Friday, September 02, 2016

The Spectre Of Bernoulli

I used to know an elderly man who had taught Latin in a prestigious fee-paying school in the east of England. ‘Many of my pupils,’ he recalled, ‘would wonder, quite reasonably, why they should compulsorily read a language which no one speaks.’ He smiled to himself. ‘My reply was always the same: when you leave my tutelage, I doubt that any of you will retain anything but a tenuous grasp of Latin. However, your English should be exemplary.’

He must have had the ‘dead language’ argument bowled at him from every conceivable angle for forty years; and yet, that same straight bat of his always dealt comfortably with it. Even so, I am certain that almost all students have come up against a subject which they were not only thrilled to see the back of, but also confident that they would never need to revisit in later life. I was one. I studied ‘Further Physics’ – even the name is scary – just prior to my first spell at university. One of its constituent topics – Bernoulli’s principle (Figure 99.1) – practically drove me nuts, not least because it seemed to fly in the face of common sense. Luckily, my Physics teacher, who was much smarter than he looked, forced the penny to drop just in time for the exam.

Figure 99.1: Bernoulli’s magnum opus (pardon my use of Latin), published in 1738, was the first ‘bible’ of fluid mechanics. Readers fluent in Latin will be able to translate its front cover without too much difficulty.

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That was thirty years ago. Since then, I have morphed into a multidisciplinary life scientist, and Bernoulli’s principle had, thankfully, never raised its contrary head – until this year. While sponsor confidentiality forbids me to elaborate on current research, I think I am at liberty to state that it involves something called hydraulic conductance, which appertains to the behaviour of pressurized fluids permeating biological tissues.

Like nearly all laboratory kit these days, the analytical equipment I am using is entirely computer-controlled. An ingenious microfluidics system controls fluid pressure through a digital sensor and records subsequent tiny changes in flow rate. I have spent most of this year conducting a comprehensive validation program, proving that this rather expensive toy does what it says on the tin. If I increase the system pressure, the fluid flows faster in direct proportion.

Last week, the plot thickened. If I exchanged the sensor for one with different optimal settings, the flow data came out different. According to the computer, the fluid movement had slowed. How come? Surely, given that only the sensor had been changed, it should have yielded the same results as before.

Then came an ominous ‘Eureka’ moment: Bernoulli had returned to haunt me. He had also solved the puzzle. Daniel Bernoulli (1700-82) (Figure 99.2) was a Swiss mathematician who studied fluidic movement under controlled pressure. His world-renowned principle states that if there is a pressure reduction in a system of steady fluid movement, its flow rate will increase, and vice versa (Figure 99.3). I discovered that the tubing passing through the second sensor had a larger cross-sectional area than that of the first. A-ha! This had increased the internal pressure and thus reduced the speed of flow (Figure 99.4).

Figure 99.2: The godfather of hydrodynamics

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Figure 99.3: This simple schematic demonstrates the relationship between system pressure and fluid flow.

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Figure 99.4: A theoretical chart showing my recent findings. I had initially expected the two curves to be more or less superimposed on one another. Bernoulli put me right.

Copyright © 2016 Paul Spradbery

As we still say in Latin: Quod Erat Demonstrandum.

Copyright © 2016 Paul Spradbery