Relationship between reynolds number and friction factor formula

Darcy friction factor formulae - Wikipedia

relationship between reynolds number and friction factor formula

The Fanning friction factor, named after John Thomas Fanning, is a dimensionless number . The formulas below may be used to obtain the Fanning friction factor for common applications. . For the turbulent flow regime, the relationship between the Fanning friction factor and the Reynolds number is more complex and is. The Darcy Weisbach equation relates frictional head loss (or pressure drop) in the friction factor is a function of Reynolds Number and pipe roughness/pipe. This formula is derived by investigating the correlation between friction in turbulent pipe flow and its influencing factors, i.e., Reynolds number.

This energy input is needed because there is frictional energy loss also called frictional head loss or frictional pressure drop due to the friction between the fluid and the pipe wall and internal friction within the fluid. The Darcy Weisbach Equation, which will be discussed in this article, is commonly used for a variety of calculations involving frictional head loss, pipe diameter, flow rate or velocity, and several other parameters.

The friction factor, which is used in the Darcy Weisbach equation, depends upon the Reynolds number and the pipe roughness.


Recall that pipe flow will be turbulent for a Reynolds number greater than Fully developed flow will be present in a pipe or conduit beyond the entrance length. The entrance length is where the velocity profile is adjusting to the constant profile that is present throughout the fully developed flow region.

The diagram at the left illustrates the concept of the entrance region and fully developed flow. Most pipe and conduit flow of gases and liquids with a viscosity similar to water will be turbulent flow.

Forces acting on the fluid during single phase steady flow in a pipe. Fanning Friction Factor The friction factor is found to be a function of the Reynolds number and the relative roughness.

Fanning friction factor - Wikipedia

Experimental results of Nikuradse who carried out experiments on fluid flow in smooth and rough pipes showed that the characteristics of the friction factor were different for laminar and turbulent flow. In this case, the friction factor of the Fanning equation can be calculated using the Hagen-Poiseuille equation see Poiseuille Flow. At high Reynolds number, the friction factor of rough pipes becomes constant, dependent only on the pipe roughness.

Karman-Nikuradze Equation Nikuradse measured the velocity profile and pressure drop in smooth and rough pipes where inner surfaces of rough pipes were roughened by sand grains of known sizes. The distance of two successive points is 6 cm.

relationship between reynolds number and friction factor formula

The friction coefficient and Reynolds Number are calculated according to Herrera and Felton Forty six tests were carried out among them thirty tests were selected randomly to establish a relationship between f and Re, while sixteen others were used for evaluating the derived relationship. Regression analysis was used to calibrate and validate the proposed power law equation Eq.

The Least Squares method's system of equations which includes the basic equations must be solved to determine the unknown coefficient and constant a and b of the proposed equation.

Fluid Mechanics: Laminar & Turbulent Pipe Flow, The Moody Diagram (17 of 34)

These equations along with Eq. A linear regression analysis two equations system is used to determine A and B as follow: To facilitate statistical analysis the software SPSS was used in this research. Mean square error of predicted friction coefficients with the proposed power law equation versus laboratory measured friction coefficients was used for validation of equations: This table also indicated a wide rage of laboratory measured Reynolds Number from Characteristics of the rock particles and flow hydraulics and summary of the laboratory tests results n: Test number, s bed slope of flume, Q: Reynolds Number of flow across the rockfill basket, f: Correlation between friction coefficient and Reynolds Number for a sediment laden flow through pervious rockfill dams, b: Validation of proposed equation As shown in Fig.

As shown in Fig.


A comparison between previous researches and present study has been done in Table 2. Experiments of StephensonHerrera and FeltonKorkias well as the first experiment of Li et al.

relationship between reynolds number and friction factor formula

These restrictions cause incapability for the resulted equations of mentioned researchers to predict the friction coefficient for the present study' range of Re.

This is because in the resulted equations the extrapolation of Re out of the tested ranges is not allowed.

  • Use the Friction Factor to Calculate Frictional Head Loss (Pressure Drop) for Pipe Flow
  • Fanning friction factor

Ghazimoradi and MasumiSamani et al. Therefore, their resulted equations are capable to predict comparable friction coefficient of sediment free flow for the Re values in the range of present study.

relationship between reynolds number and friction factor formula

As shown, a good precision is revealed in the results of present study Eq. Flow type, Reynolds Number and mean rock particle size of various researches f-Re tests are the tests to be conducted to find the friction coefficient and Reynolds Number relationship Fig. A Comparison between f values calculated with different equations and the measured values in the laboratory tests In Fig.

relationship between reynolds number and friction factor formula

This parameter for Eq. This difference is attributed to four restrictions in the experiments of Eq.