Discharge coefficient, orifice meter

Figure 2-18. Flow coefficient C for square edged orifices. By permission, Crane Co. [3], Technical Paper 410 Engineering Div. (1976) and Fluid Meters, Their Theory and Application Part 1, 6th Ed., 1971, American Society of Mechanical Engineers and, Tuve, G. L. and Sprenkle, R. E., Orifice Discharge Coefficients for Viscous Liquids, Instruments Nov. 1933, p. 201.

This meter may thus be considered as an orifice meter with a variable aperture, and the formulae already derived are therefore applicable with only minor changes. Both in the orifice-type meter and in the rotameter the pressure drop arises from the conversion of pressure energy to kinetic energy and from frictional losses which are accounted for in the coefficient of discharge. The pressure difference over the float —AP. is given by ... 

Wafer flowing at 1500 cm3/s in a 50 mm diameter pipe is metered by means of a simple orifice of diameter 25 nnn. If the coefficient of discharge of the meter is 0.62, what will be the reading on a mercury-underwater manometer connected to the meter ... 

The flow of water through a 50 mm pipe is measured by means of an orifice meter with a 40 mm aperture. The pressure drop recorded is 150 mm on a mercury-under-water manometer and the coefficient of discharge of the meter is 0.6. What is the Reynolds number in the pipe and what would you expect the pressure drop over a 30 m length of the pipe to be ... 

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 flow of liquid in a 25 mm diameter pipe is metered with an orifice meter in which the orifice has a diameter of 19 mm. The aperture becomes partially blocked with dirt from the liquid. What fraction of the area can become blocked before the error in flowrate at a given pressure differential exceeds 15 per cent Assume that the coefficient of discharge of the meter remains constant when calculated on the basis of the actual free area of the orifice. 

A liquid hydrocarbon is fed at 295 K to a heat exchanger consisting of a 25 mm diameter tube heated on the outside by condensing steam at atmospheric pressure. The flow rate of the hydrocarbon is measured by means of a 19 mm orifice fitted to the 25 nnn feed pipe. The reading on a differential manometer containing the hydrocarbon-over-water is 450 mm and the coefficient of discharge of the meter is 0.6. 

The coefficient of discharge Cd for a particular orifice meter is a function of the location of the pressure taps, the ratio of the diameter of the orifice to the inside diameter of the pipe dJdY, the Reynolds number in the pipeline Re, and the thickness of the orifice plate. 

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... 

The difference between an orifice meter and a venturi meter or flow nozzle is that for both of the latter there is no contraction, so that A2 is also the area of the throat and is fixed, while for the orifice, A2 is the area of the jet and is a variable and is, in general, less than the area of the orifice A0. For the venturi tube or flow nozzle the discharge coefficient is practically a velocity coefficient, while for the orifice the value of C or K is much more affected by Cc than it is by Cv. 

Bean, H. S., Buckingham, E., and Murphy, P. S., Discharge Coefficients of Square-Edged Orifices for Measuring the Flow of Air, U.S. National Bureau of Standards Research Paper 49, ASME Fluid Meters Report, 1931. 

It has been reported that in the case of orifice plates and nozzles, the correlation of the discharge coefficient with Reynolds number is the same for LH2 as for water. Similarly, tests of several commercially available turbine-type meters seem to show that the calibration constant (pulses per unit volume) for LH2 will differ by only about 1% from the value for water. 

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. 

The coefficient of discharge = (uav from pitot)/(uav from orifice meter). 

The value of the coefficient of discharge Cd for orifice meters depends on the properties of the flow system, the ratio of the orifice diameter to the upstream diameter, and the location of the pressure-measuring taps. Values of Cd for sharp-edged orifice meters are presented in Fig. 14-55. These values apply strictly for pipe orifices with throat taps, in which the downstream pressure tap is located one-third of one pipe diameter from the downstream side of the orifice plate and the upstream tap is located one pipe diameter from the upstream side. However, within an error of about 5 percent, the values of Cd indicated in Fig. 14-55 may be used for manometer taps located anywhere between the orifice plate and the hypothetical throat taps. 

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