Relationship between reynolds number and friction factor equation

Fanning friction factor - Wikipedia

relationship between reynolds number and friction factor equation

The Hagen-Poiseuille equation for laminar flow indicates that the head loss is The relationship between the friction factor and Reynolds number can be. In this paper relationship between friction coefficient and Reynolds Number for . The profile was exploited to calculate total head loss (Δh) and the average. The Blasius empirical correlation for turbulent pipe friction factors is derived from where the exponent p is a function of the Reynolds number, y is the radial power law represented by equation (2) or the so called logarithmic law of the wall .

For a smooth pipe, the roughness term is neglected and the magnitude of the friction factor is determined by fluid Reynolds number alone.

relationship between reynolds number and friction factor equation

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. 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. Defining K, the loss coefficient, by allows for easy integration of minor losses into the Darcy-Weisbach equation.

K is the sum of all of the loss coefficients in the length of pipe, each contributing to the overall head loss.

Darcy friction factor formulae - Wikipedia

Although K appears to be a constant coefficient, it varies with different flow conditions. Factors affecting the value of K include: Tabulated values of K are for components in isolation - with long straight runs of pipe upstream and downstream. Some very basic information on K values for different fittings is included with these notes and in most introductory fluid mechanics texts. For more detail see e. To calculate losses in piping systems with both pipe friction and minor losses use in place of the Darcy-Weisbach equation.

Figure 1a presents schematic of the set up used in this research. The test procedure started with adjusting the bed slope, turning on the pump and flowing water into the flume, then the discharge was adjusted to a desired value through regulating the downstream water level by means of the adjustable gate.

Losses in Pipes

The water discharge was measured by means of the triangular weir and once the steady state flow was established through the system, sediment feeder started working with a constant rate g s Water surface profile inside the rockfill dam was precisely measured by drawing it on the Plexiglas flume outside wall. Usually this was down when the equilibrium state of sediment transport through the rockfill dam was achieved.

relationship between reynolds number and friction factor equation

As shown, in this figure the water depths h were measured at 14 points along the rockfill basket; i. The distance of two successive points is 6 cm. 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. 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.

Fanning friction factor

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.