How Do You Calculate Reynolds Number for Flow Exiting a Rectangular Duct?

In summary, the problem involves calculating Reynold's Number for flow exiting a rectangular duct at a velocity of 11 m/s. The flow is measured at a distance of 10 cm below the exit and becomes 0 at a distance of 8 cm from the center. The author assumes the flow is symmetric and essentially in a pipe with a diameter of 0.16 m. Using the given values, the Reynolds number is calculated to be 1.147e+05. However, the concept of Reynolds number becomes meaningless once the fluid leaves the pipe, as it is now a jet and the concepts of walls and characteristic length no longer apply.
  • #1
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Homework Statement


Hi everyone,

This problem concerns calculating Reynold's Number of flow after exiting a duct. The duct that the flow exits is rectangular. The flow is measured directly underneath the center of the duct at a distance of 10 cm below the exit (Y-axis). Flow is measured at 11 m/s. It is determined that the velocity becomes 0 at a distance of 8 cm outward from the center (X axis). I am assuming that the flow is symmetric and thus the flow is esentially in a pipe with a radius of 8 cm.


Homework Equations



Re = "rho"*V*d/"mu"

The Attempt at a Solution



"rho" = density = 1.20 kg/m^3
V = velocity of air = 11 m/s
d = diameter of pipe = 2*0.08m = 0.16 m
"mu" = viscosity of air = 1.8418e-05 kg/m*s

plugging those into the equation above yields: Re=1.147e+05

I guess my question is regarding my assumtion of the pipe. Was I correct in my assumption?
 
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  • #2
After the fluid leaves the pipe, the concept of a Reynolds number is kind of meaningless. Furthermore, the number can be based upon anything. Sure, pipe flow Reynolds numbers based on diameter are well known and can be a sure-fire way to indicate laminar vs turbulence. However, once the fluid leaves the pipe, you no longer have simple pipe flow. You now have a jet, and the concepts of walls and such no longer apply.

You certainly can measure the velocity and viscosity. After that, the characteristic length can be whatever you want it to be, there is no wrong answer. Having said that, you can also no longer use the pipe flow Moody diagram and so on and so forth.
 
  • #3


it is important to carefully consider all assumptions made in a calculation. In this case, your assumption of the flow being essentially in a pipe with a radius of 8 cm is reasonable, as long as the flow is indeed symmetric. However, it is always important to verify these assumptions through further analysis or experimentation. Additionally, it would be helpful to provide a diagram or more information about the setup to ensure accuracy in the calculation. Overall, your calculation appears to be correct based on the given information.
 

1. What is the formula for calculating Reynolds number?

The formula for calculating Reynolds number is Re = ρ * v * L / μ, where Re is the Reynolds number, ρ is the density of the fluid, v is the velocity of the fluid, L is the characteristic length of the flow, and μ is the dynamic viscosity of the fluid.

2. What is the purpose of calculating Reynolds number?

The purpose of calculating Reynolds number is to determine the type of flow in a fluid system, whether it is laminar or turbulent. This is important in understanding the behavior and characteristics of the fluid flow, and to design efficient and effective systems.

3. How do you determine the velocity of the fluid in the Reynolds number formula?

The velocity of the fluid can be determined by measuring the volumetric flow rate and cross-sectional area of the pipe or channel. It can also be calculated using the Bernoulli's equation or by using a velocity probe.

4. What is the characteristic length in the Reynolds number formula?

The characteristic length is a measure of the size of the flow in the direction of the flow. For example, in a pipe, the characteristic length would be the diameter of the pipe. In other cases, it could be the length of a wing or the diameter of a sphere.

5. What is the significance of a high or low Reynolds number?

A high Reynolds number indicates that the flow is turbulent, while a low Reynolds number indicates that the flow is laminar. This affects the behavior and performance of the fluid, and it is important to consider when designing systems or conducting experiments.

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