Application of the Poiseuilleequation to the treatment of laminar flowmeter calibration data

An equation relating volume flow rate through a laminar flowmeter to differential pressure and other parameters is developed. The development begins with the Poiseuille equation, to which a correction for inertial pressure loss is made. Calibration data are fitted to a corrected equation relating volume flow rate, differential pressure, density, viscosity, mass flow rate and a parameter K with dimension of inverse length. The estimate of the value of K and of the two coefficients is determined by an iterative procedure. The calibration equation used in inferring the volume flow rate through the flowmeter is the solution of an equation that is quadratic in the volume flow rate. A set of laminar flowmeter calibration data for air, nitrogen, helium and argon illustrates the method. The relative residual standard deviation at mid-range for the calibration equation for the set of data is 0.055%.