SCALE EFFECT LAB EXERCISE
Definition
The scale effect is a physical phenomenon.
Stated simply, as a an object increases in size the ratio of its surface area to volume decreases.
The change in the ratio occurs because the surface area increases as the square and the volume as the
cube.
Surface area of a cube
S
S
Surface area = S X S X 6 = 6S
2
Volume of a cube
S
S
S
Volume = S x S X S = S 3
Plot the shaded data below on a sheet of graph paper. X axis = Side (cm), Y axis = Ratio
Side (cm) = X
Surface Area = S X S X 6
Volume = S X S X S
Ratio = Y
0.5
1
2
3
4
5
6
7
1.5
0.125
6
1
24
8
54
27
96
64
150
125
216
216
294
343
12
6
3
2
1.5
1.2
1
0.86
State in your own words the meaning of these data.1
1See
the end of this handout for how not to answer this question.
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Lab Activities
Surface to Volume Ratio  Milk cartons
Measure the surface area of the milk cartons
Pint (cm2 )
Side
Quart (cm2 )
Half Gallon cm2 )
1
2
3
4
5
6
Total Surface =
Measure the volume of the cartons
Pint (ml)
Quart (ml)
Half Gallon (ml)
Total Volume=
Calculate the surface to volume ratio
Pint
Quart
Half Gallon
X =Total Surface
Total Volume
Y = Ratio of S/V
Plot the ratio on a sheet of graph paper
Group discussion: Assuming that the density of milk = 1 g/ml, what implications do these data have
regarding the potential maximum size of terrestrial organisms?
Scale Effect and Diffusion  Use the lab computer for the following exercise
Time how long it takes the simulation of a diffusing molecule to leave the four circles on the screen.
Circle
Radius (cm)
Trial 1
(sec)
Trial 2
(sec)
Trial 3
(sec)
Average
(sec)
1
2
3
4
Plot the results on a sheet of graph paper: X axis = radius, Y axis = average time
Group discussion: What implications do these data have regarding the maximum potential size of cells?
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Scale Effect and Flow  Graduated cylinders
Measure the diameters of the openings drilled into the plastic graduated cylinders provided. Time
how long it takes for 500 ml to drain through the hole (ml/sec)
Cylinder
Trial 1
(ml/sec)
Diameter
(mm)
Trial 2
(ml/sec)
Trial 3
(ml/sec)
Average
(ml/sec)
A
B
C
D
Plot the results on a sheet of graph paper. X axis = diameter, Y axis = Average rate
Group discussion: What do these data indicate regarding the rate of flow of blood through blood
vessels and air through airways?
Scale Effect and Flow  Computer Simulation
Load PhysioEx in computer and go to module Cardiovascular Dynamics and Experiment Vessel
Resistance.
Perform the flow exercise above using the following settings:
1. Pressure = 200 mmHg; Viscosity =3; Length = 25
2. Vary the radius starting at 1 mm and increase in increments of 0.2, that is the first recording is
at 1.0, then next at 1.2, the next 1.4, etc., up to a radius of 6.0
3. Record the data and graph the results. Compare your graph with the computer generated
graph.
What is the significance of the shape of the graph?
Radius
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
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Flow Radius Flow Radius Flow Radius Flow Radius Flow
Rate
Rate
Rate
Rate
Rate
2.1
3.2
4.3
5.4
2.2
3.3
4.4
5.5
2.3
3.4
4.5
5.6
2.4
3.5
4.6
5.7
2.5
3.6
4.7
5.8
2.6
3.7
4.8
5.9
2.7
3.8
4.9
6
2.8
3.9
5
2.9
4
5.1
3
4.1
5.2
3.1
4.2
5.3
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