The orifice meter

Inserting the value Aj = CcAq in equation 6.15, then for an incompressible fluki in a horizontal meter  

Using a coefficient of discharge Cd to take account of the frictional losses in the meter and of the parameters C, ai, and a2.  

For a meter in which the area of the orifice is small compared with that of the pipe  

For the isothermal flow of an ideal gas, from equation 6.16 and using Co as above  

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Orifice Meter The most widely used flowmeter involves placing a fixed-area flow restriction (an orifice) in the pipe carrying the fliiid. This flow restriction causes a pressure drop that can be related to flow rate. The sharp-edge orifice is popular because of its simplicity, low cost, and the large amount of research data on its behavior. For the orifice meter, the flow rate for a liquid is given by... 

The orifice meter, in which the fluid is accelerated at a sudden constriction (the orifice) and the pressure developed is then measured. This is a relatively cheap and reliable instrument though the overall pressure drop is high because most of the kinetic energy of the fluid at the orifice is wasted. 

Because of its simplicity the orifice meter is commonly used for process measurements, and this instrument is suitable for providing a signal of the pressure to some comparator as indicated in Figure 6.1. 

The flow is also metered using a 15 cm orifice plate across which the pressure differential is 50 mm on a mercury-undcr-waler manometer. What is the coefficient of discharge of the orifice meter ... 

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. 

An orifice meter with a diameter of 3 in. is mounted in a 4 in. sch 40 pipeline carrying an oil with a viscosity of 30 cP and an SG of 0.85. A mercury manometer attached to the orifice meter reads 1 in. If the pumping stations along the pipeline operate with a suction (inlet) pressure of lOpsig and a discharge (outlet) pressure of 160psig, how far apart should the pump stations be, if the pipeline is horizontal ... 

Figure 8.5 shows a Venturi meter. The theory is the same as for the orifice meter but a much higher proportion of the pressure drop is recoverable than is the case with orifice meters. The gradual approach to and the gradual exit from the orifice substantially eliminates boundary layer separation. Thus, form drag and eddy formation are reduced to a minimum. 

An orifice in a pipeline, as in Fig. 10.5a, may be used as a meter in the same manner as the venturi tube or the flow nozzle. It may also be placed on the end of the pipe so as to discharge a free jet. The coefficients are practically identical in the two cases. The difference between the orifice in the present discussion and that in the earlier sections of this chapter is that here the pipe walls are nearer to the edge of the orifice so that there is less contraction of the jet, resulting in a higher value of Cc, and also there is a much larger value of the velocity of approach. For the numerical values of the coefficients to apply, the ratio DJDX should be less than %, where D0 and Di are the diameters of the orifice and the approach pipe, respectively. In the orifice meter the... 

Patel, B. R. and Sheikoholeslami, Z., Numerical modelling of turbulent flow through the orifice meter, International Symposium on Fluid Flow Measurement, Washington, D.C., November 1986. 

The orifice meter equations are 6.19 and 6.21 the latter being used when /[l — (A0/Ai)2] approaches unity. 

From the reading taken from the pitot tube, the velocity in the pipe, and hence the mass flowrate, can be calculated. From the orifice meter, the mass flowrate can also be calculated and compared with the accurate value. 

Water is flowing through a 150 mm diameter pipe and its flowrate is measured by means of a 50 mm diameter orifice, across which the pressure differential is 2.27 x 104 N/m2. The coefficient of discharge of the orifice meter is independently checked by means of a pitot tube which, when situated at the axis of the pipe, gave a reading of 100 mm on a mercury-under-water manometer. On the assumption that the flow in the pipe is turbulent and that the velocity distribution over the cross-section is given by the Prandtl one-seventh power law, calculate the coefficient of discharge of the orifice meter. 

What is the pressure drop across the orifice meter in psi. 

The rate of flow of a liquid mixture is to be measured continuously. The flow rate will be approximately 40 gpm, and rates as low as 30 gpm or as high as 50 gpm can be expected. An orifice meter, a rotameter, and a venturi meter are available. On the basis of the following additional information, would you recommend installation of the orifice meter, the venturi meter, or the rotameter Give reasons for your choice. 

The theory behind the orifice meter is relatively simple and it begins with the Bernoulli equation. It can be summarized as follows ... 

Although the orifice meter is simple to use, it is not infallible. First, it requires proper installation of the plate itself. If the plate is put in backwards, erroneous readings can result. In addition, the location of the pressure taps is critical. The locations must adhere to the strict guidelines. 

Using the orifice meter as an example. Example 8.2 illustrates the sizing procedure. Calculating the orifice diameter requires assigning the pressine drop across the orifice. 

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