What is the sensitivity at 20 °C for the deflection/load characteristic?
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20 mm/kg.
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What is the sensitivity at 20 °C for the deflection/load characteristic?
20 mm/kg.
By how much does the temperature fall during the balloon's travel?
0.75 °C.
What is defined as the static sensitivity of a system?
K = D b0/a0.
What does the time constant (θ) represent in a system?
The time taken for the output quantity to reach 63% of its final value.
What type of instrument is a deadweight pressure gauge?
A null-type instrument.
What is inaccuracy in measurement often quoted as?
A percentage of the full-scale (f.s.) reading of an instrument.
What is the maximum error expected in a pressure gauge with a range of 0–10 bar and an inaccuracy of ±1.0% f.s.?
0.1 bar.
What distinguishes smart instruments from non-smart instruments?
Smart instruments incorporate a microprocessor.
What type of instrument is a cam switch counter?
A digital instrument.
What is the time constant of the temperature transducer in the balloon example?
15 seconds.
What do dynamic characteristics of a measuring instrument describe?
The behavior between the time a measured quantity changes and when the instrument output attains a steady value.
Give an example of a passive instrument.
A pressure-measuring device that translates fluid pressure into pointer movement.
What tolerance might a resistor have?
Perhaps 5%.
What is the range or span of an instrument?
The minimum and maximum values of a quantity that the instrument is designed to measure.
What could be the actual value of a resistor with a nominal value of 1000 W and a tolerance of 5%?
Anywhere between 950 W and 1050 W.
How does sensitivity drift change with temperature from 20 °C to 30 °C?
It increases from 20 mm/kg to 22 mm/kg.
What is the slope of the straight line in the output characteristic graph indicative of?
It represents the sensitivity of measurement.
What are passive instruments?
Instruments that do not require an external power source and operate using the energy from the measured signal.
What limits the improvement of measurement resolution?
Limitations on the magnitude of external energy input, heating effects, and safety reasons.
What is the equation representing a zero order instrument?
q0 = b0 qi / a0 = K qi, where K is the instrument sensitivity.
What is the null point in a deadweight gauge?
The datum level reached when the downward force of weights balances the fluid pressure.
What defines a first order instrument?
An instrument that behaves according to the equation where all coefficients except a0 and a1 are assumed zero, showing a time-dependent response.
What determines when an instrument needs recalibration?
When its characteristics have drifted from standard specifications by an unacceptable amount.
What is the process of recalibration?
Adjusting the instrument to align with standard specifications.
What limitation does a cam switch counter have?
It can only count whole revolutions and cannot detect motion less than a full revolution.
How are instruments classified?
Instruments can be subdivided into separate classes according to criteria such as accuracy, cost, and applicability.
How is non-linearity defined in measurement instrumentation?
Non-linearity is defined as the maximum deviation of any output reading from the straight line fit.
What are the types of characteristics that can affect instrument performance?
Zero drift, sensitivity drift, and both zero drift and sensitivity drift.
Which instruments commonly exhibit hysteresis?
Passive pressure gauges and Prony brakes.
Can you give an example of a zero order instrument?
A potentiometer, which measures motion and changes output voltage instantaneously as the slider is displaced.
How is measurement sensitivity calculated for the platinum resistance thermometer?
By dividing the change in resistance (7 Ω) by the change in temperature (30 °C), resulting in 0.233 Ω/°C.
Why are null-type instruments generally more accurate than deflection-type instruments?
Because calibration of weights is easier than calibrating a linear-characteristic spring.
What is the definition of accuracy in the context of instruments?
A measure of how close the output reading of the instrument is to the correct value.
How is repeatability defined?
Closeness of output readings when the same input is applied repetitively under constant conditions.
Why might a thermometer with an inaccuracy of ±0.5 °C be adequate in some situations?
Because small variations around a certain temperature do not significantly affect human comfort.
What can affect the dynamic characteristics of an instrument?
Environmental conditions outside specified calibration conditions.
What is hysteresis in measurement instruments?
Hysteresis is the difference in output readings for the same input due to factors like springs and friction.
What does sensitivity of measurement indicate?
It measures the change in instrument output when the quantity being measured changes by a given amount.
What is the initial ground temperature (T0) given in the problem?
10 °C.
What affects the accuracy of a deadweight gauge?
The calibration of the weights used.
What is the equation for a first order instrument?
a1 dq0/dt + a0 q0 = b0 qi.
What does precision describe in measurement?
An instrument’s degree of freedom from random errors.
How does the frequency of usage affect an instrument's calibration?
The rate of divergence from standard specifications varies according to the frequency of usage.
What are the response characteristics of second order instruments?
They exhibit specific output patterns based on the magnitude of the measured quantity over time.
What factors should be considered when choosing an instrument for a specific application?
Accuracy, sensitivity, linearity, and reaction to ambient temperature changes.
What is the difference between accuracy and precision?
Accuracy refers to how close a measurement is to the true value, while precision refers to the consistency of repeated measurements.
How can zero drift typically be removed?
By calibration.
What distinguishes active instruments from passive instruments?
Active instruments produce output from an external power source, while passive instruments derive output solely from the quantity being measured.
What is a zero order instrument?
An instrument that behaves according to the equation where all coefficients except a0 are assumed zero, resulting in immediate output change following a step change in the measured quantity.
What is the significance of calibration for measuring instruments?
Calibration ensures that an instrument conforms to stated static and dynamic patterns of behavior.
What can be assumed about a new instrument from a manufacturer?
It will have been calibrated and will initially behave according to the specifications.
Why is it important to choose instruments with an appropriate range?
To maintain the best possible accuracy in instrument readings.
What does the term 'measurement uncertainty' refer to?
It is frequently used in place of inaccuracy.
What is the distance traveled by the balloon in 15 seconds?
75 meters.
How are maximum input and output hysteresis expressed?
As a percentage of the full-scale input or output reading.
What is the output reading of the instrument for large values of t?
Always 0.75 °C less than it should be.
What is the sensitivity drift per degree Celsius?
0.2 (mm per kg)/°C.
What does tolerance define in measurement?
The maximum error that is to be expected in some value.
What is a common example of an analogue indicating instrument?
A liquid-in-glass thermometer.
What units are used to measure sensitivity drift?
(angular degree/bar)/°C.
What is an example of a tolerance figure for crankshafts?
Machined with a diameter tolerance quoted in microns (10^-6 m).
How do digital displays compare to analogue displays in terms of error?
Digital displays are not very prone to error unless the human reader is careless.
What type of instrument is a pressure gauge considered?
A deflection-type instrument.
What happens to the output e.m.f. of a thermometer when plunged into boiling water?
It does not rise instantaneously to 100 °C but approaches it over time.
If a pressure of 2 bar produces a deflection of 10 degrees, what is the sensitivity of the instrument?
5 degrees/bar.
What are active instruments?
Instruments that require an external power source to operate.
What is the temperature reading reported by the balloon at an altitude of 5000 metres?
-39.25 °C.
What is an example of threshold in a car speedometer?
The threshold is about 15 km/h, meaning no output is observed until this speed is reached.
What does resolution in an instrument refer to?
The lower limit on the change in input that produces an observable change in output.
What parameters are used to express the coefficients in the second order instrument equation?
Static sensitivity (K), undamped natural frequency (ω), and damping ratio (ζ).
What is sensitivity drift?
The change in sensitivity of an instrument due to environmental factors or aging.
What factors can cause sensitivity drift and zero drift?
Temperature changes, aging of components, and environmental conditions.
What is the velocity at which the submarine dives?
0.5 metres/second.
What are the expressions relating static sensitivity, undamped natural frequency, and damping ratio?
Static sensitivity = K/c, Undamped natural frequency = sqrt(c/a), Damping ratio = b/(2*sqrt(ac)).
What is a passive pressure gauge?
A type of instrument that measures pressure without requiring external energy input.
What are the three types of instrument performance characteristics mentioned?
Low precision, low accuracy; High precision, low accuracy; High precision, high accuracy.
Why are passive instruments generally cheaper to manufacture?
They have a simpler construction compared to active instruments.
What is the trade-off when choosing between active and passive instruments?
Balancing measurement resolution requirements against cost.
What type of instrument is a liquid-in-glass thermometer considered?
A first order instrument.
What is the bias (zero drift) at 30 °C?
5 mm.
What is the purpose of calibration in instruments?
To ensure output readings match those of a second standard instrument with known specifications.
What is a typical cause of dead space in instruments?
Backlash in gears.
How do manufacturers specify the threshold for instruments?
Some quote absolute values, while others quote it as a percentage of full-scale readings.
What happens to the output of a first order instrument after a step change?
The output changes over time rather than instantaneously.
What is the formula for the temperature reported by the balloon at time t?
Tr = 10 - 0.75e^(-t/15) - 0.05t + 15.
What does the exponential term in the temperature formula represent?
It represents the transient response of the temperature reading.
What is the resolution of a car speedometer with subdivisions of 20 km/h?
5 km/h, as speed cannot be estimated more accurately than this.
What is the typical damping ratio range for commercial second order instruments like accelerometers?
0.6 to 0.8.
What is the zero drift coefficient?
A measure of zero drift in volts/°C related to temperature changes.
What are the types of damping responses for a second order instrument?
Heavy damping, critical damping, and light damping.
What is the desirable relationship between the output reading of an instrument and the quantity being measured?
The output reading should be linearly proportional to the quantity being measured.
What is a major drawback of indicating devices?
Human intervention is required to read and record a measurement.
Give an example of an active instrument.
A float-type petrol tank level indicator that modulates an external voltage source.
What is a key difference in measurement resolution between active and passive instruments?
Active instruments allow greater control over measurement resolution through adjustment of external energy input, while passive instruments have limited resolution based on their design.
What forms can the external power source take in active instruments?
The external power source is usually electrical but can also be pneumatic or hydraulic.
Why is it important to consider time lag in control systems?
Because there is a delay between a measured quantity changing and the instrument indicating that change.
What is hysteresis in the context of instrument output characteristics?
The non-coincidence between loading and unloading curves.
What are static characteristics of measuring instruments concerned with?
The steady-state reading that the instrument settles down to, such as accuracy.
What are the advantages of null-type measuring instruments?
They provide high accuracy and are less affected by external factors.
What type of instrument is described by the standard equation for a second order system?
Second order instrument.
What is required for analogue instruments to interface with microcomputers?
An analogue-to-digital (A/D) converter.
What is the time constant associated with the temperature reading lag?
15 seconds.
How is sensitivity drift quantified?
By sensitivity drift coefficients for each environmental parameter.
Which damping is usually targeted when designing a second order instrument?
Critical damping.
What does tolerance describe in the context of measuring instruments?
The maximum deviation of a manufactured component from a specified value.
How is non-linearity usually expressed?
As a percentage of the full-scale reading.
How does a deadweight gauge measure pressure?
By balancing weights on a piston against fluid pressure until a null point is reached.
What types of signals can measurement systems output?
Electrical voltage, electrical current, optical signal, or pneumatic signal.
What factors can cause an instrument's behavior to diverge from its specifications?
Mechanical wear, dirt, dust, fumes, and chemicals in the operating environment.
What is the significance of static characteristics in instruments?
They determine the performance of an instrument under specified standard calibration conditions.
What does the cam in a cam switch counter do?
Opens and closes a switch on each revolution.
What type of measuring instrument is the altitude-measuring instrument described in the balloon example?
Approximately zero order.
What is the zero drift per degree Celsius?
0.5 mm/°C.
How do digital instruments interface with control computers?
They can be interfaced directly without conversion.
What influences the resolution of an instrument?
The fineness of the output scale divisions.
What is a common example of an instrument prone to zero drift?
A bathroom scale.
What happens when an instrument suffers both zero drift and sensitivity drift?
The output characteristic is modified, showing combined effects.
What is the deflection/load characteristic of a load cell at 21 °C?
At 21 °C, the deflection for loads of 0, 50, 100, 150, and 200 kg are 0.0, 1.0, 2.0, 3.0, and 4.0 mm respectively.
What is the general differential equation for a second order measuring instrument?
The general form is: a(d²y/dt²) + b(dy/dt) + cy = Kx, where a, b, c are parameters of the system.
What is a petrol-tank level indicator an example of?
A float pivot output device used to measure liquid levels.
What is the general relation between input and output in a linear, time-invariant measuring system?
It can be expressed using a specific mathematical equation involving constants.
What happens to the equation for dynamic characteristics when considering step changes in the measured quantity?
It simplifies to a more manageable form.
What is the significance of understanding how different types of instruments respond to changes in measurand?
It helps in practical applications of measurement.
What is the formula for calculating sensitivity of measurement?
Sensitivity = scale deflection / value of measurand producing deflection.
What is the relationship between temperature at altitude (Tx) and ground temperature (T0)?
Tx = T0 - 0.01x.
What is the threshold of an instrument?
The minimum level of input required before a detectable change in output reading occurs.
How can the first order instrument equation be rearranged?
q0 = (b0/a0) qi [1 + (a1/a0) D].
What is the main characteristic of an analogue instrument?
It provides a continuous output that varies as the measured quantity changes.
How does a digital instrument differ from an analogue instrument?
A digital instrument has an output that varies in discrete steps, allowing only a finite number of values.
How is resolution sometimes specified?
As an absolute value or as a percentage of full-scale deflection.
How does zero drift affect an instrument's readings?
It modifies the zero reading, causing a constant error over the full measurement range.
Why are calibrations and specifications of an instrument only valid under controlled conditions?
Because variations in ambient conditions like temperature and pressure can affect performance.
What type of output do indicating instruments provide?
An audio or visual indication of the measured quantity.
What is the relationship for temperature at a depth of x metres?
T_x = T_0 - 0.01x, where T_0 is the surface temperature.
What causes hysteresis in a pendulum-scale mass-measuring device?
Different magnitudes of friction forces depending on the direction of movement.
What is dead space in measurement instruments?
The range of input values over which there is no change in output value.
At what velocity does the balloon rise?
5 metres/second.
Which type of instrument is more convenient for regular use?
Deflection-type instruments.
What is more commonly quoted for an instrument, accuracy or inaccuracy?
Inaccuracy figure.
What does reproducibility describe?
Closeness of output readings for the same input when measurement conditions vary.
What is an example of an analogue instrument mentioned in the text?
The deflection-type pressure gauge.
What are the disadvantages of using an A/D converter?
It adds cost and introduces conversion time, which can impair control accuracy.
How is measurement sensitivity expressed?
As the ratio of output (y) to input (x).
What is the time constant of the temperature transducer in the unmanned submarine?
50 seconds.
What is the error in the temperature reading at 10 seconds and 50 metres altitude?
0.36 °C.
What are the disadvantages of deflection-type measuring instruments?
They can be affected by external factors and may provide less accuracy compared to null-type instruments.
What are static characteristics of measuring instruments?
They include accuracy, precision, sensitivity, and repeatability.
What is the ideal damping ratio for critically damped response in instruments?
0.707.
What is zero drift?
The shift in the zero point of an instrument's output when no input is applied.
What does sensitivity drift define?
The variation in an instrument’s sensitivity of measurement as ambient conditions change.
How can hysteresis affect the output of a variable inductance displacement transducer?
Due to magnetic hysteresis in the iron core.
What is the relationship between hysteresis and dead space?
Any instrument that exhibits hysteresis also displays dead space.
What is zero drift also known as?
Bias.
How can instruments be divided based on their output?
Into indicating instruments and those with a signal output.
What is an example of a component affected by temperature changes in instruments?
The modulus of elasticity of a spring.
Why is the distinction between analogue and digital instruments important?
Due to the growth of microcomputers in automatic control systems.
What are the two main ways environmental changes affect instruments?
Zero drift and sensitivity drift.
What happens to the output of a second order instrument with a damping ratio of 0?
It exhibits constant amplitude oscillations.
How does the deflection/load characteristic change at 35 °C?
At 35 °C, the deflection for loads of 0, 50, 100, 150, and 200 kg are 0.2, 1.3, 2.4, 3.5, and 4.6 mm respectively.
What is the difference between precision and accuracy?
High precision does not imply high accuracy; a high precision instrument may have low accuracy.
What happens to the exponential term as time increases?
It approximates to zero.
What is the effect of increasing the damping ratio in a second order instrument?
Reduces oscillations and overshoot.
