Vena contracta

The fifth type of tap is unique in that the downstream tap location varies depending of the orifice P ratio. This tap is located at the vena contracta the location where the stream issuing from the orifice attains its minimum cross section. The location of this tap is defined from the upstream face of the orifice as is the D/2 tap. The downstream tap for corner, flange, and pipe taps is measured from the downstream face of the orifice. Vena contracta taps maximize the measured differential pressure. For modem transmitters this is not an important consideration and this type of tap is no longer widely used. 

Cavitation and Flashing From the discussion on pressure recoveiy it was seen that the pressure at the vena contracta can be much lower than the downstream pressure. If the pressure on a hquid falls below its vapor pressure (p,J, the liquid will vaporize. Due to the effect of surface tension, this vapor phase will first appear as bubbles. These bubbles are carried downstream with the flow, where they collapse if the pressure recovers to a value above p,. This pressure-driven process of vapor-bubble formation and collapse is known as cavitation. 

Vena-contracta taps. The upstream static hole is one-half to two pipe diameters from the plate. The downstream tap is located at the position of minimum pressure (see Fig. 10-19). 

Permanent pressure loss across a concentric circular orifice with radius or vena-contracta taps can be approximated for turbulent flow by... 

Discharge Coefficients and Gas Discharge A compressible fluid, upon discharge from an orifice, accelerates from the puncture point and the cross-sec tional area contracts until it forms a minimum at the vena contracta, If flow is choked, the mass flux G, can be found at the vena contrac ta, since it is a maximum at that point, The mass flux at the orifice is related to the mass flux at the vena contracta by the discharge coefficient, which is the area contraction ratio (A at the vena contracta to Ay at the orifice) ... 

For two-phase flow, the phase contraction coefficients Cqc. nd Col relate the area of each phase Ac and A at the vena contracta to the known area of the orifice Ay. Thus ... 

For gas-phase choked flow, the pressure ratio at the vena contracta is ... 

The minimum case is when rhe diameter of vena contracta of the plume is about 80% of the upper surface diameter and is located approximately one-third of a diameter above the source. I he spreading angle of rhe plume is set ro 25". For low-temperature sources, Skistad - recommends the maximum case, whereas rhe minimum case best fits the measure ments for larger, high-temperature sources. 

L/D Minimum of 5, or tong enough to expand " vena contracta ... 

Lush has proposed cavitation criteria for these components using the empirical data of Tullis and BalP and Boccadoro and Angell . The cavitation index used is based on conditions at the throat of a valve and, correspondingly, the vena contracta of an orifice plate. 

The area of flow decreases from A at section 1 to Ao at the orifice and then to A2 at the vena contracta (Figure 6.14). The area at the vena contracta can be conveniently related to the area of the orifice by the coefficient of contraction Cc, defined by the relation ... 

The loss coefficient is seen to be a function only of the geometry of the system (note that the assumption of plug flow implies that the flow is highly turbulent). For most systems (i.e., flow in valves, fittings, etc.), the loss coefficient cannot be determined accurately from simple theoretical concepts (as in this case) but must be determined empirically. For example, the friction loss in a sudden contraction cannot be calculated by this simple method due to the occurrence of the vena contracta just downstream of the contraction (see Table 7-5 in Chapter 7 and the discussion in Section IV of Chapter 10). For a sharp 90° contraction, the contraction loss coefficient is given by... 

The simplest and most common device for measuring flow rate in a pipe is the orifice meter, illustrated in Fig. 10-7. This is an obstruction meter that consists of a plate with a hole in it that is inserted into the pipe, and the pressure drop across the plate is measured. The major difference between this device and the venturi and nozzle meters is the fact that the fluid stream leaving the orifice hole contracts to an area considerably smaller than that of the orifice hole itself. This is called the vena contracta, and it occurs because the fluid has considerable inward radial momentum as it converges into the orifice hole, which causes it to continue to flow inward for a distance downstream of the orifice before it starts to expand to fill the pipe. If the pipe diameter is D, the orifice diameter is d, and the diameter of the vena contracta is d2, the contraction ratio for the vena contracta is defined as Cc = A2/A0 = (d2/d)2. For highly turbulent flow, Cc 0.6. 

The complete Bernoulli equation, as applied between point 1 upstream of the orifice where the diameter is D and point 2 in the vena contracta where the diameter is d2, is... 

The orifice coefficient shown in Fig. 10-8 is valid to within about 2-5% (depending upon the Reynolds number) for all pressure tap locations except pipe and vena contracta taps. More accurate values can be calculated from Eq. (10-10), with the parameter expressions given in Table 10-1 for the specific orifice and pressure tap arrangement. 

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