Mathematics and Biology

Conclusions Radial Dependence

Math Awareness Month 1999

Poiseuille's Law: A Visualization of Flow

We now consider combinations of the parameters changing. As in all of the earlier visual explorations of the flow, each graph will have a black portion referring to the current values, while the red portion refers to the standard values. The table below corresponds to 5 percent changes in the pressure (P), viscosity (V) and radius (R) (+ or -). Recall that the standard values are P=50 mmHg, n=0.05 P, and r=0.015 mm.

Challenge! See if you can guess which of the situations will occur:

  • Parameters change, but the velocity and flow do not.
  • The flow goes up, but the maximum velocity does not.
  • The flow goes down, but the maximum velocity does not.
  • The flow stays the same, but the maximum velocity goes up.
  • The flow stays the same, but the maximum velocity goes down.
If one of these situations does not occur for the specific values chosen below, will it ever occur? When or why not?

Click on the links to see the graphics:
P-V-R-
P-V-
P-V-R+
P-R-
P-
P-R+
P-V+R-
P-V+
P-V+R+
V-R-
V-
V-R+
R-
Standard
R+
V+R-
V+
V+R+
P+V-R-
P+V-
P+V-R+
P+R-
P+
P+R+
P+V+R-
P+V+
P+V+R+


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D. Brian Walton is supported by a National Science Foundation Graduate Research Fellowship.