110 HYDKAULICS AND ITS APPLICATIONS 



The weight of water w leaving the vessel per second is determined by 

 weighing. Then if v be its mean velocity in a horizontal direction, the 



momentum per second leaving the tank in this direction = - . To 



produce this flux of momentum a constant horizontal force of magnitude 



- Ibs. must be impressed on the jet, a force which can only be due to an 



otherwise unbalanced pressure on the side of the tank opposite to the orifice. 

 We have then, taking moments about the knife edge : 



w v 

 W x = . d where d = depth of orifice below knife edge 



v = . g . -y feet per second 

 w d 



Wax 



.'. <? = 



w d v 2 g li 



This method is only suitable for experiments on a small scale. A third 

 method, which has been applied very successfully, 

 consists in measuring the actual velocity at several 

 points in the cross section of the vena contracta by 

 means of a Pitot Tute (Arts. 68, 1.01). If then v is 

 the velocity at any radius x, the total discharge = 



2 TT v x dx cubic feet per second. If a curve be 







plotted having as abscissae the values of x and as 

 ordinates the corresponding values of 2 TT x v, the 

 area under this curve will represent the discharge 



per second, from which the mean velocity may be obtained by dividing by 



the area of the jet. 



(2) The coefficient of contraction, C e , may be measured by using a ring 

 (Fig. 58), surrounding the jet at the vena contracta, and fitted with 

 micrometer measuring screws, which may be adjusted until just touching 

 its surface. 1 



(3) The coefficient of discharge, C, may be determined directly by 

 measuring the quantity Q in cubic feet discharged per second from the 

 orifice a, under a head h. 



Then C = $= 



1 For a sketch of a contraction gauge, and for experiments on the measurements of the 

 coefficients in the case of a large jet forming part of a Pel ton Wheel installation, see a paper 

 by W. R. Eckhart, " Proc. Inst. Mech. Engineers," 190910. Also Engineering, January H, 

 1910, p. 59. 



