Tubes hydraulic diameter

D diameter of containing vessel or tube hydraulic diameter of duct... 

Reactant concentration on the outer catalyst surface Reference tracer concentration Diameter of the channel (tube), hydraulic diameter Molecular diffusion coefficient Effective diffusion coefficient Diameter of particle... 

The connection that has been shown in Section VIII to exist between burn-out in a rod bundle and in an annulus leads to the question of whether or not a link may also exist between, for example, a round tube and an annulus. Now, a round tube has its cross section defined uniquely by one dimension—its diameter therefore if a link exists between a round tube and an annulus section, it must be by way of some suitably defined equivalent diameter. Two possibilities that immediately appear are the hydraulic diameter, dw = d0 — dt, and the heated equivalent diameter, dh = (da2 — rf,2)/ however, there are other possible definitions. To resolve the issue, Barnett (B4) devised a simple test, which is illustrated by Figs. 38 and 39. These show a plot of reliable burn-out data for annulus test sections using water at 1000 psia. Superimposed are the corresponding burn-out lines for round tubes of different diameters based on the correlation given in Section VIII. It is clearly evident that the hydraulic and the heated equivalent diameters are unsuitable, as the discrepancies are far larger than can be explained by any inaccuracies in the data or in the correlation used. 

If vapour condenses on the outside of a vertical tube of diameter d , then the hydraulic mean diameter for the film is ... 

One of the possible ways to account for the effect of roughness on the pressure drop in a micro-tube is to apply a modified-viscosity model to calculate the velocity distribution. Qu et al. (2000) performed an experimental study of the pressure drop in trapezoidal silicon micro-channels with the relative roughness and hydraulic diameter ranging from 3.5 to 5.7% and 51 to 169 pm, respectively. These experiments showed significant difference between experimental and theoretical pressure gradient. 

The liquid alone pattern showed no entrained bubbles or gas-liquid interface in the field of view. The capillary bubbly flow, in the upper part of Fig. 5.14a, is characterized by the appearance of distinct non-spherical bubbles, generally smaller in the streamwise direction than at the base of the triangular channel. This flow pattern was also observed by Triplett et al. (1999a) in the 1.097 mm diameter circular tube, and by Zhao and Bi (2001a) in the triangular channel of hydraulic diameter of 0.866 mm. This flow, referred to by Zhao and Bi (2001a) as capillary bubbly... 

The flow regime maps shown in Fig. 5.16a,b indicate that typical flow patterns encountered in the conventional, large-sized vertical circular tubes, such as bubbly flow, slug flow, churn flow and annular flow, were also observed in the channels having larger hydraulic diameters ([Pg.216]

The convective and nucleate boiling heat transfer coefficient was the subject of experiments by Grohmann (2005). The measurements were performed in microtubes of 250 and 500 pm in diameter. The nucleate boiling metastable flow regimes were observed. Heat transfer characteristics at the nucleate and convective boiling in micro-channels with different cross-sections were studied by Yen et al. (2006). Two types of micro-channels were tested a circular micro-tube with a 210 pm diameter, and a square micro-channel with a 214 pm hydraulic diameter. The heat transfer coefficient was higher for the square micro-channel because the corners acted as effective nucleation sites. 

Available data sets for flow boiling critical heat flux (CHF) of water in small-diameter tubes are shown in Table 6.9. There are 13 collected data sets in all. Only taking data for tube diameters less than 6.22 mm, and then eliminating duplicate data and those not meeting the heat balance calculation, the collected database included a total of 3,837 data points (2,539 points for saturated CHF, and 1,298 points for subcooled CHF), covering a wide range of parameters, such as outlet pressures from 0.101 to 19.0 MPa, mass fluxes from 5.33 to 1.34 x lO kg/m s, critical heat fluxes from 0.094 to 276 MW/m, hydraulic diameters of channels from 0.330 to 6.22 mm, length-to-diameter ratios from 1.00 to 975, inlet qualities from —2.35 to 0, and outlet thermal equilibrium qualities from -1.75 to 1.00. 

Re = (tube, slit or spacer with hydraulic diameter d )... 

All the relationships presented in Chapter 6 apply directly to circular pipe. However, many of these results can also, with appropriate modification, be applied to conduits with noncircular cross sections. It should be recalled that the derivation of the momentum equation for uniform flow in a tube [e.g., Eq. (5-44)] involved no assumption about the shape of the tube cross section. The result is that the friction loss is a function of a geometric parameter called the hydraulic diameter ... 

It is important to use the hydraulic diameter substitution (D = Dh) in the appropriate (original) form of the dimensionless groups [e.g., VVRe = DVp , f = ef/(2LV2/D)] and not a form that has been adapted for circular tubes (e.g., tVRe = AQp/jtDjx). That is, the proper modification... 

The Reynolds number, based on a hydraulic diameter, is Reo = puD/fi. In general the hydraulic diameter is given as D = 4AC/P, where Ac is the channel cross-sectional area. For a laminar flow, an analytic solution for flow in cylindrical tubes provides... 

When the inlet length is expressed in terms of number of gap widths , the difference between the flow in a tube and the flow in an annulus of narrow gap differs only by 25% [(0.05 - 0.04)/0.05]. This situation is an indication that the growth of the laminar boundary layers from the wall to the center of the channel is similar in both cases. Because duct friction coefficients, a measure of momentum transfer, do not vary by more than a factor of 2 for ducts of regular cross sections when expressed in terms of hydraulic diameters, the use of the inlet length for tubes or parallel plates can be expected to be a reasonable approximation for the inlet lengths of other cross sections under laminar flow conditions. In the annular denuder, the dimensionless inlet length for laminar flow development, L, can be expressed as... 

Noncircular tubes are often used in various compact heat exchangers and the Reynolds number in these tubes is of interest. For noncircular tubes such as square, rectangular, elliptic, and triangular tubes, the so-called hydraulic diameter, D.H.y defined as... 

The entropy creation A due to head loss in the tubes is related to the heat transfer area A via the hydraulic diameter D = 4AcLN/A. Since the mass rate M is given by M = pvAcN = mAcN, Eqn. (9) yields ... 

Transition from laminar to turbulent flow within the condensed film can occur when the vapor is condensed on a tall surface or on a tall vertical bank of horizontal tubes [45] to [47]. It has been found that the film Reynolds number, based on the mean velocity in the film, um, and the hydraulic diameter, D, can be used to characterize the conditions under which transition from laminar flow occurs. The mean velocity in the film is given by definition as ... 

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