Flow measurements

The details of design and construction of various flow meters are shown in many standard chemical engineering and fluid mechanics texts. Some reviews and advice in choosing flowmeters for particular duties are available in the literature.10-12 

The Continuity and Bernoulli Equations may be used to derive equations relating flow rate to measured pressure difference for the Venturi meter (and the orifice plate meter discussed below). 

Applying Bernoulli s Equation (16), along a streamline between points 1 and 2 and assuming the meter is horizontal, r, = z2, and that the velocities are constant across a cross-section, gives  

Continuity, assuming constant density p, Equation (10), gives M2 = ui(Ai/A2). Substituting for U2 into Equation (33) and rearranging gives  

Adding Cd, a discharge coefficient, to account for frictional losses (assumed zero in Bernoulli s Equation) and other non-idealities, we get Equation (36), the operating equation for the Venturi meter. 

As illustrated by the earlier examples, there is no direct method for the measurement of heat Consequently, heat has to be determined by means of its effects. The older unit quantity of heat - the calorie - was therefore defined in terms of a measurement instruction  

One 15 °C calorie (cali5 ) is the amount of heat required to raise the temperature of 1 g of water from 14.5 to 15.5 °C under standard atmospheric pressure.  

Because heat is merely one form of energy, as are the electrical and mechanical energies (Mayer, 1842 Joule, 1843 Golding, 1843, according to Dahl, 1963), a special unit for heat is unnecessary. Today, in the International System of Units (SI), heat is expressed in the unit of energy 

Conversion between the old unit (cal) and new SI unit (J) is made as follows  

The latter is the International Steam Table calorie (cahr), one of the two calories still in use of a number of older calories (e.g., the 15 °C water calorie corresponding to 0.9996801 calix) (Stifle, 1961). 

A number of considerations should be evaluated before a flow measurement method can be selected for any appHcation. These considerations can be divided into four general classifications fluid properties ambient environment measurement requirements and economics. 

Reynolds dumber. One important fluid consideration in meter selection is whether the flow is laminar or turbulent in nature. This can be deterrnined by calculating the pipe Reynolds number, Ke, a dimensionless number which represents the ratio of inertial to viscous forces within the flow. Because 

Most flow meters are designed and caHbrated for use on turbulent flow, by far the more common fluid condition. Measurements of laminar flow rates may be seriously in error unless the meter selected is insensitive to velocity profile or is specifically caHbrated for the condition of use. 

m blent Environment. The environment around the flow conduit must be considered in meter selection. Such factors as the ambient temperature and humidity, the pipe shock and vibration levels, the avadabiHty of electric power, and the corrosive and explosive characteristics of the environment may all influence flow meter selection. Special factors such as possible accidental flooding, the need for hosedown or steam cleaning, and the possibiHty of lightning or power transients may also need to be evaluated. 

Enough space must be available to properly service the flow meter and to install any straight lengths of upstream and downstream pipe recommended by the manufacturer for use with the meter. Close-coupled fittings such as elbows or reducers tend to distort the velocity profile and can cause errors in a manner similar to those introduced by laminar flow. The amount of straight pipe required depends on the flow meter type. For the typical case of an orifice plate, piping requirements are normally Hsted in terms of the P or orifice/pipe bore ratio as shown in Table 1 (1) (see Piping systems). 

Here pi = p2 = patm- Because the two reservoirs are of large diameter, Vi and V2 are both approximately zero. With these simplifications, the equation simplifies to  

The friction losses are associated with the flow in a 75 m length of 50 mm pipe including one gate valve, one globe valve, two short curvature elbows, a contraction (at A) and an expansion at B. At this stage, neglecting the contraction and expansion losses, one can express the loss term in terms of the unknown velocity V as  

Edwards et al. [1985] have published the following values of K for various fittings  

Assuming the flow to be laminar and Rcmr 15. The total head loss is then  

A trial and error method gives, V = 0.43m/s. Check the value of Re ii = 121.13 X 0.43 = 26.52 which is in laminar range and is also larger than the value of 15 assumed above. 

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Flow measurements for diesel injectors under a pressure drop of 0.6 bar. 

Flow measurements using tracers are performed in all piping systems carrying oil, gas or water including separators, compressors, injector systems, and flares. Calibration of elsewhere difficult accessible flow meters is regularly performed by the tracer methods, which are based on international standards. Tracer flow measurements are also well suited for special purposes... 

Figure 1 Tracer flow measurements using the time of transit method...

Figure 2. Principle of 3 phase flow measurements by the continuous dilution tracer method.

T. Sevel, NH. Pedersen, C.E. Weinell, B. Lind-Nielsen, North Sea Flow Measurements Workshop, 1996, Peebles, Scotland... 

The latter contribute to the fluxes in time-varying conditions and provide source or sink terms in the presence of chemical reaction, but they have no influence on steady state diffusion or flow measurements in a non-reactive sys cem. 

Flowers of zinc Flow improvers Flow injection analysis Flow measurement... 

Flow measuring equipment must generally be wet caHbrated to attain maximum accuracy, and principal flow meter manufacturers maintain extensive facihties for this purpose. In addition, a number of governments, universities, and large flow meter users maintain flow laboratories. 

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