Vena contractu

If the fluid enters the pipe from a duct of larger cross-section, the existence of a radial velocity component gives rise to the formation of a vena contractu near the entry to the pipe but this has been neglected here. 

The liquid passes through a throttling valve, orifice plate or any other mechanical constriction (Figure 3.12a). If the pressure in vena contractu falls below the cavitation pressure (usually the vapor pressure of the medium), millions of microcavities will be generated. Those cavities will subsequently collapse as the liquid jet expands and pressure recovers. 

The fluid forms a neck, called the vena contractu just downstream of the tube entrance. The flow into the neck is caused by the radial inward velocity of the fluid approaching the tube. Because it is coming inward, the fluid overshoots the tube wall and goes into the neck. This neck is surrounded by a collar... 

In Equation 2.9, area a2 is the area of flow at the point of pressure measurement (P2). Generally, the area at the point of pressure measurement (at vena contractu) is less than the area of the orifice, and it is difficult to calculate the area at vena contractu. Matirematically, the area of vena contracta is calculated as ... 

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