Measurement by flow through a constriction

In measuring devices where the fluid is accelerated by causing it to flow through a constriction, the kinetic energy is thereby increased and the pressure energy therefore 

If the frictional losses are neglected, and the fluid does no work on the surroundings, that is Wg and F are both zero, then  

Inserting the value of u in terms of 2 in equation 6.13 enables U2 and G to be obtained. 

For an ideal gas in non-isothermal flow. If the pressure and volume are related by Pi/ — constant, then a similar analysis gives  

It should be noted that equations 6.16 and 6.17 apply provided that P2/PV is greater than the critical pressure ratio Wc. This subject is discussed in Chapter 4, where it is shown that when P2/P1 Wc, the flowrate becomes independent of the downstream pressure P2 and conditions of maximum flow occur. 

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