heart mass as a % of body mass for families of birds from two sources. What does Bishop conclude from this figure? Do you have any additional thoughts?
The author is using data about heart function to estimate metabolic rate. Study the methodology described in the attached 1995 paper pg. 2154 (Bishop, C. and Butler, P., 1995. Physiological modelling of oxygen consumption in birds during flight.Journal of Experimental Biology,198(10), pp.2153-2163.)
The basic idea is that metabolic rate (ml of O2 consumed per min) can be calculated as the product of the heart rate (beats per min), the stroke volume (ml of blood) and difference in between the fractional volume of the oxygen contents of arterial and mixed venous blood in ml of oxygen per ml of blood (ml of O2 per ml of blood). Each of these 3 elements scales with body mass. (See equation 1 in the 1997 paper.)