Orifice meters vena contracta

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. 

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). 

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. 

One important complication appears in the orifice meter that is not found in the venturi. Because of the sharpness of the orifice, the fluid stream separates from the downstream side of the orifice plate and forms a free-flowing jet in the downstream fluid. A vena contracta forms, as shown in Fig. 8.19. The jet is not under the control of solid walls, as is the case in the venturi, and the area of the jet varies from that of the opening in the orifice to that of the vena contraeta. The area at any given point, e.g., at the downstream tap, is not easily determinable, and the velocity of the jet at the downstream tap is not easily related to the diameter of the orifice. Orifice coefficients are more empirical than those for the venturi, and the quantitative treatment of the orifice meter is modified accordingly. 

Prepare recovery. Because of the large friction losses from the eddies generated by the reexpanding jet below the vena contracta, the pressure recovery in an orifice meter is poor. The resulting power loss is one disadvantage of the orifice meter. The fraction of the orifice differential that is permanently lost depends on the value of P, and the relationship between the fractional loss and p is shown in Fig. 8.20. For a value of p of 0.5, the lost head is about 73 percent of the orifice differential. 

This includes orifice plates, ISA nozzles, conical inlets and venturi tubes, all of which depend on the measurement of the pressure drop across a restriction through which the whole of the flow is passed. Figure 11.10 shows a sketch of a typical orifice meter which consists of a concentric square edged circular hole in a thin plate, which is clamped between the flanges of the pipe. The minimum section of the stream tube occurs downstream from the orifice with the formation of a vena contracta at section 2. A typical connection would be one diameter... 

A typical sharp-edged orifice is shown in Fig. 3.2-4. A machined and drilled plate having a hole of diameter Dq is mounted between two flanges in a pipe of diameter Z>,. Pressure taps at point 1 upstream and 2 downstream measure p, — Pz- The exact positions of the two taps are somewhat arbitrary, and in one type of meter the taps are installed about 1 pipe diameter upstream and 0.3 to 0.8 pipe diameter downstream. The fluid stream, once past the orifice plate, forms a vena contracta or free-flowing jet. 

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