8 TURBULENT FLUID MOTION AND SKIN FRICTION. 
extension to very long planks is equivalent to extending the curve beyond D so that 
it approaches the base-line ultimately. On the other hand, the analogy with the problem 
of flow through pipes suggests that the curve approximates ultimately to a line at a 
finite distance above the base-line. In the latter case, the best single power must 
increase again at some stage and ultimately approach V* again. However, it is generally 
recognized that all that can be said is that any reasonable extension of the curve beyond 
D must lie within certain limits, that in fact being the statement made by W. Froude* 
in this respect; we are not able yet to decide between alternative methods. 
14. In conclusion a few remarks may be made on the general problem of ship resist- 
ance. It is usual to divide up the total resistance into three parts: frictional, eddy- 
making, and wave-making resistance. An alternative method is to think of the direct 
action upon each element of the wetted surface; this action may be resolved into a 
normal pressure p and a tangential force R at each point. The integrated effect of R 
gives the total skin friction, while the resultant of the pressure distribution may be called 
the body or form resistance. In the ship problem it is assumed that the latter corre- 
sponds in the main to the wave resistance, together with that due to eddy-making of 
the more obvious kind; however, in general, the distribution of normal pressure and of 
tangential force will be interdependent and will each be affected by all the circumstances 
of the motion. It would be of interest to have some case analysed in this way, with the 
pressure distribution determined experimentally. This method has been adopted in the 
corresponding problem in aeronautics, which is simpler in some respects. For an airship 
envelope, in the form of a surface of revolution, the pressure distribution can be found 
experimentally ; the difference between the resultant and the total resistance then gives 
the skin friction.t If there were, for the same case, experimental determinations of the 
distribution of velocity over the envelope, it would be possible to compare the total skin 
friction with the resultant of a distribution of tangential force k pv? taken over the surface. 
Results for submerged bodies in water might be deduced from those in air by the law 
of similarity ; but it would be preferable if direct results could be obtained, experimentally, 
for the distributions of normal pressure and of velocity for simple forms intermediate 
between the plank and the ordinary type of ship model. 
* W. Froude, Brit. Assoc. Reports, 1874, p. 255. 
7 Ci. L. Bairstow, Applied Aerodynamics, p. 357. 
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