464 



Mi*. W. N. Shaw. On a Pneumatic [Apr. 24, 



where the a's represent the actual measured areas of the four 

 orifices. 



It is evident that the practical realisation of this hydrodynamic 

 analogue is by no means difficult. We require simply a "source" 

 and a " sink " communicating, the one with the other, by two pairs 

 of apertures in two separate boxes, which must be of such a size that 

 the kinetic energy of the entering streams is practically completely 

 dissipated in the boxes. The two boxes must also be connected by a 

 tube in which there must be placed an apparatus for detecting the 

 existence of a flow between the boxes. 



The hydrodynamic analogue suggested itself to me in the course of 

 the study of a number of problems in ventilation depending upon the 

 flow of air between nearly-closed connected spaces, for example, 

 adjoining rooms. In such cases the differences of pressure which 

 produce the flow are very minute, amounting perhaps to a few 

 hundredths of an inch of water, and the corresponding variations in 

 the density of air may be safely disregarded. Under such circumstances 

 the air will follow the laws of flow of an incompressible fluid, and equa- 

 tions identical with those quoted above will hold for the flow of air. 



Measurements made upon the flow of air in order to determine the 

 coefficient of contraction have, been hitherto such as may be termed 

 "absolute"; that is to say, the head and the flow have each been 

 separately expressed in absolute measure and the value of R deter- 

 mined by taking the ratio of the head to the square of the flow. 

 This process is exactly analogous to measuring the electrical resist- 

 ance of a wire by finding the electromotive force between its ends 

 and the current which flows along it. 



M. Murgue, in a work on ' The Theory and Practice of Centrifugal 

 Ventilating Machines ' (translated by A. L. Steavenson), has shown 

 that the internal resistance of a centrifugal fan to the flow of air 

 through it can be calculated from the effects produced on the flow by 

 varying the size of a second orifice through which the air has to pass. 

 This process is evidently parallel to calculating the internal resistance 

 of a battery by finding the effect produced upon the current by vary- 

 ing the external resistance. The development of the electrical analogy 

 seems to afford a novel method of comparing resistances to the motion 

 of air, and of verifying the laws of flow, and one which requires only 

 a detector and not an anemometer, and is independent of the con- 

 stancy of the flow. Whether it could be used practically to test the 

 laws of flow and measure the pneurnatic constants for various orifices 

 to a higher degree of accuracy than has hitherto been attained, 

 evidently depends upon the sensitiveness of the arrangement. In 

 order to try this, I have had constructed what may be called a pneu- 

 matic analogue of the Wheatstone Bridge. It is represented in fig. 1, 

 and consists of three wooden boxes, A, B 1} B 2 . 



