Calculating Entrance Lengths in Hydrodynamics

In summary, the dimensionless entrance length is defined as z+=zh/(Re*Dh) and is not limited to the actual channel length. If zh exceeds the channel length, it just means that the flow has not fully developed at the end of the channel.
  • #1
pauleck
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Hi everybody,
first of all, sorry for any grammatical mistakes, I am a non-native English speaker.
So here is my concern,

the dimensionless (hydrodynamic) entrance length is defined as:

z+=zh/(Re*Dh)

,where zh is the hydrodynamic entrance length, Re is the Reynolds number, and dh is the hydraulic diameter of the duct.

If zh exceeds the total channel length L, do I have to assume zh=L for calculating z+??

Thank you very much
 
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  • #2
pauleck said:
If zh exceeds the total channel length L, do I have to assume zh=L for calculating z+??

No. The entrance length is longer than the channel length, and the dimensionless entrance length is longer than the dimensionless channel length. zh is not limited to the actual channel length. If zh>L it just means that at the end of the channel the flow hasn't fully developed yet.
 
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1. What is the concept of entrance length in hydrodynamics?

The entrance length in hydrodynamics refers to the distance from the entrance of a pipe or channel to the point where fully developed flow is achieved. It is an important parameter in fluid mechanics as it affects the flow characteristics and pressure drop in the system.

2. Why is it important to calculate entrance lengths in hydrodynamics?

Calculating entrance lengths is important because it helps in understanding the behavior of fluid flow in a system. It also allows for the accurate prediction of pressure drop and flow rates, which is crucial in designing and optimizing fluid systems.

3. How is entrance length calculated in hydrodynamics?

Entrance length can be calculated using various methods such as empirical equations, dimensional analysis, and numerical simulations. The most commonly used method is the empirical equation known as the Blasius equation, which relates the entrance length to the Reynolds number and pipe geometry.

4. What factors affect the entrance length in hydrodynamics?

The entrance length is primarily affected by the fluid properties, flow rate, pipe geometry, and surface roughness. A higher Reynolds number, larger pipe diameter, and smoother pipe walls result in longer entrance lengths. Additionally, the type of fluid (Newtonian or non-Newtonian) and the presence of obstacles can also influence the entrance length.

5. How can entrance lengths be minimized in hydrodynamics?

To minimize entrance lengths, the fluid flow can be gradually accelerated or streamlined using an inlet contraction. This helps in reducing the distance required for the flow to fully develop. Additionally, using a smooth and straight pipe with a larger diameter can also help in minimizing entrance lengths.

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