Turbulence in pipe flow (Reynold's Number)

[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

 

[SteamKing]

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

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

 

[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.

 

[jabotabek]

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.

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

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.

 

[PJC01]

for bringing up this interesting topic. Turbulence in pipe flow is a complex phenomenon that is influenced by several factors, including the Reynold's Number.

The Reynold's Number is a dimensionless parameter that describes the ratio of inertial forces to viscous forces in a fluid flow. It is calculated by multiplying the fluid velocity, density, and pipe diameter and dividing by the fluid viscosity. In simple terms, it represents the relative importance of inertial forces (tendency to continue moving) compared to viscous forces (resistance to flow) in a fluid.

In pipe flow, the Reynold's Number plays a crucial role in determining the type of flow, whether it is laminar or turbulent. At low Reynold's Numbers, the flow is laminar, meaning that the fluid particles move in smooth, orderly layers. As the Reynold's Number increases, the flow becomes more turbulent, characterized by chaotic, random motion of fluid particles.

The presence of a blockage in a pipe can disrupt the smooth flow of fluid and cause turbulence to occur. This is because the blockage creates a disturbance in the flow, increasing the Reynold's Number and causing the flow to transition from laminar to turbulent. The critical diameter of the blockage that will result in turbulence depends on the fluid properties and the Reynold's Number. There is no specific formula for calculating this critical diameter, as it can vary depending on the specific conditions of the flow.

In terms of blood flow, blockages in arteries can indeed cause turbulence to occur. This can be problematic as it can lead to the formation of blood clots and increase the risk of cardiovascular diseases. Understanding the relationship between Reynold's Number and turbulence can help researchers better understand and predict the behavior of blood flow in narrowed or blocked arteries.

In conclusion, the Reynold's Number is a crucial parameter in determining the type of flow in pipes, and it can also be influenced by the presence of blockages. Further research and experimentation are needed to fully understand the effects of blockages on turbulence in pipe flow and its implications in various applications, including blood flow in the human body.