Analytical Formula for the Mean Velocity Profile in a Pipe Derived on the Basis of a Spatial Polynomial Vorticity Distribution

The derivation of the mean velocity profile for a given vorticity distribution over pipe cross-section is presented in this paper1. and are axisymmetric, which means that radius only variable. importance vortex field flow analysis discussed paper. polynomial function with four free parameters chosen distribution. Free determined using boundary conditions. There also two exponents polynomial. These based on comparison analytical formula experimental data. Experimental data taken from Princeton superpipe consist 26 profiles wide range Reynolds numbers (Re). This more precise than previous one it possible to use number <31,577; 35,259,000>. easy use, integrate, or derivate. empirical formulas as Re included All information prediction mentioned It necessary know average v(av), R, be able predict turbulent pipe.