Effect of Variable Viscosity on Boundary Layers, With a Discussion of Drag Measurements

This work extends a previously reported investigation of the boundary-layer problem associated with the steady laminar flow of a perfect gas along a thin flat insulated plate. In the earlier study the viscosity was assumed constant and the distributions of velocity and temperature were obtained for a wide range of conditions. Part I of the present paper shows, for Prandtl number 0.733 (air) and Mach number of the undisturbed stream 2, the velocity and temperature distributions in the boundary layer under various assumed viscosity variations. Part II gives the distributions for various Prandtl numbers and Mach numbers, assuming the same viscosity functions as used by von Kármán and Tsien. Part III is devoted to a discussion of the method of interpretation of traverse tests of the efficiency and flow coefficients of nozzles or other passages. The results of Part I show that the variation of viscosity with temperature does not alter the equilibrium temperature of the plate, and hence the reading of a plate thermometer. This result is extended in Part II where it is shown that θ at the plate wall is equal to the same quantity when μ is taken constant to within 1 per cent in all cases studied. Furthermore, φU′ at the plate wall does not vary greatly, so that the drag coefficient CD is equal to 1.28/(Re)1/2 to within 5 per cent for most of the cases investigated. In Part III a passage efficiency as usually calculated is found to be subject to two errors, one of which reduces and the other of which increases the test result. The net effect is to cause the standard traverse test to give a conservative estimate of the efficiency. The flow coefficient as determined by traverse tests is somewhat higher than the correct one.