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FOR determines the slope, intercept, and correlation coefficient for the above experimental data. 9998. Figure 1-7 gives a plot of Reynolds number against power number. The figure shows that Equation 1-3 gives a perfect fit of the experimental data. Problem 1-2 In a fluid flow experiment, the volumetric rate of fluid through a pipe is dependent on the pipe diameter and slope by the following equation. 025 ft. blade turbine Y-Actual Y-Estimate 60 ~ 50 40 Power Number 3O 20 10 0 2 4 6 8 10 12 14 Reynolds Number Figure 1-7.
S. Kwong, "On the Thermodynamics of Solutions" An Equation of State Fugacities of Gaseous Solutions," Chem. , Vol. 44, 1949, p. 233. 10. Underwood, A. J. , "Fractional Distillation of Multicomponent Mixtures Calculation of Minimum Reflux Ratio," J. Inst. , Vol. 32, 1946, p. 614. 11. Gjumbir, M. and Z. Olujic, "Effective Ways to Solve Single Nonlinear Equations," Chem. , July 23, 1984, pp. 51-56. 12. , "Finding Your Roots," Chem. , April 25, 1988, pp. 85-92. 13. Sargent, R. W. , A Review of Methods for Solving Nonlinear Algebraic Equation, Foundations of Computed Aided Chemical Process Design, Engineering Foundation, New York, Vol.
N th Order Ordinary Differential Equations We consider the solutions of the Nth order differential equations of the form: ( dy d2y d3y dn-'y a n y ) ~ , ~ .. - 0 F x,y, dx dx 2 ' d x 3 '" dxn-I ' d x n (1-112) Equation 1-112 has the highest derivative of the order n, and is ordinary because there is only one independent variable, x. We can obtain a unique solution when some additional information such as values of y(x) and its derivatives at some specific values of x are known. Therefore, for an N th order equation, we require such N conditions to arrive at the unique solution y(x).