# Turbulence in pipe flow (Reynold's Number)

1. Aug 29, 2014

### jabotabek

I have some confusion about how blockages result in the laminar/turbulent flow of fluids in pipes.

From my understanding, there is a certain diameter of a blockage in a pipe that will cause the flow to transition from laminar to turbulent (depending on the velocity of flow, etc.)

What is the relationship between Reynold's Number and this?

Is there any way to calculate the critical diameter of blockage that will result in turbulence?

I am thinking about this in terms of blood flow, where the narrowing or blockage of arteries may cause turbulence to occur.

Thanks

2. Aug 29, 2014

### SteamKing

Staff Emeritus
The Reynold's number for internal flow in circular pipes is calculated as:

Re = v D / $\nu$

where v is the flow velocity, D is the internal diameter of the pipe, and $\nu$ is the kinematic viscosity of the fluid.

Laminar flow in pipes generally occurs when Re < 2000 approx. and fully turbulent flows aren't developed until Re > 4000. The range in between is known as the transition zone.

Turbulent flow in pipes is usually sought after, since the resistance to flow in the fully turbulent condition tends toward a value which is independent of the Reynolds number. OTOH, the resistance to flow in the laminar condition is inversely proportional to the Reynolds number, and even though the Reynolds number for laminar flow is lower than for turbulent flow, the pumping losses can be quite higher, given a certain system of pipes through which the flow must travel.

As an example of this, heavy petroleum products have high kinematic viscosities, and pumping this material thru even large pipe can generate large losses because the flow is either in the laminar or transition zones. By heating the products before pumping, the viscosity of the material can be greatly reduced, which increases the Reynolds number of the flow at the velocities which are desirable for piping systems, thus putting the flow into the fully turbulent regime, and reducing the amount of power required to pump such material.

http://udel.edu/~inamdar/EGTE215/Laminar_turbulent.pdf [Broken]

Last edited by a moderator: May 6, 2017
3. Aug 29, 2014

### bigfooted

SteamKing, I think what jabotabek is asking is how this behavior changes when you put an obstacle in the flow. You can force the transition to turbulence at a lower Reynolds numbers by disturbing the flow but if the Reynolds number is too low, then relaminarization occurs.

4. Aug 30, 2014

### jabotabek

Thank you SteamKing and bigfooted for your inputs on this topic.

Do you know if there is any way to determine the critical diameter of a pipe which will cause turbulence? (See image)

The flow velocity, dynamic viscosity and pipe dimensions are known.

Last edited by a moderator: May 6, 2017