Moody Friction Factor - drop in friction with increase in Re, why??

[RktRider]

This is really just a general question about the Moody Diagram. I understand that the friction factor is inversly proportional to the Reynolds number by definition of the equation. But from a physical standpoint, why does this decrease in friction with increase in velocity occur? Do the kinectic forces overcome the viscous forces of the fluid?

 

[butelja]

The Reynolds number is the ratio of momentum forces to viscous forces. So, I believe your assumption that kinetic (momentum) overcomes viscous forces at high Reynold's numbers is correct. Consider the limiting cases of 0 and infinite Reynold's numbers. Near 0, there is no momentum, and all forces are viscous. Near infinity, viscous forces are negligible, and momentum forces govern.

 

[vtl]

Also, consider a case where water flow in the horizontal pipe. If no friction then there is constant velocity through out. If there is friction(due to pipe roughness) then there is shear between the water and the pipe walls, as a result the water slowdown.

 

[olynyk]

Keep in mind that just because there is a decrease in friction factor with higher velocity does not imply a decrease in actual friction force with higher velocity. Reynolds number varies as the first power of the fluid velocity, and friction factor decreases as Reynolds number increases (this is governed by the Colebrook equation from which the Moody charts are made). This is not a polynomial dependency, it has to do with logarithms. We can say for sure though that friction factor f declines with increasing Reynolds # (and thus increasing speed).

However, then head loss (as governed by the Darcy-Weisbach equation) varies as the second power of the fluid velocity, and the first power of the friction factor! So even though friction factor is going down, frictional losses are going up.

Combining all these dependencies, we find that head loss increases according to somewhere between the first and second power of fluid velocity - probably close to a 2nd-order dependency since the decline in friction factor is slow with increasing Reynolds number.

 

[Cockroach]

VTl, the velocity profile is approximately parabolic across the diameter of the pipe.

The fluid thus flows fast at the centre line bore axis, meaning significantly less resistance to flow in comparison to the immediate vicinity along the interior walls of the pipe.

There are other profiles, typically the parabola is discussed in fluid textbooks.

Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada

 

[25362]

The concept of the non dimensional "friction factor" may be confusing but one should remember that it was created to replace the expression function of the Reynolds number, f (Re), in short just f, and should be looked upon as such.

Kindly note that hydraulics uses the Darcy friction factor, while aerodynamics and heat transfer commonly refer to the Fanning friction factor which is one-quarter as large. When using results from literature one has to exercise care to make sure one has the right coefficient.

 

[sailoday28]

RktRider (Mechanical) 6 Feb 01 6:48 STATES
"I understand that the friction factor is inversly proportional to the Reynolds number by definition of the equation"

This is generall true, except in the transition region between laminar and turbulent flow
and at high Reynolds numbers where the friction factor remains essentially constant.

 

[hydrae]

Cockroach
The Classic Parabola velocity profile of laminar flow is extremly rare, take the case of water distribution systems where pipe diameters are sized for fire flow and normal use are household demand, a 6 inch pipe flowing at 10 gpm is turbulent which has a plug flow profile.

The Hazzen-Williams equations which are used extensively in the water works industry compares the velocity to the pressure drop raised to the .54 power, which confirms that pressure drop is proportional to slightly less than the square of the velocity.

Hydrae

 

[30ale]

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[25362]

The drop in the value of "f", the friction factor, with increasing Re numbers on Newtonian fluids, relates to the boundary layer where shear stresses between the tube wall and the fluid takes place. This fluid layer is considered "laminar" even in turbulent flow and is very important because it offers resistance to mass and heat transfer from the wall to the bulk of the fluid and viceversa.

Its thickness decreases with increasing kinetic energy of the fluid. In a smooth tube of radius R, the layer thickness drops from 0.0043*R at Re=10,000, to 0.00055*R at Re=100,000. It would continue in being reduced at higher Re values in smooth tubes, were it not for the effect of the conduit wall rugosities expressed as [ε]/D, the ratio of the height of the wall surface unevenness to the pipe diameter.