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The definition of absolute and percentage error allows to find the result for the total error in the pressure measurement is:
P = ( 1000 ± 2 ) kPa
ΔP = ±2 kPa
The magnitudes is a quantity that in addition to its value has an error due to the instruments or measurement method used, therefore the correct way to express a value is:
Magnitude = value ± absolute error
Statistical errors can be expressed in several ways:
- Absolute (Δx). It corresponds to the uncertainty or appreciation of the instruments or the propagation of uncertainty in the equations.
- Relative (e_r). Indicates the fraction of the error, it is the relationship between the absolute error and the magnitude.
- Percentage (e%). It is the relative error expressed as a percentage or relative error by 100%
In all measurements, the worst case is always taken, that is, all errors go in the same direction.
They indicate the percentage errors due to non-linearity 0.15% and the error due to hysteresis 0.05%. the measurement value is P = 1000 kPa.
Let's look for the absolute errors.
[tex]e_r = \frac{\Delta P}{P} = e%/100[/tex]
[tex]\Delta P = P \ \frac{percentage \ error }{100}[/tex]
We apply this expression to each type of error.
Non-linearity.
[tex]\Delta P_1 = 1000 \ \frac{0.15}{100}[/tex]
ΔP₁ = 1.5 kPa
Hysteresis.
[tex]\Delta P_2 = 1000 \ \frac{0.05}{100}[/tex]
ΔP₂ = 0.5 kPa
The total absolute error in the worst case is the sum of the two errors,
[tex]\Delta P_{total} = \Delta P_1 + \Delta P_2[/tex]
[tex]\Delta P_{total}= 1.5 +0.5 \\\Delta P_{total} = 2 kPa[/tex]
The measurement should be given in the following way:
P = 1000 ± 2 kPa
In conclusion using the definition of absolute and percentage error we can find the result for the total error in the pressure measurement is:
P = ( 1000 ± 2 ) kPa
ΔP = ±2 kPa
Learn more here: brainly.com/question/15114851
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