A catheter-sensor system for invasive pressure measurements has a catheter with a length of 1 m and a diameter of 2.5 mm. The catheter is filled with water at 20 C, with viscosity = 0.001 Pa.s and density = 103 kg/m3. The diaphragm elasticity Ed equals 0.5x1015 N/m5. a. Draw the simplified electrical model of the pressure measurement set-up that includes the catheter and the diaphragm and determine the transfer function of the pressure measurement system. b. Compute the natural frequency and damping ratio of this system. c. The current system has a damping ratio that is far from optimal. Suppose you are pinching the catheter for a small length lx so that the catheter diameter reduces to 0.2mm. Assuming the pinch to affect the resistance only, determine the length lx such that an optimal damping ratio = 0.7 is obtained. d. Suppose that the assumption of purely resistive effects of the pinch cannot be made. Discuss (without calculations) the consequences on the derivation of lx.
Theory and Design for Mechanical Measurements
Measurement is a term that refers to analyzing a manufactured component regarding the degree of accuracy for dimensions, tolerances, geometric profile, roundness, flatness, smoothness, etc. Measurement always involves comparing the manufactured component or the prototype with a standard specimen whose dimensions and other parameters are assumed to be perfect and do not undergo changes with respect to time.Precisely in mechanical engineering the branch that deals with the application of scientific principles for measurements is known as metrology. The domain of metrology in general deals with various measurements like mechanical, chemical, thermodynamic, physical, and biological measurements. In mechanical engineering, the measurements are limited to mechanical specific such as length, mass, surface profile, flatness, roundness, viscosity, heat transfer, etc.
Basic principles of engineering metrology
Metrology is described as the science of measurement, precision, and accuracy. In other words, it is a method of measurement based on units and predefined standards.
A catheter-sensor system for invasive pressure measurements has a catheter with a length of 1 m and a diameter of 2.5 mm. The catheter is filled with water at 20 C, with viscosity = 0.001 Pa.s and density = 103 kg/m3. The diaphragm elasticity Ed equals 0.5x1015 N/m5.
a. Draw the simplified electrical model of the pressure measurement set-up that includes the catheter and the diaphragm and determine the transfer function of the pressure measurement system.
b. Compute the natural frequency and damping ratio of this system.
c. The current system has a damping ratio that is far from optimal. Suppose you are pinching the catheter for a small length lx so that the catheter diameter reduces to 0.2mm. Assuming the pinch to affect the resistance only, determine the length lx such that an optimal damping ratio = 0.7 is obtained.
d. Suppose that the assumption of purely resistive effects of the pinch cannot be made. Discuss (without calculations) the consequences on the derivation of lx.
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