Flow in Round Tubes

The study of flow and elasticity dates to antiquity. Practical rheology existed for centuries before Hooke and Newton proposed the basic laws of elastic response and simple viscous flow, respectively, in the seventeenth century. Further advances in understanding came in the mid-nineteenth century with models for viscous flow in round tubes. The introduction of the first practical rotational viscometer by Couette in 1890 (1,2) was another milestone. 

Fig. 27. Approximate boundary of the low-velocity burn-out regime for water flowing in round tubes. The low-velocity regime lies to the left of any given curve [from Macbeth (M2)].

Serizawa et al. (2002) studied experimentally, through visualization, the two-phase flow patterns in air-water two-phase flows in round tubes. The test section for air-water experiments consisted of a transparent silica or quartz capillary tube with circular cross-section positioned horizontally. The two-phase flow was realized through a mixer with different designs, as shown in Figs. 5.4 and 5.5. The air was injected into the mixer co-axially while water was introduced peripherally. 

Flow In Round Tubes In addition to the Nusselt (NuD = hD/k) and Prandtl (Pr = v/a) numbers introduced above, the key dimensionless parameter for forced convection in round tubes of diameter D is the Reynolds number Re = (.7 ) u where G is the mass velocity G = m/Ac and Ac is the cross-sectional area Ac = kD2I4. For internal flow in a tube or duct, the heat-transfer coefficient is defined as... 

R. E. Drexel, and W. H. McAdams, Heat Transfer Coefficients for Air Flowing in Round Tubes, and Around Finned Cylinders, NACA ARR No. 4F28 also Wartime Report W-108,1945. 

Example 12.5.a-l Axial Dispersion Model for Laminar Flow in Round Tubes... 

Equation (3.5-4) is simply another statement of the power-law model of Eq. (3.5-2) applied to flow in round tubes, and is more convenient to. use for pipe-flow situations (D2). Hence, Eq. (3.5-4) defines the flow characteristics just as completely as Eq. (35-2). It has been found experimentally (M3) that, for most fluids K and n are constant over wide ranges of 8F/D or D Apl4L. For some fluids this is not the case, and K and n vary. Then the particular values of K and ri used must be valid for the actual 8 VID or D API4L with which one is dealing in a design problem. This method using flow in a pipe or tube is often used to determine the flow properties of a non-Newtonian fluid. 

Axial Dispersion Model for Turbulent Flow in Round Tubes An empirical correlation given by Wen and Fan (1975) for turbulent flow in a round tube is ... 

The most basic state of motion for fluid in a pipe is one in which the motion occurs at a constant rate, independent of time. The pressure flow relation for laminar, steady flow in round tubes is called Poiseuille s Law, after J.L.M. Poiseuille, the French physiologist who first derived the relation in 1840 [12]. Accordingly, steady flow through a pipe or channel that is driven by a pressure difference between the pipe ends of just sufficient magnitude to overcome the tendency of the fluid to dissipate energy through the action of viscosity is called Poiseuille flow. 

Thi.s equation may be used for turbulent flow in round tubes or for turbulent flow outside round tubes. 

Dl. De Bortoli, R. A., and Masnovi, R., Effect of dissolved hydrogen on burnout for water flowing vertically upwards in round tubes at 2000 psia, WAPD-TH-318 (1957). 

DeBortoli, R. A., and R. Masnovi, 1957, Effect of Dissolved Hydrogen on Burnout for Water Flowing Vertically Upward in Round Tubes at 2000 psia, USAEC Rep. WAPD-TH-318, Pittsburgh, PA. (5) Ded, J., and J. H. Lienhard, 1972, The Peak Pool Boiling Heat Transfer from a Sphere, AIChE J. 18(2)331-342. (2)... 

Taylor (T2) and Westhaver (W5, W6, W7) have discussed the relationship between dispersion models. For laminar flow in round empty tubes, they showed that dispersion due to molecular diffusion and radial velocity variations may be represented by flow with a flat velocity profile equal to the actual mean velocity, u, and with an effective axial dispersion coefficient Djf = However, in the analysis, Taylor... 

Axiai Dispersion Modei for Laminar Fiow in Round Tubes The exact two-dimensional equation for laminar flow in tubes is given by Eqs. (4.10.27) and (4.10.28) ... 

For example, in a laminar or PoiseuiEe flow in a round tube of radius for a given initial mixture composition, flashback (or blowoff)... 

The above conclusion must certainly be taken with a measure of reserve as regards the mass velocity, for at very low velocities it appears reasonable to expect that the relative motion between vapor and liquid in a boiling channel will be affected sufficiently to influence the burn-out flux. Barnett s conclusion also applies to simple channels, whereas Fig. 35 discussed in Section VIII,C shows that a rod-bundle system placed in a horizontal position is likely to incur a reduction in the burn-out flux at mass velocities less than 0.5 x 106 lb/hr-ft2, presumably on account of flow stratification. Furthermore, gravitational effects induced in a boiling channel by such means as swirlers placed inside a round tube can certainly increase the burn-out flux as shown by Bundy et al. (B23), Howard (H10), and Moeck et al. (Ml5). 

There are several possible explanations of the apparent conflict between Figs. 34 and 35. One possible explanation, for example, would be that the vertical upflow curve drawn in Fig. 34 may not be a straight line, but should perhaps curve upwards (the data itself shows some signs of this) toward the uppermost point of the horizontal flow line, which corresponds to the rod bundle in question. It will be seen later, however, that this would not appear to be the explanation. In addition, there is the fact that all the horizontal flow data in Fig. 34, as well as the new data in Fig. 35, are for a test pressure of 1215 psia, whereas the vertical upflow data in Fig. 34 refer to 1000 psia. Although there is no evidence to indicate the effect of pressure in the case of rod-bundle systems with round tubes, it is found that increasing pressure from... 

A5. Alessandrini, A., Bertoletti, S., Gaspari, G. P., Lombardi, C., Soldaini, G., and Zavattarelli, R., Critical heat flux data for fully developed flow of steam and water mixtures in round vertical tubes with an intermediate nonheated section, CISE-R69 (1963). 

H7. Hines, W. S., Forced convection and peak nucleate boiling heat transfer characteristics for hydrazine flowing turbulently in a round tube at pressures to 1000 psia, Rept. No. 2059, Rocketdyne, Canoga Park, California (1959). 

Staniforth, R., Stevens, G. F., and Wood, R. W., An experimental investigation into the relationship between burnout and film flow-rate in a uniformly heated round tube, AEEW-R430, H. M. Stationery Office, London (1965). 

Katto Y (1978) A generalized correlation for critical heat flux for the forced convection boihng in vertical uniformly heated round tubes. Int J Heat Mass Transfer 21 1527-1542 Khrustalev D, Faghri A (1996) Fluid flow effect in evaporation from liquid-vapor meniscus. ASME J Heat Mass Transfer 118 725-747... 

The flow through helically configured, round tubes was first examined by Eustice (12) in 1910 and the first theoretical analysis was published by Dean in 1927 and 1928 (13). He showed that the fluid flow could be characterized by the dimensionless group... 

The vibration induced by the fluid flowing over the tube bundle is caused principally by vortex shedding and turbulent buffeting. As fluid flows over a tube vortices are shed from the down-stream side which cause disturbances in the flow pattern and pressure distribution round the tube. Turbulent buffeting of tubes occurs at high flow-rates due to the intense turbulence at high Reynolds numbers. 

In an annular test section, the flow channel cross session is subdivided into two subchannels surrounding each solid surface. Round tube correlation is applied to each subchannel, i, to obtain WBi. The correlation for an annulus then becomes... 

Alessandrini, A., S. Bertoletti, G. P. Gaspari, C. Lombardi, G. Soldrini, and R. Zavattarelli, 1963, Critical Heat Flux Data for Fully Developed Flow of Steam-Water Mixtures in Round Vertical Tubes with an Intermediate Nonheated Section, Centro Informationi Studi Esperienzi Rept. CISE-R-69, Milan, Italy. (5)... 

Becker, K. M., 1971, Measurement of Burnout Conditions for Flow of Boiling Water in Horizontal Round Tubes, Atomenergia-Aktieb Rep. AERL-1262, 25, Nykoping, Sweden. (3)... 

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