Laminar Pipe Flow: Displacement, and Momentum Thicknesses

1. Dec 13, 2014

Disquoveri

Hello. I'm new to the forums. I apologize if I have posted this in the wrong topic area.

I'm new to this hydrodynamics area and I'm trying to learn the concepts of boundary layer thicknesses. My question is about laminar pipe flow and calculating displacement and momentum thicknesses. I was wondering if finding the displacement and momentum thicknesses in a pipe flow is the same as finding them in flow over a flat-plate.

I found the displacement thickness over a flat plate to be:
$\delta_1 = \int_0^\infty (1-\frac{u\rho}{u_{\infty}\rho_{\infty}})dy$

And the momentum thickness is:
$\delta_2 = \int_0^\infty \frac{\rho u}{\rho_{\infty}u_{\infty}} (1-\frac{u\rho}{u_{\infty}\rho_{\infty}})dy$

Thank you.

2. Dec 13, 2014

Staff: Mentor

In the region where the thicknesses are small compared to the radius of the pipe, you can treat flow in the entrance region to a pipe as flow over a flat plate. However, as the thicknesses become greater, neglect of the curvature becomes less acceptable.

Chet

3. May 21, 2015

cabon7969

Hello Sir,
I just want to know further in this topic that
"Can we calculate displacement thickness for fully developed laminar flow in pipes"

4. May 21, 2015

Staff: Mentor

For fully developed laminar flow in pipes, the boundary layer has penetrated to the center of the pipe, and the displacement thickness is R.

Chet

5. May 24, 2015

cabon7969

Hello Sir ,
I did not understand how the displacement thickness becomes R.
According to me, displacement thickness is the distance by which streamline get deflected due to effect of boundary layer and also it can be stated as imaginary increase in thickness of wall due to boundary layer.
But for the fully developed laminar flow this thickness will be constant, but i don't know what it will be ?

6. May 24, 2015