MEASURING OF AIR. 425 



\\ ith horizontal flow and inconi[)rcssible liquids where h 

 and 7 are constant, we obtain after integrating 



<-'' ^ P ^ ^ 



—- -r ~ = constant. 



For compressible liquids where 7 / (/)) we hnd 



Zg J 7 



C' ^ f dp _ 



~r I — — constant 



where the term / ' has to he integrated for the existing relation 



y 7 

 between p and 7. 



In these equations p is the hydrodynaniic pressure, accord- 

 ing to Bernouilli's definitions, and changes into the hydrostatic 

 pressure when the motion of the liquid ceases, in which case 

 c = 0. 



It may be mentioned that the error resulting from tine 

 assumption of 7 constant for com[)ressible liquids is very small 

 under the conditions prexailing when air of a pressure such 

 as is used for running purposes is measured. Assuming for 

 example, 100 lb. absolute pressure and 650° F. absolute tem- 

 perature {i90.6°F.) for the air main and a drop of pressure 

 across the orifice of i lb. or 27.75 i"^^'' water column, which 

 is ample for exact readings, the density will decrease from 

 0.4155 lbs. to 0.4125 lbs. per cub. ft. with adiabatic expansion. 



If 7 l)e taken to be constant the error is. therefore, 0.72%. 



Contrary to Bernouilli's definitions three dift'erent pressuces 

 of a liquid in motion are usually defined in technics, i.e. the 

 static, the dynamic and the total pressure. The total pressure 

 is the pressure shown by a Pitot tube, bent parallel to and 



towards the stream. The kinetic energ\- of the liquid '' , 



is defined as dynamic pressure and Ijy subtracting the d\namic 

 pressure from the total pressure, the static pressure is obtained, 

 which therefore is the same as the above defined hydrodynamic 

 pressure. Hence we have the equation 



pt = pyt + /></ 



or pt = pst -^ y ■ —- 



With the exception of the static pressure />.,/ (or 

 hydrodynamic pressure when using the first definitions given 

 above) this equation does not contain any pressures at all. The 



term 7 . — represents the kinetic energy of the unitv of volume 



i.e. the capacity to perform work resultmg trom the velocity 

 of the liquid. By inserting, for instance, a pitot tube into a stream 

 of water, where ^,,^^0, a certain amount of the liquid is 



