# Hydrodynamic Entry Length of Flow Through Circular Annulus

• Disquoveri
In summary, if the gap between the cylinders is small compared to the radii of the cylinders, you can treat it as flow between parallel plates. If the inner radius is much smaller than the outer radius, then you are essentially dealing with flow in a circular tube.

#### Disquoveri

I might be going crazy or searching at the wrong places. Is there an empirical formula for solving the hydrodynamic entry length of laminar flow through a circular annulus? Thanks!

If the gap between the cylinders is small compared to the radii of the cylinders, then you can treat it as flow between parallel plates. Do you have an estimate of the hydrodynamic entry length for flow between parallel plates? If the inner radius is much smaller than the outer radius, then you are essentially dealing with flow in a circular tube. Do you have an estimate of the hydrodynamic entry length for flow in a circular tube?

Chet

Thanks for your help, Chet. (Also, thanks for answering my question on displacement, momentum, enthalpy, etc. thicknesses in circular pipes.)

The gap between the cylinders is not small compared to the inner cylinder though. I have the gap to be 0.015 m, the the inner cylinder radius is 0.012 m, but the outer cylinder radius is 0.027 m. Can I still use the estimate of entry length for flow between parallel plates? The estimation of entrance length is given as L_e = Re*D/K, where K = 20 for circular tube and K = 100 for parallel plates. From simulations done on COMSOL, I know that fully developed velocity profile is achieved within the tube length. The entry length for a circular tube overestimates the entry length/point of fully developed velocity profile.

Disquoveri said:
Thanks for your help, Chet. (Also, thanks for answering my question on displacement, momentum, enthalpy, etc. thicknesses in circular pipes.)

The gap between the cylinders is not small compared to the inner cylinder though. I have the gap to be 0.015 m, the the inner cylinder radius is 0.012 m, but the outer cylinder radius is 0.027 m. Can I still use the estimate of entry length for flow between parallel plates? The estimation of entrance length is given as L_e = Re*D/K, where K = 20 for circular tube and K = 100 for parallel plates. From simulations done on COMSOL, I know that fully developed velocity profile is achieved within the tube length. The entry length for a circular tube overestimates the entry length/point of fully developed velocity profile.
The entry length for a circular tube is going to be longer than for an annulus if the Re is defined in terms of the outer diameter for both. So, to be conservative, why not just use the value K=20.

In the entrance region, irrespective of whether it's an annulus or just a tube, the boundary layer growth is initially going to be that for the Blasius solution. This is because the inlet velocity profile is flat, and the boundary layer thickness is negligible compared to the radius of curvature. So it's the same as for flow over a flat plate. So I would determine a nominal boundary layer thickness from the Blasius solution, and divide that by the tube radius (or half the gap between the cylinders in the case of an annulus). When that number is about equal to unity, this would give a reasonable approximation to the entry length. I guess this is how they came up with the values of the entry length for a tube or for parallel plates. Try this, and see what you get.

Chet

## 1. What is the hydrodynamic entry length of flow through circular annulus?

The hydrodynamic entry length of flow through circular annulus refers to the distance that a fluid must travel before reaching fully developed flow in a circular annular channel. It is an important parameter in fluid mechanics that is used to determine the behavior of fluid flow in this type of channel.

## 2. How is the hydrodynamic entry length calculated?

The hydrodynamic entry length can be calculated using the equation L = 0.05ReD, where L is the entry length, Re is the Reynolds number, and D is the diameter of the inner cylinder in the annular channel. This equation is based on empirical data and is applicable for laminar and turbulent flow.

## 3. What factors affect the hydrodynamic entry length?

The hydrodynamic entry length is affected by several factors, including the geometry of the annular channel, the velocity of the fluid, and the properties of the fluid, such as viscosity and density. Additionally, the type of flow (laminar or turbulent) will also affect the entry length.

## 4. Why is the hydrodynamic entry length important?

The hydrodynamic entry length is important because it affects the behavior of fluid flow in circular annulus channels. When the fluid is not fully developed, there may be variations in velocity and pressure along the channel, which can impact the accuracy of any calculations or experiments being performed using this type of channel.

## 5. How can the hydrodynamic entry length be reduced?

The hydrodynamic entry length can be reduced by increasing the velocity of the fluid, decreasing the viscosity of the fluid, or changing the geometry of the annular channel. Additionally, using a smaller diameter for the inner cylinder can also help to reduce the entry length. However, it is important to note that the entry length cannot be completely eliminated, as there will always be a distance required for the fluid to reach fully developed flow.