3 replies to this topic

[Praj06]

what is the momentum correction factor and kinetic energy correction factor for laminar flow and turbulent flow?

[sheiko]

Hi,

Where have you heard from that terms?

[kkala]

During flow, energy per unit mass of fluid at a pipe cross section (Bernoulli theorem) is composed of potential + flow + kinetic energy, that is h*g+p/ρ+0.5*v² (h=reference height, p=pressure, ρ=fluid density, v=fluid velocity, g=gravity acceleration). Concerning the kinetic energy, we consider v=volumetric flowrate/cross section. But there is a velocity distribution on the cross section; actual kinetic energy per unit mass (taking squares of all distribution velocities into account) is a bit different to above 0.5*v². Thus the latter is multiplied by a correction factor α (depending on Re number) and energy per unit mass becomes h*g+p/ρ+0.5*α*v².
See also http://www-mdp.eng.c...sis/node41.html '> http://www-mdp.eng.c...sis/node41.html .
Frankly, I have not applied it so far in pipe calculations, having forgotten it. It may not be significant in calculations that we do (high velocities and laminar flow seem contradictory).
Having not met the momentum correction factor, it seems to be similar concerning momentum equation in fluid flow. http://nptel.iitm.ac...s/Unit6/6_1.pdf '> http://nptel.iitm.ac...s/Unit6/6_1.pdf gives some explanations / values. It also indicates that these correction factors could be useful in open channel flow.

[katmar]

I haven't come across a momentum correction factor, but I think if the Bernoulli equation is expressed in the correct form the terms become momentum fluxes, so maybe it is the same thing as the kinetic energy correction factor - just expressed slightly differently.

The kinetic energy correction factor is very often not well dealt with in the text books. As Kostas has pointed out, the kinetic energy term is expressed as αv²/(2g) - and is known as the velocity head. The factor α is required because instead of integrating to get the true average of v², we cheat a bit and take the average of v² to be equal to the square of the average velocity ( i.e. velocity = flowrate/area ). It makes a difference whether you square first, or average first. α would be 1.0 for a truly flat velocity profile and is greater than 1.0 for any real life profile. In practical terms it is close enough to 1.0 in fully turbulent flow that we can ignore it, and for laminar flow it is 2.0.

Where it becomes important is when we come to calculate pressure drops in pipes and fittings. In turbulent pipe flow we multiply the velocity head by ƒL/D, where ƒ is the Moody friction factor, L is the length and D is the pipe inside diameter. When it comes to laminar flow we could introduce the value of 2 for α, but what everyone does is define a laminar flow friction factor that includes the effect of this 2. This makes the arithmetic much easier - we keep the same definition for velocity head (ignoring α) and because we have to have a new expression for friction factor in laminar flow anyway, we might as well include the correction there.

A similar thing is done with the resistance coefficients (K values) for pipe fittings. We define the K values to include the value of α just to keep the arithmetic easy.

There is just one exception when it comes to minor losses. What is often called the "exit loss", but which is more accurately the acceleration loss, is the kinetic energy in the stream issuing from the discharge of the pipe. This energy is lost (except where very carefully designed diffusers are used in compressible flow - but that's another story) and is equal to one velocity head. There is no way of getting away from it that here you have to use the correct value of α to get the "exit loss" correct. But in practice this is not at all important. In laminar flow the velocity is low enough that one velocity head is insignificant - and even if doubled with an α value of 2, it is still insignificant. The K values of fittings in laminar flow can go into the hundreds, or even thousands, and one measly little 2.0 isn't going to bother anybody. Thousands of engineers ignore it every day, and their designs still work!

Edited by katmar, 05 October 2012 - 02:44 PM.