37 



is the angle of flow across the wire, and 



a and b are constants depending upon the wire size, and upon the ther- 

 mal conductivity, density, and specific heat of the fluid. 



The constants a and b may be determined by calibration; that is by 

 placing the wire in a stream the velocity of which may be varied at will. 

 Equation [26] shows that the voltage drop iR across the wire is a function of 

 the square root of the fluid velocity and also that the wire should be oper- 

 ated in a plane perpendicular to the flow for maximum sensitivity, i.e., 



p 2 



CALIBRATION AND SENSITIVITY 



Quantitative applications of hot-wire techniques to water have been 

 achieved, but only under more highly controlled conditions than those de- 

 scribed in this report. For the qualitative survey conducted on the tanker 

 model, wire calibrations were unnecessary and consequently, were not obtained. 

 Also, provided sufficient sensitivity to velocity fluctuations existed for the 

 survey, the limitations of frequency response described later in this appendix 

 were not remedied. 



Calibration of hot-wires in water have been performed at the Taylor 

 Model Basin and reported in Reference 17- In spite of the added complication 

 of more rapid dirt accumulation on the wire in water than in air, consistent 

 and repeatable calibrations can be made by brushing the wires immediately 

 prior to each resistance measurement. The two constants a and b of Equation 

 [26] can therefore be determined in a stream of variable, but known velocity. 



A simple calculation of the relative sensitivity of a tungsten wire 

 (0.0003- inch diameter) in air and in water, at normal operating conditions and 

 at the same Reynolds number has been made. The sensitivity of a hot wire 

 placed perpendicular to the stream Is defined as the rate of change of E with 

 respect to U for a constant i. Thus from [26] 



b(RR £ 

 \dT)r ' 2iR R rtYV 



< aU /.. 2iR R „vw L ' 



Also, for the constant-current technique the normal operating condition in 

 water is taken to be that current required to raise the temperature of the 

 wire approximately 15° C above the temperature of the water at the mean free- 

 stream velocity of operation. In air a temperature elevation of 150 to 200 C 

 at mean free-stream velocity may be taken as normal. The comparison showed 

 the hot wire to be about five times more sensitive in water than in air at 

 the same Reynolds number because of the greater thermal conductivity and 



