Steady-state flow in a nozzle

The nozzle is a relatively short device, a few pipe diameters long at most, and the flow will establish itself so rapidly that the control engineer may safely content himself with a steady-state analysis. We may begin with the analysis of Section 4.2, which led to the differential form of the energy equation (4. IS) for fluid flow where no useful work is done. This is repeated below  

Because of the normally small length of the nozzle, it is reasonable to omit the effect of friction in this preliminary analysis of nozzles. (Frictional effects are customarily catered for in nozzle analysis by using the concept of nozzle efficiency.) Setting dF = 0 in equation (4.15) gives the differential for fluid speed as  

We may integrate equation (5.1) from the entrance to the downstream station  

To proceed with the integration of the second term, we need to specify how specific volume, v, varies along the nozzle with pressure. Three possible classes of behaviour are possible. 

This will apply to a high degree of accuracy to the flow of liquid through a nozzle. It will be shown later that it serves reasonably well also as an approximation for gas flow at low pressure ratios. 

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