The Determination of the Density Distribution of a Gas Flowing in a Pipe from Mean Density Measurements

Information about the density distribution of a gas flowingin a pipe is obtained by measuring the mean densities alongstraight lines across the pipe. The density distribution isrepresented by a Fourier series with variable coefficients whichsatisfy a Volterra type integral equation of the first kind.This equation is solved and a numerical technique for calculatingthe solution is given.     

Two Interpolatory Cubic Splines

The third order and the uniform cubic spline are defined andshown to have O(h³) and O(h⁴) convergence respectively whenused for interpolation.