mean of a parabola

Strangely, I just can't find the method from google how to find a mean value from a parabola?

Any help?

Cheers

What do you mean by the "mean value" of a parabola?

Given that parabola can be defined as:

[INDENT]*y = ax2 + bx + **c* [/INDENT]I do not understand what you are looking for.

Actually I should state that more clearly.

I have a velocity profile that is parabolic in a pipe. I want to find the mean velocity of this profile. How can I do it? I remember that V_mean = something * V_max.

Any guiding light?

Cheers

If your pipe has a circular cross-section, won't you want the mean of a paraboloid, not a parabola? They are not the same.

Parabola: V_mean = (2/3)*V_max Paraboloid: V_mean = (1/2)*V_max

Basically:

Integral of (velocity field) * d(area element), over the area of interest, divided by the area. \int_0^R \int_0^{2\pi} v(r,\theta) r d\theta dr / (\pi R^2) with v(r,\theta) presumably something like V_max*(1-a*r^2).

jpkotta said: Basically:

Integral of (velocity field) * d(area element), over the area of interest, divided by the area. \int_0^R \int_0^{2\pi} v(r,\theta) r d\theta dr / (\pi R^2) with v(r,\theta) presumably something like V_max*(1-a*r^2). That's right, and in this context, the velocity is generally zero at the boundary, so v(r,\theta) = V_max*(1 - r^2/R^2).

Thanks both.

I have gotten it somewhere that say V_mean = (2/3)* V_max (laminar) V_mean = (49/60) * V_max (Turbulent)

Any idea where this originate from?

Of course jpkotta has the best answer from the mathematical perspective. That's the way for calculating mean.

Cheers