In a gas thermometer, following the perfect gas law (PV =

Identify the sensing element, signal-modification element, and indicator or recorder element in the following measurement devices. You may need to research the principles of operation to answer the questions. (a) A mechanical automobile speedometer. (b) An automobile fuel gage. (c) A human body thermometer with a liquid crystal display.

You find a micrometer (a thickness-measuring device) of unknown origin and use it to measure the diameter of a steel rod that is known to have a diameter of 0.5000 in. You use the micrometer to make 10 independent measurements of the rod diameter, and the results are 0.4821,0.4824,0.4821,0.4821,0.4820,0.4822,0.4821, 0.4822, 0.4820, and 0.4822. Estimate the systematic error and the maximum random error in these measurements.

You attempt to determine the validity of a bathroom scale by repeatedly placing 20 lb of accurate weights on it. Ten readings were obtained with values of 20.2, 20.2, 20.6, 20.0, 20.4, 20.2, 20.0, 20.6, 20.0, and 20.2 lb. Estimate the systematic error and the maximum random error of the measurements.

Identify which of the following measurements are intrusive and which are nonintrusive. Justify your answers. (a) Measuring a person's oral temperature with a thermometer. (b) Measuring the speed of a bullet using high-speed photography. (c) Determining the temperature of a furnace by an optical thermal-radiation device. (d) Measuring the speed of an automobile with a radar gun.

Determine whether the following measurements are intrusive or nonintrusive. You may need to research the details of the measurement process. (a) Measuring amperage of current in a wire using clamp-on ammeter. (b) Measuring flow of fluid in a pipe by installing an orifice meter in the pipe. (c) Measuring composition of gases in an exhaust using a device which optically measures transmitted infrared radiation. (d) Determining the surface temperature of a pipe using a thermometer that measures the emitted infrared radiation. (e) Rotational speed of a shaft indicated by a strobotachometer.

Determine if the following errors are of random or systematic type. Justify your response. (a) A digital scale, that always shows 0.2 lb when no weight is applied. (b) Vibration of the needle of an automobile speedometer. (c) Consistent temperature difference between two sensors reading the air temperature in the same room.

Determine if the following errors are systematic or random. Justify your response. (a) Effect of temperature on the circuitry of an electronic measurement device. (b) Effect of parallax on the reading of a needle-type analog voltmeter. (c) Effect of using an incorrect value of emissivity in the readings of an infrared thermometer.

Determine if the following errors are systematic or random. Justify your response. (a) Variation in a pressure transducer reading due to variation in ambient temperature. (b) Noise induced into the output of an instrument due to magnetic fields in the surroundings. (c) Variation in the makeup of a drug due to a malfunction of a mixer in a drug mixing tank.

Determine if the following uncertainties are systematic, random, or a combination that needs further analysis. (a) Va riation in the yield of com in a field; explain. (b) Deterioration of asphalt/concrete in a highway; explain. (c) Variation of height of the same type of trees in an orchard; explain. (d) Variation in the drying time of concrete columns in construction of a highway; explain.

Determine if the following variations are systematic, random, or a combination that needs further analysis. (a) Va riation in the number of visits per day of a popular website (e.g. Yahoo) for a given day of the week (e.g. Thesday); explain. (b) Variation in the rider-ship of a bus or train line in a given day of the week (e.g. Monday); explain. (c) Variation in the rider-ship of a bus or train line in different days of the week; explain.

A digital device has a decimal indicator showing up to three significant figures. An equivalent analog device has 1000 divisions over the span. Can we determine which instrument is more accurate? Explain.

A velocity-measuring device can measure velocities in the range 0 to 50 mls. What is the span of this device?

What are the spans of the following pressure gages: (a) The gage measures pressure from 5 psig vacuum to 50 psig. (b) The gage measures pressure from 70 cm Hg vacuum to 200 kPa. (c) The gage measures pressure from 10 kPa to 150 kPa.

You need to measure a pressure, which has a value between 60 kPa and 100 kPa. Four pressure-measuring devices of comparable quality are available: Device A, range 0-100 kPa Device B, range 0-150 kPa Device C, range 50-100 kPa Device D, range 50-150 kPa Which device would you choose? Explain your answer.

digital output voltmeter has an input range of 0 to 30 V and displays three significant flgur.es XX.x. The manufacturer claims an accuracy of 2% of full scale. With a voltage readmg of 5 V, what are the percent uncertainties of the reading due to accuracy and resolution?

Digital voltmeters often have a choice of ranges. The ranges indicated on a typical voltmeter are 0-3, 0-30, 0-300, and 0-3000 AC volts. The output is represented with four significant digits. Determine the following: (a) Resolution uncertainty for each range (in V). (b) If it has an accuracy of 2% of full range for each range, determine the absolute uncertainty of measurement in each case. (c) Determine the relative (percent of reading) uncertainly if, for a measurement of 25 volts, the ranges 30,300, or 3000 were used.

A bourdon gage (a mechanical device to measure gage pressure, the pressure relative to atmospheric pressure), which has a range of 0 to 50 psi, reads +0.5 psi when measuring atmospheric pressure. It is claimed to have an accuracy of 0.2% of full-scale reading. What is the expected error in the measurement of 20 psi in psi and in percent of reading? How can you reduce the error produced by this gage?

A voltmeter with a range of 0 to 100 V reads 2 V when the leads are shorted together. The manufacturer claims an accuracy of 4% of full scale. Estimate the maximum error when reading a voltage of 80 V in both volts and as a percentage of reading. If the voltmeter is adjusted so that the reading when the leads are shorted together is 0 V, estimate the maximum percent error when reading 80 V.

You have two temperature gages available to you. One measuring 100-500C and the other with a range of 100-1000C. Each has an uncertainty of 2 % of its span. To measure a temperature of about 300C, which of the two will you choose? Why?

A pressure sensing device has an electrical output and is approximately linear. When the input is 100 kPa, the output is 5 mV and when the output is 1000 kPa, the output is 125 m V. What is the sensitivity of this device?

A pressure sensing device has an electrical output and is approximately linear. When the input is 10 psi, the output is 10 mV and when the input is 100 psi, the output is 150 mY. What is the sensitivity of this device?

In a gas thermometer, following the perfect gas law (PV = mRT), pressure change is an indication of temperature variation if the volume is constant. Determine if an increase in initial filling pressure will change the sensitivity of the device.

Figure P2.23 shows the variation of the output of a sensor with respect to its input. (a) How does the sensitivity of the sensor vary fro.m A to C? (b) Would you recommend using the device in the A-B or B-C range?

In a multirange instrument (such as a multirange voltmeter), how does sensitivity vary with range? Explain.

In an analog output device, which has a voltage output, how can you increase the sensitivity of the device?

A common fluid-flow measuring device is called a venturi tube. (See Chapter 10.) For this device, the fluid-flow rate, Q, is proportional to the square root of the measured pressure drop, t1P, (Q = C(t1P)1I2 where Cis approximately constant). (a) Derive a relation for sensitivity of Q with respect to t1P. (b) Determine if the sensitivity increases or decreases with an increase in the pressure drop. (c) Would you recommend such a device for larger or smaller values of the pressure drop?

A linear device converts an input force into an output displacement. The ideal sensitivity of this device is 0.1 cm/N and the input span is 200 N. What will be the ideal output span? What will the output span be if the actual sensitivity is 0.105 cmIN? What will the % error in the output span be?

A static calibration is performed on a pressure-measuring device called a bourdon gage with a nominal range of 0 to 100 psi. The results of this calibration are shown in Table P2.28. (a) Plot the data and fit a straight line through them. (b) Prepare a deviation plot and estimate the accuracy and repeatability errors, both as a percentage of the output span.

A sttic calibration is performed on a bourdon gage pressure measuring device with a nommal range of 0 to 1 MPa. The results of this calibration are shown in Table P2.29. (a) Plot the data and fit a straight line through them. (b) Using deviation plots, estimate the accuracy and repeatability errors, both as a percentage of the output span.

A force measuring device called a load cell has an electrical voltage output. A load cell with a range of 0 to 100 N has a nominal full-scale output of 40 m V. By using accurate weights, this load cell has been calibrated and the results are presented in Table P2.30. (a) Plot the results and fit a straight line to the data. Find the formula for this straight line in both the form force = f(mV output) and the form mV output = g(force). (b) Compute the deviations between the data and the correlating straight line. Prepare a deviation plot and determine the accuracy and repeatability of the load cell.

What is the difference between static and dynamic calibration? What type of calibration would you recommend for (a) an oral thermometer, (b) a pressure gage used in a water line, and (c) a car speedometer? Explain your reasoning.

The time constant of a temperature-measuring device is 0.5 s. This device is used to measure the temperature of the air in a room that is changing at about 5C/h. Do you consider this to be a static or a dynamic measurement? Why?

The time constant of a temperature-measuring device is 0.5 s. This device is used to easure the temperature of the air in a room that is changing at about lF/h. Do you consIder this to be a static or a dynamic measurement? Why?

Two thermometers, one larger than the other, are dipped in ice water from ambient temperature. Which one will reach the equilibrium temperature faster? Why?

Explain the usefulness and appropriateness of the concepts of time constant, response time, rise time, and settling time for (a) zero-order, (b) first -order, (c) overdamped second-order, and (d) underdamped second-order systems.

Answer the following questions: (a) High-intensity discharge (HID) lamps come to full brightness in about 5-10 minutes. A light meter, which can detect instant light level, is used to record the light output of an HID lamp. Is this a static or dynamic measurement? Explain. (b) The pressure inside a car cylinder cycles at 1500 times per minute at an engine speed of 3000 rpm (revolutions per minute). Can a pressure transducer with a response time of 2 seconds resolve the pressure variation? What value response time would you recommend? Explain your answers. (c) A utility meter measures the power draw of a plant every 15 minutes. One of the highest consumers of power in the plant is a 100 kW heater that goes on for 4 minutes every other lO-minute period. Will the meter accurately record the variation in power consumption of this plant? Explain.

You have just purchased an old sports car. When the engine is idling at 1000 rpm, you press on the throttle and change the rpm to 3000 rpm. You notice that the tachometer overshoots 3000 rpm and oscillates for a couple of seconds about 3000 rpm until it becomes steady. Is this a zero-, first-, or second-order measuring system? What characteristic of the tachometer might you change to eliminate the oscillations?

A thermometer, initially at a temperature of 20C, is suddenly immersed in a tank of water with a temperature of 80C. The time constant of the thermometer is 2 s. What temperature will the thermometer read after 5 s?

A thermometer initially at a temperature of 75F is suddenly immersed in a tank of water with a temperature of 180F. The time constant of the thermometer is 2 s. What temperature will the thermometer read after 4 s?

A thermometer, initially at a temperature of 20C, is suddenly immersed into a tank of water with a temperature of BOC. The time constant of the thermometer is 4 s. What are the values of the rise time and the 90% response time?

A thermometer, initially at a temperature of 75F is suddenly immersed into a tank of water with a temperature of 180F. The time constant of the thermometer is 4 s. What are the values of the rise time and the 90% response time

A nominally linear electrical output force measuring device has the following manufacturer specifications: Input range Full-scale output Linearity Hysteresis Repeatability Zero balance Temperature effect on: Zero Span 0-1oo lbf 30mV 0.1 % full scale 0.08% full scale 0.03 % full scale 2 % full scale 0.002 % full scale/oF 0.002 % of reading/oF The device is used in an environment where the ambient temperature is not controlled and can vary between 50 and 95F. For an input of 20 lbf: (a) What will be the nominal output voltage? (b) Estimate the uncertainty due to each of the error sources that can be determined from the specifications. Express the uncertainties both in age of reading. Do not attempt to combine the uncertainties.

A nominally linear electrical output force measuring device has the following manufacturer specifications: Input range 0-1000 N Full-scale output 24 mV Linearity 0.1 % full scale Hysteresis 0.08% full scale Repeatability 0.05% full scale Zero balance 1 % full scale Temperature effect on: Zero 0.002 % full scaler C Span 0.002% of readingl C The device is used in an environment where the ambient temperature is not controlled and can vary between 10 and 35C. For an input of 200 N: (a) What will be the nominal output voltage? (b) Estimate the uncertainty due to each of the error sources that can be determined from the specifications. Express the uncertainties both in millivolts and as a percentage of reading. Do not attempt to combine the uncertainties.