HEAT FROM SMALL CYLINDERS IN A STREAM OF FLUID. 
405 
of the wire an anemometer capable of giving an accurate measure of air-velocity 
without reference to a calibration in terms of some other form of wind-measuring' 
instrument. The problem is analogous to the determination of the constants of 
platinum wire for the purposes of thermometry ; in fact standard thermometer wire 
is the most suitable for the purpose of hot-wire anemometry in that its electrical 
constants are usually determined with great accuracy. 
The specifications described in the next section were carried out independently of 
any previous work, and as they offer several distinct advantages with regard to the 
construction of a practical standard of anemometry, it has been thought by the writer 
worth while to describe them in some detail. The special type of instrument developed 
may be called a linear anemometer consisting only of a single wire, and is especially 
suited for the study of turbulent flow and the analysis of sharp gradients of velocity 
such as are to be found in the neighbourhood of obstacles in streams, in jets, &c. The 
advantage to be derived from the use of a single wire lies in the fact that it is 
possible to measure with considerable accuracy the velocity in the neighbourhood of 
the wire with no appreciable disturbance of the flow at a distance of a few diameters 
away. This statement is easily verified from the classical solution of the flow of a 
stream past a cylindrical obstacle. In the case of a circular cylinder of radius a in a 
stream of a perfect fluid of undisturbed velocity V, the velocity potential of the 
point (r, 0) is given by <p — V (r + a 2 Ji’) cos 0, 0 being measured from the down¬ 
stream direction of the stream. It is easily proved that the maximum velocity at a 
distance r, (r > a), occurs for 0 = 7 t/2 and is given by q — V (l+d'/r 2 ). Thus at a 
distance r = 10«, the velocity of the stream is disturbed by only 1 per cent, of its 
value ; hence, in the case of a 3 mil anemometer wire, the theoretical resolving power 
in measuring a sharp gradient may roughly be set at 15 mils (about 0'04 cm.), the 
accuracy of velocity measurement being set at 1 per cent. 
Section 17. General Considerations on the Design of Hot-Wire Anemometers. 
The Kelvin bridge connections employed in the determination of the convection 
constants, as described in Part II., offered so many advantages that this system of 
connections was at once taken as the starting point in the design of an instrument for 
the measurement of wind-velocity. 
The experiments showed that over the entire range of diameters employed, the 
power required to maintain the wire at the same resistance, corresponding to a tempe¬ 
rature 0° C., is given by the formula 
W = Bv/V + C, where B = /3(0-0 o ), /3 = & [l + 0*00008 (0-0 o )], 
and /3 0 = 1*432 x 10 -3 v a ; furthermore, C = C„ + E where the radiation is given 
by E = 2 tt«x 0*514 (0 /1OOO) 5 ' 2 , C 0 = y y (0—0 O ) [1 + 0*00114 (0 —0 O )], and finally 
