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Question 3. 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 viscosityn = 0.001 Pa.s and density p = 10 kg/m². The diaphragm elasticity Ed equals 0.5x105 N/m³. 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 Ix so that the catheter diameter reduces to 0.2mm. Assuming the pinch to affect the resistance only, determine the length Ix such that an optimal damping ratio 5 = 0.7 is obtained. d. Suppose that the assumption of purely resistive effects of the pinch cannot be made.

Question 3. 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 viscosityn = 0.001 Pa.s and density p = 10 kg/m². The diaphragm elasticity Ed equals 0.5x105 N/m³. 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 Ix so that the catheter diameter reduces to 0.2mm. Assuming the pinch to affect the resistance only, determine the length Ix such that an optimal damping ratio 5 = 0.7 is obtained. d. Suppose that the assumption of purely resistive effects of the pinch cannot be made.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Question 3. 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 viscosityn = 0.001 Pa.s and density p = 10 kg/m?. The diaphragm elasticity Ed equals 0.5x105 N/m³. 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 Ix so that the catheter diameter reduces to 0.2mm. Assuming the pinch to affect the resistance only, determine the length Ix 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 Ix. Help: Assuming laminer or Poiseuille flow, Rc can be calculated using length L (m), radius r (m) and liquid viscosity n (Pa.s) as Rc=8nL/(ar* ). Lc=AP/(dF/dt) (Pa.s²/m³ )=AP/aA where a is acceleration (m?/s). Le=m/A? =pL/(rr² ), m mass of liquid (kg), p density of fluid (kg/m³), Cd=1/Ed
Transcribed Image Text:Question 3. 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 viscosityn = 0.001 Pa.s and density p = 10 kg/m?. The diaphragm elasticity Ed equals 0.5x105 N/m³. 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 Ix so that the catheter diameter reduces to 0.2mm. Assuming the pinch to affect the resistance only, determine the length Ix 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 Ix. Help: Assuming laminer or Poiseuille flow, Rc can be calculated using length L (m), radius r (m) and liquid viscosity n (Pa.s) as Rc=8nL/(ar* ). Lc=AP/(dF/dt) (Pa.s²/m³ )=AP/aA where a is acceleration (m?/s). Le=m/A? =pL/(rr² ), m mass of liquid (kg), p density of fluid (kg/m³), Cd=1/Ed
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