Carleton Engineering SCE Faculty A. Adler Courses MCG4150 Midterm 2005 |

## MCG4150: Midterm 2005
Directions:
You have 80 minutes to complete this exam.
Each question has equal marks.
This is a closed book exam; however,
you are permitted to bring a 8.5" × 11"
sheet of notes into the exam.
You are permitted to use a calculator.
You may not communicate with anyone during the exam except the instructor.
You may make assumptions to simplify the problems as long a they don't change the calculations by more than 10%. You may use the following conditions for your calculations: - Atmospheric pressure, P
_{atm}: 101.3 kPa - Density of air at P
_{atm}: 1.21 kg/m^{3} - 1 cmH
_{2}O = 98 Pa
### 1. Esophageal balloon CatheterIn order to estimate pleural pressure, an esophageal balloon catheter is used. The catheter is 1.5m long with an inner diameter of 1mm. In order to inflate the balloon, a pressure of 20 cm H_{2}O is applied, and giving the balloon a volume of 2 ml. Assume that the compliance of the catheter is zero and the compliance of the balloon is infinite.**1A.****Estimate the compliance and inertance of the gas in the catheter**.**answer:**Volume Bubble = 2e-6 m3 Volume Catheter = 1.5*pi*(1e-3/2)^2 = 1.18e-6 m3 Absolute Pressure at 20cmH2O = 101.3 + 20/9.8 = 103.34 kPa Density at 20cmH2O = (1.21)*(103.34)/(101.3) = 1.23 (can ignore) Inertance in catheter = rho*L/pi/rē = (1.23)*1.5/pi/(1e-3/2)^2 = 2.35e6 kg/m4 Compliance in catheter = V/P = pi*rē*L/P = pi*(1e-3/2)^2*1.5/103340 = 1.14e-11 m5/N Compliance of bubble = V/P = 2e-6/103340 = 1.94e-11 m5/N**1B.**Based on the compliance and inertance, the catheter may be modelled using lumped parameter model.**Estimate the resonance frequency (f**_{n}) of the catheter based on these parameters**answer:**Effective Inertance Model bubble as cylinder of 2cm x 1cm2 Radius = sqrt(1/pi) = .562cm Inertance of bubble = rho*L/pi/rē = (1.23)*0.02/pi/(5.62e-3)^2 = 248 kg/m4 ==> Ignore Effective Inertance = 2.35e6 kg/m4 Effective Compliance = 3.08e-11 m5/N Freq = (1/2/pi)*1/sqrt(Inertance*Compliance) = 1/2/pi/sqrt(2.35e6*3.08e-11)= 18.7 Hz Absolute Pressure at 20cmH2O = 101.3 + 20/9.8 = 103.34 kPa Density at 20cmH2O = (1.21)*(103.34)/(101.3) = 1.23 (can ignore) Inertance in catheter = rho*L/pi/rē = (1.23)*1.5/pi/(1e-3/2)^2 = 2.35e6 kg/m4 Compliance in catheter = V/P = pi*rē*L/P = pi*(1e-3/2)^2*1.5/103340 = 1.14e-11 m5/N Compliance of bubble = V/P = 2e-6/103340 = 1.94e-11 m5/N### 2. Measurement of obstructive lung disease**2A.**Measurement of esophageal pressure allow calculation or airways resistance (R_{aw}) Briefly discuss a simple mechanical model of the lungs and indicate the role of R_{aw}and its relation to obstructive lung disease.**2B.**The pressure sensor is based on a semiconductor strain guage placed on a diaphragm which bends under pressure.**Sketch a diagram of a such pressure transducer.**The compliance of the diaphragm is its ratio of deformation to pressure change.**If the strain guage were made of metal instead of semiconductor, would the diaphragm be required to be more or less compliant?**
Last Updated: $Date: 2006-03-06 10:30:58 -0500 (Mon, 06 Mar 2006) $ |