1683skin-friction coefficient increase with the increasing values of m as in the case of constant properties for all x*.The results indicate that the variations of thermal conductivity and viscosity to the local Nusselt number and the local skinfriction coefficient are quite significant. Care must be taken in using the constant properties solution.The variational method combined with CSMP program has been found to be fruitful in the solution of this complex problem. Particularly, it was found that the CSMP program in solving this type of problem is very simple and straightforward. The great potential of such a combined technique and the CSMP program are still to be fully exploited in other engineering problems.

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A digital-computer program has been written for calculating the viscous drag of streamlined bodies of revolution in constant-density axial flow. The integral approach adopted incorporates recently improved methods for predicting the transition point and for calculating the turbulent boundary layer. The Inputs to the computer program are the body geometry, the associated invlscid pressure distribution, and the body-length Reynolds number. Agreement of calculated and measured drag coefficients is good, particularly in cases where the transition point is predicted accurately. ADMINISTRATIVE INFORMATION The work reported here was supported by the in-house independent research program of the David W. Taylor Naval Ship Research and Development Center (DTNSRDC) and funded under Task Area ZR-023-0101, Work Unit 1-1541-002. Comparison of the computed results with towlng-tank measurements shows (1) that the accuracy of the two Granville methods for predicting transition is roughly equal if transition occurs on the forebody and (2) that the drag is predicted accurately if the transition prediction is accurate, The turbulent-boundary-layer theory on which the calculations are based includes the Schoenherr frictional line; the program can be forced to reproduce the Schoenherr line as its predicted drag coefficient by setting the pressure gradient equal to zero, setting the body radius equal to a constant sufficiently large value, and forcing transition at the nose. Granville uses the Schoenherr line as a baseline for his method because of its classical and scientific importance in turbulentboundary-layer theory. In the figures in this report which present calculations done by this theory, the Schoenherr line has been drawn in for comparison; it is an easy matter to draw in other lines which are in widespread use, such as the 1957 International Towing Tank Conference correlation line for ship models. A method for predicting the viscous drag of a body of revolution has also been reported by Nakayama and Patel. It is similar to the method of Granville reported here in that an entrainment equation is used (but with a more restricted one-parameter system) and in that careful consideration is given to the region near the tail where the boundary layer is thick. Four alternative methods of predicting the transition point are available, one of which is that of Granville. Good agreement with measured results is reported. A second method, reported by Cebeci, Mosinskls, and Smith, uses the more time-consuming differential formulation of the boundary-layer equations, with an eddy-viscosity profile. These authors provide two alternative methods for predicting transition, one of which is that of Granville. Again, good agreement with measured results is reported.

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