It is a well-known fact that the coefficicnt of the molecular viscosity in air is found to increase with air temperature. For instance, an empirical formula given by Grindy and Gibson is as follows
1); η=0.0001702(1+0.00329θ+0.0000070θ
2) in c. g. s. units, where θ is the temperature in Centigrades. Afterware's, some analogous empirical formulae have been obtained by Rankine
2), Millikan
(3) and others. Correspondingly, it will be seen that the coefficient of the eddy viscosity increases with air temperature. On both theoretical and observational grounds, L. F. Richardson
(1) believes that, eddy viscosity depen_??_s on the temperature difference between ground and air and on the wind velocity. In order to determine approximate'y the quanti ative relationship from the pilot-balloon observations with single theodolite; H. M. Treloar
(2) has expressed it as follows: ν=70(1+0.1
T)
V, in which
V is the wind velocity at a height of 50 meters,
T the difference of temperature in Fahr. between surface soil an_??_ air at 10 feet. Here, the basis of his method rests on the assumption that the coefficient of surface friction is a universal cons ant.
In this paper, we determined the eddy viscosity from an empirical formula of the ascending velocity of the pilot-balloon. When the compres-sibility of air has to be allowed, for the total resistance to the translation through an air of the balloon, in the corresponding directions, we are led by consideration of dimensions to a formula where α is the radius of balloon, ν is the kinematic coefficient of eddy viscosity, κ denotes the elasticity, viz. κ=ρ
dp/
dp.
V is the ascending velocity of the balloon, and ρ the air density. Also, ζ is a numerical constant depending on the nature of the surface of the balloon, and
n and
m are the constants to be determined. Here, the force
Qg is the excess of the gravity of the balloon over its total lift of the hydrogen gas, viz. where Ρ denotes the density of air, σ the hydrogen gas in the balloon, and
g the acceleration of gravity. Let
Lg denote the free lift of the balloon and
W the weight of it, hence we have
R=(
Q-
W)
g=
Lg at any height, where the balloon balanees between its resistance force and lift. It follows, substituting from (1) and (2) the coefficient of the kinematic eddy viscosity gives By using the boserved pilot-balloon's data from the double theodorite made at Haneda branch station of the C. M. O. located in the compoun 1 of the Tokyo Air-port from Sept. to Dec. in 1934, the values of
n and
m were found viz.
n=1,
m=1.591.
(1) At the stational state of the atmosphere, we may put ∂
p/∂
z=- ρ
g and
T=
Ts-δ
z, hence we have
dp/
dρ=
g/
g-δ
R_??_
RT in which
R is the gas constant and δ the lapse rate of the atmospheric temperature. Wherefore, on making these substitutions, the expression (3) becomes From the data obtained by the observations made with the double theodolites from July 1932 to August 1933 at Haneda,
(2) we found the value of_??_as the function of the surface air temperature (
ts). This empirical relation may be written in the form in c. g. s. units and
ts is in Centigrade. Let us put
v0 as the value of ν when
p=760mm,
ts=0 and at the ground
z=0, we shall have in c. g. s. units.
Now we may neglect the small terms of the developed equation of (4) for obtaining a first approximation, and by the substitution of (5) in (4), we get the equation of the coefficien of the kinematic eddy viscosity in c. g. s. units;
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