Smooth pipes

For laminar flow (Re < 2000), generally found only in circuits handling heavy oils or other viscous fluids, / = 16/Re. For turbulent flow, the friction factor is dependent on the relative roughness of the pipe and on the Reynolds number. An approximation of the Fanning friction factor for turbulent flow in smooth pipes, reasonably good up to Re = 150,000, is given by / = (0.079)/(4i e ). 

E] Smooth pipe data. Data fits within 4% except at Nsc> 20,000, where experimental data is underpredicted. 

Friction Factor and Reynolds Number For a Newtonian fluid in a smooth pipe, dimensional analysis relates the frictional pressure drop per unit length AP/L to the pipe diameter D, density p, and average velocity V through two dimensionless groups, the Fanning friction factor/and the Reynolds number Re. 

For smooth pipe, the friction factor is a function only of the Reynolds number. In rough pipe, the relative roughness /D also affects the friction factor. Figure 6-9 plots/as a function of Re and /D. Values of for various materials are given in Table 6-1. The Fanning friction factor should not be confused with the Darcy friction fac tor used by Moody Trans. ASME, 66, 671 [1944]), which is four times greater. Using the momentum equation, the stress at the wall of the pipe may be expressed in terms of the friction factor ... 

In laminar flow,/is independent of /D. In turbulent flow, the friction factor for rough pipe follows the smooth tube curve for a range of Reynolds numbers (hydrauhcaUy smooth flow). For greater Reynolds numbers,/deviates from the smooth pipe cui ve, eventually becoming independent of Re. This region, often called complete turbulence, is frequently encountered in commercial pipe flows. The Reynolds number above which / becomes essentially independent of Re is (Davies, Turbulence Phenomena, Academic, New York, 1972, p. 37) 20[3.2-2.46ln( /D) ... 

Fluid flow is also critical for proper operation of a hydraulic system. Turbulent flow should be avoided as much as possible. Clean, smooth pipe or tubing should be used to provide laminar flow and the lowest friction possible within the system. Sharp, close radius bends and sudden changes in cross-sectional area are avoided. 

Region 3 (Re > 3000) corresponds to turbulent motion of the fluid and R/pu2 is a function of both Re and e/d, with rough pipes giving high values of R/pu2. For smooth pipes there is a lower limit below which R/pu2 does not fall for any particular value of Re. 

HARTNETT and KOSTIC 26 have recently examined the published correlations for turbulent flow of shear-thinning power-law fluids in pipes and in non-circular ducts, and have concluded that, for smooth pipes, Dodge and Metzner S(27) modification of equation 3.11 (to which it reduces for Newtonian fluids) is the most satisfactory. 

The chosen value of 0.0015 for R/pu2 is reasonable for a smooth pipe over most of the range of Reynolds numbers encountered in this exercise. 

Farooqi, S. 1. and Richardson, J. F. Trans. Inst. Chem. Eng. 60 (1982) 292-305. Horizontal flow of air and liquid (Newtonian and non-Newtonian) in a smooth pipe Part 1 Correlation for average liquid holdup. 

Horn I ipure. 1.7, ihe friction factor for a smooth pipe is ... 

The right-hand side of equation 10.224 gives numerical values which are very close to those obtained from the Blasius equation for the friction factor (j> for the turbulent flow of a fluid through a smooth pipe at Reynolds numbers up to about 106. 

For a smooth pipe, therefore, the complete Universal Velocity Profile is given by ... 

Using the Blasius equation (equation 11.46) to give an approximate value for R/pu2 for a smooth pipe ... 

For hydrodynamically smooth pipes, through which fluid is flowing under turbulent conditions, the shear stress is given approximately by the Blasius equation ... 

When the thickness of the laminar sub-layer is large compared with the height of the obstructions, the pipe behaves as a smooth pipe (when e < <5 /3). Since the thickness of the laminar sub-layer decreases as the Reynolds number is increased, a surface which is hydrodynamically smooth at low Reynolds numbers may behave as a rough surface at higher values. This explains the shapes of the curves obtained for plotted against Reynolds number (Figure 3.7). The curves, for all but the roughest of pipes, follow the... 

For flow in a smooth pipe, the friction factor for turbulent flow is given approximately by the Blasius equation and is proportional to the Reynolds number (and hence the velocity) raised to a power of -2. From equations 12.102 and 12.103, therefore, the heat and mass transfer coefficients are both proportional to w 75. 

Derive an expression relating the pressure drop for the turbulent flow of a fluid in a pipe to the heat transfer coefficient at the walls on the basis of the simple Reynolds analogy. Indicate the assumptions which are made and the conditions under which you would expect it to apply closely. Air at 320 K and atmospheric pressure is flowing through a smooth pipe of 50 mm internal diameter, and the pressure drop over a 4 m length is found to be 150 mm water gauge. By how much would you expect the air temperature to fall over the first metre if the. wall temperature there is 290 K ... 

The Reynolds number of a gas flowing at 2.5 kg/nrs through a smooth pipe is 20,000. If the specific heat of the gas at constant pressure is 1.67 kJ/kg K, what will the heat transfer coefficient be ... 

Friction factor correlations, smooth pipes 67 - — Darcy and Fanning 67, 68 -- — Moody 65... 

For adiabatic, steady-state, and developed gas-liquid two-phase flow in a smooth pipe, assuming immiscible and incompressible phases, the essential variables are pu, pG, Pl, Pg, cr, dh, g, 9, Uls, and Uas, where subscripts L and G represent liquid and gas (or vapor), respectively, p is the density, p is the viscosity, cr is the surface tension, dh is the channel hydraulic diameter, 9 is the channel angle of inclination with respect to the gravity force, or the contact angle, g is the acceleration due to gravity, and Uls and Ugs are the liquid and gas superficial velocities, respectively. The independent dimensionless parameters can be chosen as Ap/pu (where Ap = Pl-Pg), and... 

Direct measurements of turbulent heat transfer in smooth pipes led to the correlation known as the Dittus-Boelter equation... 

It should be noted that Equations 13.9 and 13.10 apply to smooth pipes, whereas the pipes used for transmission of fluids usually have some surface roughness, which increases the friction factor. However, for short fluid transmission pipes, the overall pressure drop is usually dominated by the pressure drop in the pipe fittings (valves, bends, etc). Thus, for short transmission pipes, there is little point in calculating the straight pipe pressure drop accurately. If the transmission pipe is long (>100 m) and straight, then the Fanning friction factor can be correlated as7 ... 

Rf = ratio of rough pipe friction factor to smooth pipe friction factor, 1.0-2.9... 

The constants in this equation were modified by Nikuradse from observed data taken in smooth pipes as follows ... 

Equation (6-35) is also known as the von Karman-Nikuradse equation and agrees well with observations for friction loss in smooth pipe over the range 5 x 103 < NRe < 5 x 106. 

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