Darcy-Weisbach friction factor

An incompressible fluid flows in a laminar steady fashion through a long pipe with a linear pressure gradient. Describe the velocity profile and determine the relationship for the Darcy-Weisbach friction factor. 

Because we do not have the slope to determine u, we will use the following equation that results from the definition of the Darcy-Weisbach friction factor ... 

It is also called the Darcy-Weisbach friction factor, named after the Frenchman Henry Darcy (1803-1858) and the German Julius Weisbach (1806-1871), the two engineers who provided the greatest contribution in its development. It should not be confused with the friction coefficient Cf [also... 

Darcy-Weisbach) friction factor for turbulent flow... 

In the above equation, L is the length over which the pressure drop p — p2 is to be calculated pi is the absolute pressure of the flow at an upstream point 1, and p2 is the absolute pressure of the flow at a downstream point 2 / is the Darcy-Weisbach friction factor that can be determined from the Moody Diagram y is the adiabatic exponent (equal to 1.4 for air) and Mi is the Mach number of the flow at the upstream point 1. In addition to the pressure equations, the following equation of state of ideal gas is also needed ... 

AHf= head loss due to friction (in units of length) fp = Darcy-Weisbach friction factor Cl = constant... 

The friction factor is used in the Darcy-Weisbach equation for calculation of pressure drop for turbulent flow in an empty pipe. The mixer pressure drop is given by... 

Method for calculation of major losses of liquids. First determine fluid properties such as the density, and dynamic viscosity at the operating temperature. Determine the inner diameter of the pipe, and evaluate its absolute roughness based on Table 20.3. Then calculate the Reynolds number for average velocity of the liquid. Afterwards, either use the Moody chart to evaluate the Fanning friction factor based on the Reynolds number and relative roughness, or compute the Colebrook equation by successive iterations. Finally, use the Darcy-Weisbach equation to determine the friction head loss. 

The additional pressure losses between (A) and (B) include the friction losses and pressure losses in all the pipe fittings such as valves, elbows, expansions, contraction branches, and bypasses. Pressure is also lost at entry and exit as well. Such pressure losses are expressed in terms of the Darcy-Weisbach equation and in terms of pressure loss factors for each fitting. 

The Darcy-Weisbach Equation applies to a wide range of fluids, while the Hazen-Williams Equation is based on empirical data and is used primarily in water modeling applications. Each of these methods calculates friction losses as a function of the velocity of the fluid and some measure of the pipe s resistance to flow (pipe wall roughness). Typical pipe roughness values for these methods are shown in Table 3.3. These values can vary depending on the product manufacturer, workmanship, age, and many other factors. 

Many equations are available to show the relationship between fluid flow and pressure drop in a given pipeline. The equations typically involve a friction factor that is dependent on the pipe materials. Darcy-Weisbach and Hazen-Williams are commonly used equations. 

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