On Dines' Pressure-tube Anemometer (Continued)

Abstract

In my previous paper, I discussed the inertia effect of float of Dines' tube-anemometer. Here I have intended to discuss the effect of friction of pipe-walls on the air-currents.
I derive the method of calculation of time-lag and modification of record in the case of squall and lull.
The relation between velocities of air-current in the pressure and suction tubes w₁, w_{_??_} and motion of float dx/dt is approximately given or
where α: uppermost radius of float.
R₁, R₂: radius of pressure and suction tubes respectively.
When the velocities of air-current in the tubes are laminar, we have
where μ: viscosity of air.
L₁, L₂: length of press. and Sue. tubes respectively.
p₁, p₂: air pressure at above and below the float.
pα, pβ: wind press. and suction press. at head portion of the anemometer.
(1) is written as
It is transformed as
since p₁-p₂=cm²X₂, pα-pβ=cm²X'₂
where X is the rise of float which is keeping with p₁-p₂, and X' is supposed position of float to keep with pα-pβ.
The solution of (3) when X'=coast and at t=0 X=X₀ are
This formula is used for the motion of float when the wind varies discontinuously from X₀ to X'. Adopting the numerical values for a, R, L, etc. we can estimate the time lag and mode of modification in special case above mentioned.
If the motions in the pipes are turbulent moi ons, we have.
D: experimental constant.
The relation between X' and X is
When X'=constant and at t=0, X=X₀, we have
If the value of D is known we can calculate time lag T₀ numerically. It is independent of wind difference X'-X, and differs from the case of laminar flow.
At all events, experiment of the anemometer at actual condition is necessary.
But only from rough estimation by the above formulae, it seems plausible, that the anemograph which in this country commonly used of pipes of 7.5-10.0 metre length and 1cm diameter cannot records successfully the wind varying more rapidly than 10sec. period.
In conclusion, I wish to express my sincere thanks to Dr T. Okada, Director of the Central Meteorological Observatory, for his valuable information on this subject.