On the Frictional Resistance of a Plate

Abstract

The equations of motion of the viscous fluid are not yet solved generally. So they are solved, neglecting inertia terms or terms of small order as in Prandtl's boundary layer equations when the thickness of boundary layer is small. However if we investigate the equations of motion in detail we will find that the variation of the effect of viscosity by the place in case to deduce the viscosity terms are not taken into account. So the author found general equations of motion, taking into account these effects. The flow will change by Reynold's and Mach's number. So the equations of motion are written in the form of zero dimension in order to represent explicitly the effect of Reynold's and Mach's number. When Mach's number is given by some power of the thickness of boundary layer at the trailing edge we can solve the equations of motion, assuming properly the velocity distribution, the variation of viscosity terms and the boundary conditions. In Prandtl's boundary layer theory the velocity at the leading edge is assumed to be zero in spite of that the thickness of boundary layer is zero. So the rate of change of the velocity at the leading edge becomes to be infinity and such is not conceivable. Therefor the author assumed that the velocity at the leading edge is equal to the velocity of the general flow, decreases gradually along a plate and becomes to be zero at a point on a plate. By this assumption the author found that the frictional resistance is created only on this part and is zero on the remaining part.The formula for correction of the frictional resistance is one of important problems to discuss the resistance of ship. By this solution the author abtained the formulae for the frictional resistance coefficient in which all effects of the pressure, the temperature, the density, the length and the surface condition are taken into account.