Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/206

§ 134 The expression then becomes:—

in which $$C = 32.2\ k / \rho,$$ and for air at 10 degrees C. and 760 mm. pressure we have $$\rho = .078 ,$$ whence,—

The equation thus becomes:—

The equation is identically the same in C.G.S. absolute units, and the constant is of the same value; that is to say, $$P =$$ dynes per square c.m., $$V =$$ c.m. per second and $$\rho$$ grammes per cubic c.m. If we express $$P$$ in grammes per square c.m., and $$V$$ in metres per second, and substitute for $$\rho$$ for air at 10 degrees C., we obtain the equation in the form:—

If the velocity is given in English miles per hour it is sometimes convenient to have the expression in the form:—

§ 135. 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 $$C$$ 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 $$\frac{55}{70}$$ or approximately four-fifths of that in the case of air.

This difference is undoubtedly due to the lower kinematic viscosity of water, which is less than air in the ratio of 1 : 14. The nature of the relationship connecting the function kinematic viscosity and the changes in the value of the constant, is not very