Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/205

Rh determinations, the corrected mean of a great number of experiments made by Professor Langley, exactly a century later, gave an almost identical result.

Langley, in presenting his final result, $$k = .00166$$ as the corrected mean of his experimental records, states that the possible errors of experiment are such as to leave a probable uncertainty of about 10 per cent. The temperature and pressure corresponding to the above value are given as 10 degrees $$C.$$ and 736 m.m. mercury; if we reduce to sea level we obtain Hutton's result, $$k = .0017,$$ almost exactly.

Dines 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 $$\times$$ 1 inch greater in the proportion of 8 to 7 than for a square of equal area. The value of $$k$$ 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. This 6 per cent, difference is an actual disagreement. The planes employed by Langley for his determination were of square form.

§ 134. Resistance a Function of Density.—Employment of Absolute and Other Units.—In order that the expression $$P = k\ V^2$$ should be dimensional the constant $$k$$ must include a quantity of the dimensions $$\frac{m}{l^3} .$$ This can be eliminated by introducing the density of the fluid into the expression.

Employing British Absolute Units, let:—
 * $$P =$$ pressure in poundals per square foot.
 * $$V =$$ velocity feet per second.
 * $$\rho\;=$$ density of fluid, lbs. (mass) per cubic foot.
 * $$C =$$ constant.