ENGE808 Assignment 1

Online Submission Due: 11:59pm, 12 April 25, 2026

15 Questions; Total Mak 100 (equally distributed)

Assignment 1A (8 Questions)

Read Chapters 1-3, Measurement Systems Application and Design (E. O. Doebelin) book  and solve the following problems.  

1. Give three specific examples of measuring-instrument applications in each of the following areas:
   (a) monitoring of processes and operations,
   (b) control of processes and operations, and
   (c) experimental engineering analysis

2. (a) Make a functional block diagram for each of the figures below:
   (b)Specify which is active or passive, null or deflection type why?
   
   
3. Consider a man, driving a car along a road, who sees the opportunity to pass and decides to accelerate.
   (a) If the light waves entering his eyes are considered input and accelerator-pedal travel is taken as output, is the man functioning as an active or a passive transducer?
   (b) If accelerator-pedal travel is considered input and car velocity as output, is the automobile engine an active or a passive transducer?
4. The discharge coefficient Cq of an orifice can be found by collecting the water that flows through during a timed interval when it is under a constant head h. The formula is Consider error are the following:
   
   (a) The errors are the absolute limits.
   (b) The errors are +/-3s limits.
5. What percentage error may be expected in measuring the voltage across R₅ if R₁ = R₂ = R₃ = R₄ = R₅ = 100 and R_m = 1000 ohms? If R_m = 10,000 ohms?
   
6. A mercury thermometer has a capillary tube of 0.010-in diameter. If the bulb is made of a zero-expansion material, what volume must it have if a sensitivity of 0.10 in/F” is desired? Assume operation near 70’F. If the bulb is spherical and is immersed in stationary air, estimate the time constant.
7. A first-order instrument must measure signals with frequency content up to 100 Hz with an amplitude inaccuracy of 5 percent. What is the maximum allowable time constant? What will be the phase shift at 50 and 100 Hz?
8. Find the transfer function of a spring scale (Figure below) whose mass is negligible. Show that the steady-state time lag for a ramp input is the same whether mass is zero or not.
   

Assignment 1B (7 Questions)

Read Chapters 3, 4, Measurement Systems Application and Design (E. O. Doebelin) book, and solve the following problems. 

1. In an analog-computer study it is desired to simulate a random atmospheric turbulence whose mean-square spectral density ∅_𝑡𝑡 (𝜔𝜔) is adequately represented as 10/(1 + 𝑂𝑂.𝑂𝑂𝑂𝑂𝑂𝑂1 𝜔𝜔²), where 𝜔𝜔 is in radians per second. A white-noise generator having ∅_𝑤𝑤n (𝜔𝜔) = 10 is available. Select a suitable filter configuration and numerical values to follow the generator and produce the desired ∅𝑡𝑡 (𝜔𝜔). The output of the noise generator should “see” a filter input resistance of 10,000 ohms.
2. Tests on a gyroscope show that it can withstand any random vibration along a given axis if the frequency content is between 0 and 1,000 rad/sec and the rms acceleration is less than 80 in./sec². This gyro is to be mounted in a rocket where it will be subjected to acousticpressure-induced vibration. The transfer function between pressure and acceleration and the mean-square spectral density of pressure are as given in the figure below. Will this gyro withstand the vibration?
   
3. The output of a potentiometer is to be read by a recorder of 10,000 ohms input resistance. Nonlinearity must be held to 1 percent. A family of potentiometers having a thermal rating of 5 watts and resistances ranging from 100 to 10,000 ohms in 100-ohm steps is available. Choose from this family the potentiometer that has the greatest possible sensitivity and also meets the other requirements. What is this sensitivity if the potentiometers are single-turn (360°) units?
4. What resolution is possible with a 60-turn wire-wound potentiometer using appropriate gearing?
5. In a Wheatstone bridge, leg 1 is an active strain gage of Advance alloy and 120 ohms resistance, leg 4 is a similar dummy gage for temperature compensation, and legs 2 and 3 are fixed 120-ohm resistors. The maximum gage current is to be 0.030 amp.

   (a) What is the maximum permissible d-c bridge excitation voltage? (Use this value in the remaining parts of this problem)
   (b) If the active gage is on a steel member, what is the bridge output voltage per 1,000 psi of stress?
   (c) If temperature compensation were not used, what bridge output would be caused by the active gage increasing temperature by 100F° if the gage is bonded to steel? What stress value would be represented by this voltage? Thermal-expansion coefficients of steel and Advance alloy are 6.5 X 10-6 and 14.9 X 10-6 in./(in.-F°), respectively. The temperature coefficient of resistance of Advance is 6 X 10-6 ohm/ (ohm-F°).
   (d) Compute the value of a shunt calibrating resistor that would give the same bridge output as 10,000-psi stress in a steel member.
   

6. Perform an analysis similar to that leading to Eq. (1), assuming output loaded with Rm, for the following:
   (a) The circuit of Fig. a
   (b) The circuit of Fig. b
   (c) The circuit of Fig. c
   (d) The circuit of Fig. d
   
   
7. Air exhibits a dielectric breakdown at fields of about 50,000 volts/in. What limitation does this impose on the ultimate sensitivity of a capacitance transducer such as in the following figure?