Exercise_6 - Exercise 6 A&EP 264 Fall 2007 The Viscometer...

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Exercise 6, A&EP 264, Fall 2007 The Viscometer Reference on reserve in the Physical Sciences Library: A. Dinsdale and F. Moore, Viscosity and its Measurement, Reinhold Publishing, 1962. In this exercise a falling sphere viscometer, as described in detail in the above reference, is used to measure the viscosity of glycerine. The apparatus, shown schematically in Figure 1, consists of a vertical glass cylinder, filled with glycerine, into which steel and glass spheres of various diameters are dropped. The cylinder is equipped with optical sensors that record the terminal velocities of the spheres as they fall through the glycerine. The apparent viscosities measured with the viscometer must be corrected for the influence of the cylinder walls, which retard the motion of the spheres, to obtain the “true” viscosity of the fluid. This “wall effect” depends on the dimensionless ratio “r/R” of the sphere’s radius “r” to that of the confining cylinder “R”. The object of Exercise 6 is to measure the variation of the apparent viscosity of glycerine as a function of r/R and compare the results with two empirical expressions that may be used to account for the wall effect. Figure 1: In this experiment terminal velocities are measured for spheres falling through a viscous fluid contained in a vertical cylinder. The time at which the sphere interrupts each of 4 beams that intersect the fluid column is recorded (using a modified version of Timer.cpp). Each of the 4 beams has a light emitter and a light detector.
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The optical sensors are infrared emitter/detector pairs. The output of the emitter is infrared light at a wavelength near 1000 nm (one micron), modulated to produce a 900 Hz square wave. An LM567 integrated circuit (IC) is used with the emitter/detector pair. The emitter is an infrared LED (light emitting diode) and the detector is a silicon photo-transistor. The LM567 IC employs a voltage controlled oscillator (VCO) to set the modulation frequency of the emitter. The light seen by the detector consists of the frequency modulated light of the emitter superimposed on background infrared “noise”. In contrast to the emitted light, the background infrared light near 1000 nm is not modulated at the 900 Hz frequency, but rather exhibits a broad spectrum of random noise frequencies (with perhaps a 60 Hz modulated component from the room lights). The LM567 IC uses a “tone decoder” to separate the modulated light received from the emitter from the unmodulated background infrared light. The tone decoder is
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