Frederick William Lanchester

“ Perforated Plates.—Dines has investigated the effect of perforations as affecting the resistance of the normal plane. In one case a plane one foot square was taken and eight circular holes, each one square inch area, were punched, as illustrated in Fig. 90; no difference of pressure could be detected whether any or all of the holes were covered or open. Mr. Dines remarks:
Fig. 90. “The eight holes together take away more than 5 per cent, of the plate, yet a difference of 1 per cent, in the pressure, had it existed, would certainly have been apparent.” ”

“ Fluids other than Air.— If the whole physical properties of a fluid were represented by the symbols in the equation, or if, the equation being as it is, the fluid were incompressible and of zero viscosity, the constant would be the same for different fluids.
The experimental determination in the case of sea-water has been made by Captain Beaufoy, and independently by R. E. Froude, the results being in close agreement. In absolute units we have:—
that is to say, the value of the constant is or approximately four-fifths of that in the case of air. ”

“ The region in the rear of the plane is occupied by the turbulent “dead-water” at a pressure below that of the undisturbed fluid. When a hole is made in the plane, the air flows through from the front to the rear under the influence of the difference of pressure between its two faces. The stream of air finding its way through the perforation carries with it an amount of momentum per second, equal to the force of which the plane is relieved. ”

“ When perforations are made of great size in proportion to the dimensions of the plane, we can conceive of the efflux stream passing en masse through the dead-water without parting with the whole of its momentum, so that in such a case the plane will be relieved of a portion of its resistance. ”

“ Dines [3] has shown that the pressure depends not only upon the velocity but also upon the shape or “contour form” of the plane, and that the pressure is least for planes of compact outline, such as a square or circular disc. In his experiments he obtained values for a rectangle 16 inches 1 inch greater in the proportion of 8 to 7 than for a square of equal area. The value of given by Dines for planes of compact form is about 6 per cent, below that of Langley; the latter value is approximately equal to Dines' result for a rectangle of 4 : 1 ratio. ”

“ Thus in an infinite strip of width the layers of fluid adjacent to the face of the plane are fed by a much greater stream area than in the case, say, of a circular disc of which is the diameter, and the spurting past the edge of the plane will be correspondingly the more vigorous; this is represented diagrammatically in Fig. 88. It is evident that the plane that causes the greater displacement of the lines of flow will experience the greater pressure. ”

“ The validity of the above reasoning is unquestionable if we are dealing with a fluid whose properties are those of the Newtonian medium; the energy of turbulence being represented by a variation in the individual velocities of the particles such as will not affect their mean velocity. ”

“ It is probable that the maximum pressure on a plane under given wind conditions is not in proportion to the area exposed, and that a small plane is liable to greater extremes, and where a maximum record is made, the absolute area exposed becomes an important factor in determining the pressure per unit. ”

“ It has been proved from the behaviour of projectiles in flight that the law breaks down when the velocity of sound is approached, and without doubt this applies also to an aeroplane when a similar velocity is reached. ”

“ It might, without departing from the form of the expression, be possible to establish an empirical relationship, and it is in any ease of interest to endeavour to ascertain the probable magnitude of the constant for the particular case when viscosity becomes vanishingly small. ”

“ For planes of highly irregular form no definite rules can be laid down. An assumption that such planes are built up of simpler components will sometimes enable the value of to be assessed; but as the whole range of values lies almost within the admittedly possible allowance for experimental error, our want of knowledge on this point is not so serious as might otherwise appear. ”

“ Both these results are higher than that given by experiment for a viscous fluid, a defect that is due to the faulty hypothesis, the Newtonian medium possessing no continuity. Newton was fully conscious of this fact.
2. The Neutonian Method (Book II., Section VII. prop. xxxvii.) .—In this proposition, [5] Newton arrives at a result for a fluid possessing continuity the equivalent of which is:—
3. ”