Moody Chart

5 Key excerpts on "Moody Chart"

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  eBook - PDF

  Engineering Fluid Mechanics

  • Donald F. Elger, Barbara A. LeBret, Clayton T. Crowe, John A. Roberson(Authors)
  • 2022(Publication Date)
  • Wiley

    (Publisher)

  These regions are also labeled in Fig. 10.12. Moody Chart Colebrook (7) advanced Nikuradse’s work by acquiring data for commercial pipes and then developing an empirical equation, called the Colebrook–White formula, for the friction fac- tor. Moody (4) used the Colebrook–White formula to generate a design chart similar to that shown in Fig. 10.13. This chart is now known as the Moody Chart or Moody diagram for commercial pipes. In the Moody Chart, Fig. 10.13, the variable k s denotes the equivalent sand rough- ness. That is, a pipe that has the same resistance characteristics at high Re values as a sand- roughened pipe is said to have a roughness equivalent to that of the sand-roughened pipe. Table 10.4 gives the equivalent sand roughness for various kinds of pipes. This table can be used to calculate the relative roughness for a given pipe diameter, which, in turn, is used in Fig. 10.13 to find the friction factor. In the Moody Chart, Fig. 10.13, the abscissa is the Reynolds number Re, and the ordinate is the resistance coefficient f. Each curve is for a constant relative roughness k s /D, and the values of k s /D are given on the right at the end of each curve. To find f, given Re and k s /D, go to the right to find the correct relative roughness curve. Then, look at the bottom of the chart to find the given value of Re and, with this value of Re, move vertically upward until the given k s /D curve is reached. Finally, from this point, move horizontally to the left scale to read the value of f. If the curve for the given value of k s /D is not plotted in Fig. 10.13, then simply find the proper position on the graph by interpolation between the k s /D curves that bracket the given k s /D. To provide a more convenient solution to some types of problems, the top of the Moody diagram presents a scale based on the parameter Re f 1/2 . This parameter is useful when h f and k s /D are known but the velocity V is not.

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  eBook - ePub

  Working Guide to Pump and Pumping Stations

  Calculations and Simulations

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

    (Publisher)

  Fanning friction factor . This is simply one-fourth the value of the Darcy (or Moody) friction factor, as follows:

  Figure 4.2 Moody diagram for friction factor.

  In this book, we will use the Darcy (or Moody) friction factor only.

  The relationship between the friction factor f and Reynolds number R for various flow regimes (laminar, critical, and turbulent) are as shown in Figure 4.2 . In turbulent flow, the friction factor f is also a function of the relative pipe roughness, a dimensionless parameter obtained by dividing the absolute internal pipe roughness (e) by the inside diameter (D) of the pipe.

  Examination of the Moody diagram shows that in laminar flow, for Reynolds numbers less than 2000, the friction factor decreases as the flow rate increases, reaching a value of approximately f = 0.032 at the boundary value of R = 2000.

  In the turbulent zone, for R > 4000, the friction factor depends on both the value of R as well as the relative roughness of pipe (e/D). As R increases in value beyond 10 million or so, f is a function of the relative roughness alone. This range called the complete turbulence in rough pipes and is designated as the Moody diagram region to the right of the dashed line. The portion between the critical zone and the dashed line is called the transition zone. In this zone the influence of Reynolds number on friction factor is more pronounced. For example, the Moody diagram shows that for R = 100,000 and relative roughness of 0.001, the friction factor is approximately 0.0225.

  In the critical zone (between R = 2000 and R = 4000), the value of the friction factor is undefined. Some empirical correlations have been put forth to cover this range of Reynolds numbers, but most of the time, the turbulent zone friction factor is used to be conservative. The relative roughness of the pipe is defined as

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  eBook - ePub

  Thermal Systems Design

  Fundamentals and Projects

  • Richard J. Martin(Author)
  • 2022(Publication Date)
  • Wiley

    (Publisher)

  Moody Chart became popular instantly with piping engineers and others desiring a visual tool for estimating friction factor. See Figure 2.7 for a representation of a portion of the turbulent regime in the Moody Chart. The accepted formula to compute friction factor used by Moody to produce his diagram was developed by Colebrook (1939). Because the Colebrook formula is implicit (i.e. the desired value f is part of the formula that defines f), and as such it necessitates an iterative solution, it is not presented here. Instead, an explicit formula that was developed by Chen (1979) is given as Equation (2.19). The Chen Equation correlates very well with the Colebrook results (and Moody #1 in Figure 2.7). Because it is explicit, the Chen equation does not require iteration. Alternative friction factor charts Moody #2 and Moody #3 are discussed in the next section. Table 2.1 Expressions for friction factors, velocity profiles, and shear stresses for laminar and turbulent flows in circular pipes. Source: Martin Thermal Engineering Inc. Concept Applicable to both laminar and turbulent Applicable to laminar only Applicable to turbulent only Friction factor Chen Equation (Equation 2.18) Radial velocity profile –, κ = 0.41, B = 5 Average velocity V (= u avg)= Wall shear stress Figure 2.7 The turbulent portion of the Moody Chart #1, plotted from the Chen equation

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  Fluid and Particle Mechanics

  Chemical Engineering Division

  • S. J. Michell, M. Perry(Authors)
  • 2013(Publication Date)
  • Pergamon

    (Publisher)

  The excellent results of Nikuradse's work suffer, however, from an in-convenient limitation, namely that—being based on artifially roughened surfaces—they are not directly reproducible in engineering problems connected with pipe friction. This limitation has been partly overcome by further investigations on uncoated commercial pipes. From a series of tests, Colebrook evaluated the friction factors for a num-ber of commercially important pipes, using a modified form of the Darcy equation h '=f'ii < 3 -24 > hence obtaining the corresponding values of their equivalent roughness from eq. (3.23). Finally, by plotting the test results, Colebrook obtained a single line described by the equation 9-28 * _ 2 log-^ = 114-2 log VJ e 1 + ReVf'(e/D) (3.25) Moody (1880-1953) extended the work of Colebrook by including information on more commercial pipes, and he also presented eq. (3.25) in the form of an earlier Stanton diagram. The diagram, reproduced in Fig. 3.6, bears his name. In order that the two friction factors appearing in the Darcy equation can be identified, / ' will be called in this text the Moody friction factor. Following the steps leading to the eq. (3.16), eq. (3.24) may also be presented in the form _ f'LQ* Α/ = 4δ^ ( 3 · 2 6 ) EXAMPLE 3.5 120-8 hp are expended in pumping water through a horizontal pipe of 12 in. diameter, and 1000 ft long, at a rate of 600 cfm. Assuming a 70 per cent overall efficiency of the pump, what is the roughness of the pipe ? FIG. 3.6. The Moody friction factor diagram. FLOW IN PIPES 97 98 FLUID AND PARTICLE MECHANICS Solution At 70 per cent pump efficiency, the power required to overcome pipe friction is hp = (120-8) (0-7) But also u- (ß)(4>) And, since from which Using eq.

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  Guide C: Reference data

  • W P Jones (chair), J F Armour, B G Lawrence, H B Awbi, P D Compton, R M Harris, M J Holmes, B P Holownia, J Moss, T Muneer, H K Versteeg, F Sprenger, R Dando, M Drew, R J Harris, K Mildren(Authors)
  • 2007(Publication Date)
  • The Chartered Institution of Building Services Engineers

    (Publisher)

  Two versions of the Moody Chart have been in circulation, one using a factor 4 f and another f or λ . In 2001, the CIBSE adopted λ to be in harmony with British hydraulics engineers and international practice. The new chart has the appropriate version of the D’Arcy equation printed on it to avoid any chance of misuse. Nevertheless, with personal computers now so widespread, numerical calculations are preferred to the more difficult and inaccurate graphical method. 4.2 Notation A Cross-section area of duct (m 2 ) A c Clear area of mesh screen (m 2 ) C α Correction factor for bends of angle α , relative to α = 90° C cp Interaction factor for components in close proximity 4 Flow of fluids in pipes and ducts 4.1 Introduction 4.2 Notation 4.3 Fluid flow in straight pipes and ducts 4.4 Components and fittings 4.5 Water flow in pipes 4.6 Flow of steam in pipes 4.7 Natural gas in pipes 4.8 Air flow in ducts 4.9 Pressure loss factors for components and fittings 4.10 Pressure loss factors for pipework components 4.11 Pressure loss factors for ductwork components References Appendix 4.A1: Properties of various fluids Appendix 4.A2: Pipe and duct sizing Appendix 4.A3: Capacity ( K ) and complex networks Appendix 4.A4: Steam flow in pipes Appendix 4.A5: Compressible flow The method for calculating the pressure drop along pipes and ducts is now much simplified. Hitherto, only cumbersome iterative methods were possible, therefore many pages of pre-calculated values were provided. Since a much simpler, but still accurate equation is now available (equation 4.5), pipe sizing can be carried out directly on a simple spreadsheet for any temperature and indeed for any fluid. The CD -ROM that accompanies this Guide contains Microsoft® Excel spreadsheets for pipe and duct sizing. Pre-calculated pressure-drop tables are therefore no longer needed, and such tables have been omitted from this edition of Guide C.

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