Minimum flow area

Minimum flow area at bottom (under) of downcomer per tray, ft ... 

It is shown in Chapter 6 that the minimum flow area A2 tends to be somewhat smaller than the area Ao of the aperture because the gas leaves with a small radial inwards velocity component. Furthermore, there will be some reduction of discharge rate because of the frictional effects which have been neglected. Grouping these factors together by means of a coefficient of discharge Co, where Co < 1, gives ... 

Thus, if the pressure ratio at the minimum flow area is equal to the critical value given by equation 6.110, the flow there will be at the sonic speed. If the pressure ratio is higher than this value the flow will be subsonic and will depend on the back pressure. In both convergent and... 

To calculate the maximum velocity, we must determine the minimum flo area. From Fig. 6-14 we find that the ratio of the minimum flow area to the total frontal area is (S - d)IS . The maximum velocity is thus... 

G = mass velocity, based on minimum flow area l = fin height b = fin thickness... 

Calculate the relevant fin areas. These are heat-transfer surface of fins A j, outside heat-transfer surface of bare tube A0, total outside heat-transfer surface A, (equal to Af + A0), and ratio of maximum flow area to minimum flow area ar. For this problem... 

G = mass velocity, in lb/(h)(ft2) (= W/ac, where W = flow rate) g = gravitational constant, in ft/h2 p = density, in lb/ft3 Nr = number of tube rows crossed Ni = number of baffles ac = minimum flow area for cross flow, in ft2... 

The maximum velocity is determined from the conservation of mass requirement for steady incompressible flow. For in-line arrangement, the maximum velocity occurs at the minimum flow area between the tubes, and the conservation of mass can be expressed as (see Fig. 7—26a) pVA, pV ArOt VSj- V np,(57- — D). Then the maximum velocity becomes... 

Other devices can be used to determine the flow rate from a single measurement. These are sometimes referred to as obstruction meters, since the basic principle involves introducing an obstruction (e.g., a constriction) into the flow channel and then measuring the pressure drop across this obstruction, which depends on the flow rate. Two such devices, the venturi meter and the nozzle, are illustrated in Eigures 5.14 and 5.15, respectively. In both cases, the pressure drop from a point upstream of the meter to a point in a plane with the minimum flow area (A ) is related to the velocity V2 by the Bernoulli equation ... 

Vm = average maximum vapor velocity in the bundle (i.e., based on minimum flow area)... 

Amb Minimum flow area at centerline of one baffle, m2, ft2 A 0 Minimum free flow (or open) area on one side of an exchanger, m2, ft2... 

When a fluid flows through an orifice plate, the static pressure within the pipe varies as illustrated in Figure 4.13. Notice that just upstream of the orifice plate the static pressure reaches a maximum value. When the fluid passes through the bore of the plate it accelerates. As the fluid jet exits the other side of the plate it continues to accelerate and decrease in cross-sectional area hence, the minimum flow area is actually smaller than the area of the orifice. The location where the jet reaches its minimum cross-sectional area is referred to as the vena contracta and is where the velocity is the highest and the... 

The heat-transfer phenomena for forced convection over exterior surfaces are closely related to the nature of the flow. The heat transfer in flow over tube bundles depends largely on the flow pattern and the degree of turbulence, which in turn are functions of the velocity of the fluid and the size and arrangement of the tubes. The equations available for the calculation of heat transfer coefficients in flow over tube banks are based entirely on experimental data because the flow Is too complex to be treated analytically. Experiments have shown that, in flow over staggered tube banks, the transition from laminar to turbulent flow Is more gradual than in flow through a pipe, whereas for in-line tube bundles the transition phenomena resemble those observed in pipe flow. In either case the transition from laminar to turbulent flow begins at a Reynolds number based on the velocity in the minimum flow area of about 100, and the flow becomes fully turbulent at a Reynolds number of about 3,000. The equation below can be used to predict heat transfer for flow across ideal tube banks. 

Experiments show that the values of the average heat transfer coefficient vary with the number of vertical rows until 10 or more rows are used. The h value in this latter case remains constant. Also, the velocity used in calculating the Reynolds number is not the fluid s approach velocity but rather the maximum velocity found by using the minimum flow area ... 

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