Orifice 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. 

C is a reduction factor since the gas which passes at a high velocity through the orifice, is subject to a volume contraction downstream of the orifice ( vena contracta ). 

True flow area of orifice vena contracta... 

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 ... 

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 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. 

Consider points 1 and 2 in Figure 8.2. At point 1 in the pipe, the fluid flow is undisturbed by the orifice plate. The fluid at this point has a mean velocity ut and a cross-sectional flow area Si. At point 2 in the pipe the fluid attains its maximum mean velocity w2 and its smallest cross-sectional flow area S2. This point is known as the vena contracta. It occurs at about one half to two pipe diameters downstream from the orifice plate. The location is a function of the flow rate and the size of the orifice relative to the size of the pipe. Let the mean velocity in the orifice be u0 and let the diameter and cross-sectional flow area of the orifice be da and S0 respectively. 

Orifice Meters A square-edged or sharp-edged orifice, as shown in Fig. 10-14, is a clean-cut square-edged h<5e with straight walls perpendicular to the flat upstream face of a thin plate placed crosswise of the channel. The stream issuing from such an orifice attains its minimum cross section (vena contracta) at a distance downstream of the orifice which varies with the ratio p of orifice to pipe diameter (see Fig. 10-15). 

The velocity based on the hole area is v . The pressure Pi is the pressure upstream of the orifice, typically about 1 pipe diameter upstream, the pressure P2 is the pressure at the vena contracta, where the flow passes through a minimum area which is less than the orifice area, and the pressure P3 is the pressure downstream of the vena contracta after pressure recovery associated with deceleration of the fluid. The velocity of approach factor 1 — (AJA)2 accounts for the kinetic energy approaching the orifice, and the orifice coefficient or discharge coefficient C accounts for the vena contracta. The location of the vena contracta varies with AJA, but is about 0.7 pipe diameter for AJA < 0.25. The factor 1 — AJA accounts for pressure recovery. Pressure recovery is complete by about 4 to 8 pipe diameters downstream of the orifice. The permanent pressure drop is Pi — P3. When the orifice is at the end of pipe, discharging directly into a large chamber, there is negligible pressure recovery, the permanent pressure drop is Pi — P2, and the last equality in Eq. (6-111) does not apply. Instead, P2 = P3. Equation (6-111) may also be used for flow across a perforated plate with open area A and total area A. The location of the vena contracta and complete recovery would scale not with the vessel or pipe diameter in which the plate is installed, but with the hole diameter and pitch between holes. 

For cavitation in flow through orifices, Fig. 6-55 (Thorpe, Int. J. Multiphase Flow, 16, 1023-1045 [1990]) gives the critical cavitation number for inception of cavitation. To use this cavitation number in Eq. (6-207), the pressure p is the orifice backpressure downstream of the vena contracta after full pressure recovery, and V is the average velocity through the orifice. Figure 6-55 includes data from Tullis and Govindarajan (ASCE J. Hydraul. Div., HY13, 417-430 [1973]) modified to use the same cavitation number definition their data also include critical cavitation numbers for 30.50- and 59.70-cm pipes... 

By jet velocity is meant the value of the average velocity at the vena contracta. The velocity profile across an orifice opening such as that shown in Fig. 10.5a is seen to be nearly constant except for a small annular ring around the outside. The average velocity V is thus only slightly less than... 

If the jet is initially horizontal, as in the flow from a vertical orifice, Vx = V and Vz = O. Equation (10.54) is then readily reduced to an expression for the jet velocity in terms of the coordinates from the vena contracta to any point of the trajectory, z now being positive downward,... 

Coefficient of contraction Cc. The ratio of the area of a jet A at the vena contracta to the area of the orifice or other opening A0 is called the coefficient of contraction. Thus, A = CcAa. 

The loss of head in friction in an orifice, nozzle, or tube may be determined by writing the energy equation between some point upstream and the vena contracta of the jet. Letting H now represent the total head upstream while VA/2g is the velocity head in the jet, the equation is H - hf = V2/2g. But as V = Cv (2gH) 12 and VA/2g = ClH, the substitution of this last expression in the preceding energy equation results in two equivalent expressions for the loss of head... 

Figure 10.10 Coefficients for sharp-edged orifice with pressure differential measured either at the flanges or at the vena contracta. (Calculated from data in Refs. f24] and [25].)...

Thus, the coefficient C for an orifice meter is much less than it is for a venturi or a flow nozzle, and it also varies in a different manner with Reynolds number. Consider a pressure gradient between points in a pipe fitted with an orifice plate. Point 1 is upstream of the orifice plate. Point 2 is immediately downstream of the orifice, at the vena contracta. Point 3 is further downstream where the flow is normal, as it was at point 1, though at lower pressure owing to the orifice pressure loss. 

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