Don S. Lemons

We model an elastomeric pump that causes a viscous antibiotic fluid to flow from a pressurized, elastic, spherical reservoir through a horizontally oriented, cylindrical tube to a blood vessel. This flow, under the right conditions, becomes steady state, axially symmetric, Poiseuille flow. As a result, we can determine the length of time for the antibiotic fluid to infuse in terms of the physical properties of the fluid, of the elastomeric ball, of the tube, and of the blood vessel into which the antibiotic infuses. We also obtain a condition that signals toxicity effects and suggest a design that minimizes or eliminates this effect. This analysis is consistent with earlier experimental investigations into the flows of antibiotics from elastomeric pumps.

We describe the physics of the “Windkessel effect” and its role in smoothing the output of water produced by piston-driven pumps found in early fire engines and modern residential well houses. We also construct a simple, analytical model of its operation and apply this model to the Windkessel in Richard Newsham's 1725 fire engine. We find that Newsham's Windkessel reduces the variations in the pump output stream from a high of 80% to a low of 16%.

We demonstrate that the various equilibria that can be realized by two, identical, inflated, party balloons, each attached to one end of a rigid plastic tube, are stable—a demonstration based on A N Gent’s equation of state, which relates the pressure of the air contained with a thin elastic sphere to the sphere radius. Measurements on 12 inch party balloons illustrate these stable equilibria.

The frequency of the first digits of numbers drawn from an exponential probability density oscillate around the Benford frequencies. Analysis, simulations and empirical evidence show that datasets must have at least 10,000 entries for these oscillations to emerge from finite-sample noise. Anecdotal evidence from population data is provided.

According to Benford's first digit law, the frequency of appearance of the first digit d taken from various sets of data is log(1+(1/d)) where d = 1, 2,…9. I present a thermodynamic derivation of this law that follows from the unbiased partitioning of a conserved quantity whose pieces may fragment and combine.

A Student's Guide to Entropy - August 2013