Transcript Intrinsically Linear Variables

Intrinsically Linear Variables
• Can a least-squares linear regression analysis be used to
determine the best fit of (F,V) data to the nonlinear
expression V = k + bFc, where k is V when F = 0 ?
MATLAB’s polyfit Command
• Using MATLAB, x,y data can be fit and evaluated using least-squares
regression analysis.
Example: Fitting Ideal Gas Data
For an ideal gas, pVg=C, where p is pressure, V is volume, g is the specific heat
ratio, and C is a constant. Determine the best-fit value for g given the data:
Example: Fitting Hot-Wire Data
• Hot-wire anemometry can be used to measure local flow velocity. The
relationship between the flow velocity, U, and the anemometer circuit’s
voltage, E, is given by King’s Law (a form of the conservation of energy).
• For the following data, determine
A, B and n using LSLRA.
sensor
Example: Fitting Hot-Wire Data
• King’s Law can be transformed into linear intrinsic variables, where
Example: Fitting Hot-Wire Data