# The linearizer

The non-linearity of the hot wire anemometer in the measurement of speed has been emphasized. The relationship between the electric power supplied to the sensor and velocity of the fluid stream that invests it, given in Equation (3.7), for a CTA (in which Tw = const, Rw = const), can be written as

E1 = ( + bJU){Tw – Ta)Rw = A + BU = E + BU (3.15)

where E0 is the difference of potential that occurs at U = 0.

To determine the average speed of the stream, it is only necessary to measure the average voltage output of the anemometer and use the calibration curve. But this is fully satisfactory only if the level of turbulence is low; if this level is high, due to the nonlinearity of the calibration curve, the average voltage does not match the average speed but a lower speed.

In order to linearize Equation (3.15), it is necessary to pass the output of the anemometer through an apparatus with a transfer function which is the inverse of King’s law. Consider:

EOM = k(En – C )m

where M, C and k are constants.

If the output voltage of the anemometer is replaced by Ein (Equation 3.15):

Eut = k(E0 + BU – C )m

Making C = 0: Eout = k(b4u)m

making m = 2 Eout = kB2U

But kB2 = K, then Eout = KU. In this way, the output of the linearizer is a voltage proportional to velocity.

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