A diaphragm pressure transducer uses the deflection of a circular membrane to indicate the pressure. The membrane is composed of a steel alloy with an elastic modulus of E = 30,000,000 psi, Poisson's ratio of µ = 0.33, and density of p = 0.28 Ibm/in³. The diaphragm has a radius of a = 0.625 in. and a thickness of t = 0.125 in. The transducer has a 10 psi maximum reading. a. What is the resonant frequency for the diaphragm? b. Consider frequencies well below resonance. If you would like to know the pressure to within 0.25% of full scale, how accurately must the membrane deflection be measured (in inches)? Neglect the uncertainties in the dimensions and material properties of the diaphragm.

A diaphragm pressure transducer uses the deflection of a circular membrane to indicate the pressure. The membrane is composed of a steel alloy with an elastic modulus of E = 30,000,000 psi, Poisson's ratio of µ = 0.33, and density of p = 0.28 Ibm/in³. The diaphragm has a radius of a = 0.625 in. and a thickness of t = 0.125 in. The transducer has a 10 psi maximum reading. a. What is the resonant frequency for the diaphragm? b. Consider frequencies well below resonance. If you would like to know the pressure to within 0.25% of full scale, how accurately must the membrane deflection be measured (in inches)? Neglect the uncertainties in the dimensions and material properties of the diaphragm.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Pressure Vessels

The term pressure vessel refers to a closed container that contains gas or liquid at a different pressure than environment pressure. The pressure vessels have a wide scale of applications in our day-to-day lives and other industrial places. Some common examples of pressure vessels are gas cylinders, autoclaves, compressor vessels, etc.

Question

A diaphragm pressure transducer uses the deflection of a circular membrane
to indicate the pressure. The membrane is composed of a steel alloy with an
elastic modulus of E = 30,000,000 psi, Poisson's ratio of u = 0.33, and density
of p = 0.28 Ibm/in³. The diaphragm has a radius of a = 0.625 in. and a
thickness of t= 0.125 in. The transducer has a 10 psi maximum reading.
a. What is the resonant frequency for the diaphragm?
b. Consider frequencies well below resonance. If you would like to know the
pressure to within 0.25% of full scale, how accurately must the membrane
deflection be measured (in inches)? Neglect the uncertainties in the
dimensions and material properties of the diaphragm.

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