Question

10) A pressure sensor consisting of a diaphragm with strain gauges bonded to its surface has the following information in its specification: Ranges: 0 to 1400 kPa, 0 to 35 000 kPa Non-linearity error: ±0.15% of full range Hysteresis error: ±0.05% of full range What is the total error due to non-linearity and hysteresis for a reading of 1000 kPa on the 0 to 1400 kPa range?

Answer 1

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.

                 $e_r = \frac{\Delta P}{P} = e%/100$

                 $\Delta P = P \ \frac{percentage \ error }{100}$

             

 We apply this expression to each type of error.

Non-linearity.

                $\Delta P_1 = 1000 \ \frac{0.15}{100}$  

                ΔP₁ = 1.5 kPa

Hysteresis.

                $\Delta P_2 = 1000 \ \frac{0.05}{100}$  

                ΔP₂ = 0.5 kPa

The total absolute error in the worst case is the sum of the two errors,

              $\Delta P_{total} = \Delta P_1 + \Delta P_2$  

              $\Delta P_{total}= 1.5 +0.5 \\\Delta P_{total} = 2 kPa$

               

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

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