Jet Spread Rate K Values- Momentum diffusement

In summary, the conversation discusses the problem of equating the rate of momentum diffusement to the shear forces caused by the difference in velocities between a jet and an ambient fluid. The rate of momentum diffusement can be calculated using empirical K-values, which depend on the flow type. The question then asks if it is possible to calculate the rate of momentum diffusement directly from the velocity difference. It also considers the relationship between the momentum diffusement and the flow development, and whether a K-value less than 1 indicates inadequate diffusement. The solution proposed involves factoring in the viscosity and Reynolds number of the fluid. Additionally, the conversation mentions the description of the initial region length as 5 diameters, which could represent a K-value of
  • #1
Tom79Tom
45
3
upload_2016-10-24_11-11-30.png

The Problem Statement
I have a jet entering leaving a nozzle at ui into an ambient fluid with ue = 0
I am trying to equate the rate of momentum diffusement (or spread) to the shear forces caused by ue -ui


I understand that the rate momentum diffusement is are equated by empirical K- values (~0.1 for turbulent flow ~0.4 for laminar flow)

The Question

Is there any way to calculate the rate of momentum diffusement or spread directly from ui -ue
I am trying to understand what would happen as the flow develops from ui=0, ue = 0
Would the momentum diffusement always equal the rate of flow development or does K values < 1 indicate that a the momentum diffusement is inadequate to prevent a velocity gradient.

Attempt at a solution
I am thinking that it does as there is a length to the initial region where this occurs.
A K-value of 1 would indicate an immediate dispersal of any additional increase in ui
so no shear forces could ever develop.[/sub] and therefore no motive to cause a diffusement . A cyclical argument.
I think the K value must factor the viscosity of the fluid and its Reynolds number

Edit : sorry one other question, the initial region length is described as 5 diameters in length . Is that representative of a k value of 0.2
$$\frac{1D}{0.2}=5D$$
 

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  • #3
I'm sorry I don't have an answer for you but I was wondering if you could help me. Do you know of an underwater pressure nozzle that can increase the pressure and volume of the fluid mass by pulling in fluid from the surrounding areas of fluid around the exterior of the nozzle possibly with a Venturi or jet pump type opening before the nozzle's release?
 

Related to Jet Spread Rate K Values- Momentum diffusement

1. What is the significance of Jet Spread Rate K values in momentum diffusement?

Jet Spread Rate K values are important in understanding the spread of a jet of fluid, such as air or water, as it diffuses into a surrounding medium. They can help predict the behavior of fluid jets in various applications, such as in combustion processes or in environmental studies.

2. How are Jet Spread Rate K values calculated?

Jet Spread Rate K values are calculated by analyzing the flow of the jet and its surrounding medium using mathematical equations and experimental data. Various factors, such as the velocity, density, and viscosity of the jet and the surrounding medium, are taken into account to determine the overall spread rate.

3. What factors affect Jet Spread Rate K values?

Jet Spread Rate K values are influenced by various factors, including the velocity and shape of the jet, the density and viscosity of the jet and its surrounding medium, as well as any external forces or obstacles that may affect the jet's flow.

4. How can Jet Spread Rate K values be applied in real-world situations?

Jet Spread Rate K values can be applied in a variety of real-world situations, such as in the design of combustion systems, the optimization of industrial processes, and the prediction of pollutant dispersion in the environment. They can also be used in engineering and environmental studies to understand and control the behavior of fluid jets.

5. What are the limitations of using Jet Spread Rate K values?

While Jet Spread Rate K values can provide valuable insights into the behavior of fluid jets, they are based on mathematical models and experimental data, which may not always accurately reflect real-world conditions. Additionally, other factors, such as turbulence and irregular geometries, can also affect the spread rate of jets and may not be fully captured by Jet Spread Rate K values alone.

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