Instrumentation Measurement & Lab

Mechanical Sensors

Work the problems below. To receive any credit, you must show all work. You may submit your work in a word processing document or in a pdf file. Graphic files are not acceptable submissions. Your file submission document should be entitled Week4AYourGID (replace YourGID with your specific GID).

1. A copper metal wire is used as a strain gauge. The resistivity is 1.68×10-8 Ω.m at 20. The length and cross-sectional area of the wire are 5mm and 4*10-4 m2. The material elongates by an amount of 0.2mm in 0.2mm increments until it reaches 6mm in length. Assuming the volume remains constant, calculate the resistance at each length. You should use the standard equation for the resistance of a metal. What is that equation? Fill in the table below. Show all calculations. Calculate the difference in resistance between the resistance at each length and the resistance before strain is added. Also, calculate the change in resistance using the approximation found in equation 5.12 of your text. How does the change in length change the resistance of the gauge? Is it linear? Why or why not? (You can use Excel to create a plot and paste it in your submission if you want?) How good is the approximation?

LengthCross-sectional areaResistanceInitial resistance (at 5mm)Change in the resistanceChange in resistance using Eq.5.125mm     5.2mm     5.4mm     5.6mm     5.8mm     6mm     

1. A tensile force of 2150 N is applied to a 12 m steel beam with a cross-sectional area of 5.2 x 10-4 m2. Find the strain on the beam.
2. A strain gauge has a GF (Gauge factor) = 2.03 and R = 120 ohms and is made from wire with = 0.0034/℃ at 25℃. The dissipation factor is given as PD = 25mW/℃. What is the maximum current that can be placed through the strain gauge to keep self-heating errors below 1u (1 micro) of strain?
3. The atmospheric pressure is 14.5 psi. If the absolute pressure is 2,865.6 psi, what is the gauge pressure?
4. What is the gauge pressure in (a) kPa, and (b) N/cm2, at a distance 5.5 ft below the surface of a column of water?
5. What is the flow rate in liters per second through a pipe 32 cm in diameter, if the average velocity is 2.1 m/s?
6. A conveyer belt is traveling at 27 cm/s, and a load cell with a length of 0.72m is reading 5.4 kg. What is the flow rate of the material on the belt?