Colebrook Equation

3 Key excerpts on "Colebrook Equation"

• 

  eBook - PDF

  Albright's Chemical Engineering Handbook

  • Lyle Albright(Author)
  • 2008(Publication Date)
  • CRC Press

    (Publisher)

  For pipe, these are related to the dimensionless (Fanning) friction factor ( f ) by (5.63) A loss coefficient can be defined for any element in which energy is dissipated (pipe, fittings, valves, etc.), although the friction factor is defined only for pipe flow. All that is necessary to describe the pressure-flow relation for pipe flows is Bernoulli’s equation and a knowledge of the friction factor, which depends upon flow conditions, pipe size, and fluid properties. 5.5.3 N EWTONIAN F LUIDS 5.5.3.1 Laminar Flow For a Newtonian fluid in laminar flow, (5.64) i.e., only one dimensionless group, fN Re , is required to characterize laminar pipe flow, which has a value of 16. When this is introduced into the Bernoulli equation, the result is (5.65) which is the Hagen-Poiseuille equation. N DV V V D Re / = = ρ μ ρ μ 2 e K V fL D f f w = = ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 2 2 4 τ ρ K fL D f V f w = = 4 2 2 ; τ ρ f D Q DV N = = = 4 16 16 π μ ρ μ ρ Re Q D L = − π μ ΔΦ 4 128 420 Albright’s Chemical Engineering Handbook 5.5.3.2 Turbulent Flow For smooth pipe for Reynolds numbers from 4000 to 10 6 , the von Karman equation provides an implicit relation between the friction factor and the Reynolds number: (5.66) where is (5.67) which is independent of flow rate. 5.5.3.3 Rough Pipe Colebrook extended the von Karman equation to account for tube wall roughness ( ε / D ) as follows: (5.68) The Colebrook Equation is convenient for determining the flow rate from the allowable friction loss (e.g., driving force), tube size, and fluid properties. Published plots of f vs. N Re and ε / D (i.e., the Moody diagram) are usually generated from the Colebrook Equation. The actual size of the roughness elements on any surface will vary with the material, age and usage, deposits, dirt, scale, rust, etc. Typical values for various materials are given in Table 5.3. The most common pipe material—clean, new, commercial steel—has an effective roughness of about 0.0018 in.

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  Working Guide to Pump and Pumping Stations

  Calculations and Simulations

  • E. Shashi Menon(Author)
  • 2009(Publication Date)
  • Gulf Professional Publishing

    (Publisher)

  Initially, we assume a value for f (such as 0.02) and substitute the values into the right-hand side of Equation (4.21). A second approximation for f is then calculated. This value can then be used on the right-hand side of the equation to obtain the next better approximation for f, and so on. The iteration is terminated, when successive values of f are within a small value such as 0.001. Usually three or four iterations are sufficient. As mentioned before, for the critical flow region (2000 < R < 4000), the friction factor is considered undefined, and the turbulent friction factor is used instead. There have been several correlations proposed for the critical zone friction factor in recent years. Generally, it is sufficient to use the turbulent flow friction factor in most cases when the flow is in the critical zone. The calculation of the friction factor f for turbulent flow using the Colebrook-White equation requires an iterative approach, since the equation is an implicit one. Due to this, many explicit equations have been proposed by researchers that are much easier to use than the Colebrook-White equation, and these have been found to be quite accurate compared to the results of the Moody diagram. The Swamee-Jain equation or the Churchill equation for friction factor may be used instead of the Colebrook-White equation, as described next. Explicit Equations for the Friction Factor P. K. Swamee and A. K. Jain proposed an explicit equation for the friction factor in 1976 in the Journal of the Hydraulics Division of ASCE. The Swamee-Jain equation is as follows: ((4.22)) Another explicit equation for the friction factor, proposed by Stuart Churchill, was reported in Chemical Engineering in November 1977. It requires the calculation of parameters A and B, which are functions of the Reynolds number R

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Unit Operations in Food Engineering

  • Albert Ibarz, Gustavo V. Barbosa-Canovas(Authors)
  • 2002(Publication Date)
  • CRC Press

    (Publisher)

  170 Unit Operations in Food Engineering For Newtonian and power law fluids m = 0 and ψ = 1, it is possible to calculate the friction factor directly from Equation 7.67 or 7.68. For Bingham and Herschel–Bulkley fluids, if the value of m is not known, it is necessary to solve Equation 7.72 by iteration or by trial and error, using Equations 7.70, 7.71, and the generalized Reynolds number (Equation 7.7) to obtain the value of ψ and, finally, the value of f . 7.4.2.2 Flow under Turbulent Regime Other equations are used under turbulent regime, theoretically obtained from the denominated universal profile of velocities. However, in the calcu-lation of the friction factor, empirical or semiempirical equations are usually used. As occurs in laminar regime, the equations are dependent on the type of fluid transported. • Newtonian fluids: one equation often used for rough pipes is the Colebook equation (Welty et al., 1976; Levenspiel, 1993): (7.73) For a completely developed turbulent regime, the first term within the logarithm is negligible with respect to the second, obtaining a new equation, that of Nikuradse (Skelland, 1967; Welty et al., 1976; Levenspiel, 1993): (7.74) Another useful equation for evaluating the friction factor is the following (Levenspiel, 1993): (7.75) For values of Reynolds numbers between 2.5 × 10 3 and 10 5 and smooth pipes, Blasius (Levenspiel, 1993) obtained the following correlation: (7.76) 1 4 2 2 51 4 1 3 5 1 2 1 2 f f d ( ) = − ( ) +         log . Re . ε 1 4 2 3 7 1 2 f d ( ) =       log . ε 1 4 2 5 62 0 27 1 2 0 9 f d ( ) = − +       log . Re . . ε 4 0 316 1 4 f = ( ) . Re Transport of Fluids through Pipes 171 Another correlation frequently used for smooth pipes (Coulson and Rich-ardson, 1979) is: (7.77) Besides these equations, various researchers have proposed other correla-tions that can be more or less applied, depending on the particular charac-teristics of the transport system.

  Sign up to read

  Learn more about book