Because Q dp1/2and is not linear, the calibration will not be linear. The term
‘linearity’
should not be applied directly. The nonlinear calibration result is just a normal consequence of the physics. However, a signal conditioning stage could be inserted within the signal path to produce a linear output. This is done using logarithmic amplifiers. To illustrate this, plot the calibration curve in Problem 1.33 on a log-log scale (see C1.6). The result will be a linear curve. Alternately, you could take the log of each column and plot them on a rectangular scale to get that same result. A logarithmic amplifier (Chapter 6) performs this same function (as the plot scale or log key) directly on the signal. A linearity measure can then be extracted with some meaning. As flow rate is the variable varied and pressure drop is the variable measured in this calibration, pressure drop is the dependent variable. The flow rate and the fixed values of area and density are independent variables.