Reynolds Number and Friction Factor: How Does It Work?

In summary, an increase in Reynolds number leads to more turbulence and higher energy loss due to eddies. However, contrary to expectations, the friction factor actually decreases with increasing Reynolds number according to the Moody diagram and experimental data. This is because the drag shear stress at the wall increases with flow velocity more than the decrease in friction factor, resulting in a net increase in frictional wall stress.
  • #1
thereisnospoo
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So, I understand that when reynolds number increases, the fluid becomes more turbulent, and there is a greater energy loss due to formation of eddies. However, shouldn't this increase in reynolds number cause an increase in friction as well?

But, according to the moody diagram (http://piping-designer.com/wiki/images/0/05/Moody-Diagram.jpg)
as well as experimental data I have collected, it seems that friction factor actually decreases as reynolds number increases. How is this possible, if increasing turbulence causes more haphazard flow, wouldn't their be greater frictional forces?
 
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  • #2
The drag shear stress at the wall is equal to the friction factor times the dynamic pressure ##\rho \frac{v^2}{2}##, and the latter increases with flow velocity more than the friction factor decreases. So the net effect is an increase in the frictional wall stress.
 
Question 1:

What is the Reynolds Number?

The Reynolds Number is a dimensionless quantity that is used to predict the type of flow (laminar or turbulent) in a fluid. It is calculated by dividing the product of the fluid's velocity, density, and length scale by its dynamic viscosity.

Question 2:

How is the Reynolds Number related to friction factor?

The Reynolds Number is directly related to the friction factor, which is a dimensionless quantity that represents the amount of frictional resistance experienced by a fluid moving through a pipe. The higher the Reynolds Number, the lower the friction factor, indicating a more turbulent flow with less frictional resistance.

Question 3:

What is the significance of the Reynolds Number in fluid mechanics?

The Reynolds Number is an important parameter in fluid mechanics as it helps determine the type of flow (laminar or turbulent) and the amount of frictional resistance experienced by a fluid. It is also used to predict the onset of turbulent flow and to determine the efficiency of different flow control strategies.

Question 4:

How does the Reynolds Number affect the drag force on an object?

The Reynolds Number plays a crucial role in determining the drag force on an object moving through a fluid. At low Reynolds Numbers, the flow around an object is smooth (laminar) and the drag force is directly proportional to the object's velocity. At high Reynolds Numbers, the flow becomes turbulent and the drag force increases significantly due to the formation of vortices.

Question 5:

What are some practical applications of the Reynolds Number and friction factor?

The Reynolds Number and friction factor have numerous practical applications in various industries. They are used in the design of pipelines, pumps, and other fluid systems to ensure efficient and effective flow. They are also important in aerodynamics, hydrodynamics, and many other fields where fluid flow plays a critical role.

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