equation of flow is twofold. First, the ratio -^ is altered, 



286 Prof. W. C. Unwin on the Discharge of Water 



believes that temperature has a far less influence on the dis- 

 charge from simple orifices than Mr. Isherwood's results would 

 imply. It is difficult to explain to what the higher results 

 obtained by Mr. Isherwoodare due ; but the conjecture maybe 

 hazarded that the orifice in his experiments was very excep- 

 tionally placed. It was at the end of a bell-mouthed tube 

 some 10 inches long, a great part of which was only J inch 

 diameter ; and there was a plug-cock immediately above the 

 orifice. It seems possible that there was a good deal of fric- 

 tion in this pipe, and that the diminution of friction in this 

 part of the apparatus led to the increase of discharge as the 

 temperature increased *. 



Thus far the effect of the temperature on the capacity of 

 the reservoir and the size of the orifice has been neglected. 

 It only remains to examine whether the expansion of these 

 has any material influence on the results. 



The effect of temperature on the quantities entering into the 



D 2 

 d> 



because the mouthpiece was of brass and the reservoir of cast 

 iron ; and the former expands more than the latter. Secondly, 

 the level marks being attached to the side of the cistern, the 

 distance between these marks and the centre of the orifice in- 

 creases as the temperature rises. There is, however, an un- 

 certainty in applying a correction for the expansion of the 

 metal, because, its external surface being exposed to the air, 

 its mean temperature would be less than the temperature of 

 the water. The following estimate of the correction is there- 

 fore approximate only. 



Let e b be the expansion of brass per unit of length and per 

 degree ; 

 e c the expansion of cast iron estimated in the same way ; 

 t = the excess of temperature during the experiment 

 reckoned from 60°. 



* It is impossible to calculate, except roughly, the frictional resistance 

 of the tube to which, in Mr. Isherwood's experiments, the orifices were 

 attached. Taking 4 inches length of pipe £ inch in diameter, and neglect- 

 ing the bell-mouthed part, we get, using D'Arcy's coefficient of friction, 

 and putting the data in feet : — 



For a discharge of 0-0167 0-0374 



„ velocity 55 12-2 



„ head lost in pipe 0-6 0-12 



„ total head 5-0 1-0 



So that apparently about 12 per cent, of the head may have been lost in 

 the friction of the pipe leading to the orifice. 



