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Measurements in Fluid Mechanics 058:180:001 (ME:5180:0001) Time & Location: 2:30P - 3:20P MWF 218 MLH Office Hours: 4:00P – 5:00P MWF 223B-5 HL Instructor: Lichuan Gui [email protected] http://lcgui.net Lecture 12. Pressure-measuring instrumentation 2 What exactly is pressure? Stress tensor External forces: F1 , F2 ,, Fn Normal stresses: 11 , 22 , 33 Shear stress: 12 , 13 , 21 , 23 , 31 , 32 (12 = 21 , 13 = 31 , 23 = 32) Pressure - average normal stress (mechanical definition) - positive when compressive, negative when tensile - absolute pressure Hydrostatic pressure difference between two locations A and B – fluid density g – gravitational acceleration z – vertical upwards direction 3 What exactly is pressure? Reference pressure in surrounding environment, e.g. atmospheric pressure patm Gauge pressure: pg = p - patm Total (stagnation) pressure P0: - Static pressure: p Incompressible flow p – pressure – fluid density V – fluid velocity - Dynamic pressure: V2/2 Compressible flow – ratio of specific speeds M – Mach number Pressure changes across a normal shock wave - Upstream of the shock wave: p, p0 - Downstream of the shock wave: p’, p0’ 4 Pressure-measuring instrumentation Liquid-in-glass manometers e.g. a liquid-filled, U-shaped manometer – three different fluids with densities 1, 2, and 3 – fluid 2 must be a liquid – pressure difference between position A and B: – if both fluid 1 and 3 are gases: Static sensitivity of U-tube manometer k = 1/(2g) (fluid 1 and 3 are gases) – static sensitivity increased w. decreasing density of fluid 2 Inclined manometer k = 1/(2gcos) – static sensitivity increased with >0 5 Pressure-measuring instrumentation Liquid-in-glass manometers Error sources of liquid-filled manometer – variations of fluid densities – non-vertical positioning – capillarity – meniscus-reading errors Prandtl-type micromanometer – to reduce capillarity and meniscus-reading errors 6 Pressure-measuring instrumentation Deadweight gauges - Highly accurate device - Cumbersome in use - Standards for calibration of other pressuregauges Elastic-element gauges - Widely used, general-purpose pressure gauges 7 Pressure-measuring instrumentation Electrical pressure transducers - provide electric output signal dependent on pressure - based on electric property change (e.g. resistance, capacitance, or inductance) - result from pressure-induced displacement or deformation - require excitation power for operation - require calibration - susceptible to temperature and humidity effects - superior frequency response (great advantage over liquid-in-gas and mechanical pressure gauges) Variable-capacitance transducers As pressure increases, the flexible conductive plates will move farther apart, changing the capacitance of the transducer. This change in capacitance is measurable and is proportional to the change in pressure. 8 Pressure-measuring instrumentation Variable-resistance transducers Variable-reluctance pressure transducer 9 Pressure-measuring instrumentation Piezoelectric transducers - may be a passive sensor Strain-gauge transducers 10 Wall-pressure measurement Linear variable differential transformer When the core is centered, equal voltages are induced in two oppositely wound secondary windings and the output voltage is zero. A change of pressure moves the core, increasing the voltage induced in one secondary and decreasing the voltage induced in the other. The change in output (differential) voltage is thus a measure of the pressure. Semiconductor pressure transducers Semiconductor Distortion Gauge 11 Homework - Read textbook 8.1-8.3 on page 179 - 193 - Questions and Problems: 1 on page 203 - Due on 09/23 12