TR No. 22 
Appendix A 
RESPONSE OF CURRENT METER TO ACCELERATED FLOW 
Expressions for the resultant driving torque on the impeller of 
a current meter as a function of the geometry of the current meter, 
impeller angular velocity, and the velocity of water through the cur- 
rent meter are given by Rubin, Miller and Fox (11), and by Grey (12). 
Similar expressions are given by Lang (13) for the resultant driving 
torque on a windmilling propeller, If bearing friction and other 
torques are assumed negligible, the resultant driving torque is of 
the form 
2 
k =cu f(J), (1) 
where 
J 
li 
uf D) (2) 
and c is a constant of proportionality and is a function only of the 
geometry of the current meter. When the water velocity and the corresponding 
angular velocity of the impeller are constant, the driving torque is zero. 
Therefore 
£(J) = 03; J’ = Jo = constant - (3) 
Hence 
VA (4) 
which gives the calibration coefficient for the current meter. 
If the water velocity through the current meter consists of a time 
varying component superimposed on a constant component 
u=U+rtu'’, (5) 
where u’ is assumed small with respect to U so that the lift and drag 
forces on the impeller blades are approximately linear, then the equation 
of motion of the impeller can be written as 
1=k jw) seu £ (J). (6) 
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