Jet Spread Rate K Values- Momentum diffusement

[Tom79Tom]

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

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 u_i -u_e
I am trying to understand what would happen as the flow develops from u_i=0, u_e = 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 u_i 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
$$\frac{1D}{0.2}=5D$$

 

[vacci]

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?