# Jet nozzles effect in seawater

• TorMcOst
In summary, the conversation discusses the possibility of calculating the effect and carrying length of a high-pressure nozzle in seawater. It is suggested to use the appropriate equation that takes into account the density and viscosity of seawater. Factors such as the velocity, distance, and angle to the surface also play a role in the momentum of the fluid. The use of a 6 Moly stainless steel is recommended for the nozzle. The conversation also includes a detailed discussion on the equations and calculations involved in determining the width and velocity distribution of the jet.

#### TorMcOst

Is it possible to calculate a high-pressure nozzles effect/carrying length in seawater if the medium used in the high-pressure nozzle is seawater?

TorMcOst said:
Is it possible to calculate a high-pressure nozzles effect/carrying length in seawater if the medium used in the high-pressure nozzle is seawater?
It is not clear what one is asking. Is the high-pressure nozzle operating underwater (as opposed to shooting into the air)?

If one uses the appropriate equation, then one simply uses the density and viscosity of sea-water.

A water jet underwater will dissipate quickly in the surrounding water, but it depends on the velocity of the jet. If the nozzle is used to propel a craft then the crafts forward speed would need to be considered.

Thats right Astronuc, the high pressure nozzle operates under water and is not moving.
The diameter of the nozzle is Ø1,2mm and the media flushed through it is seawater (the same as the media it is submerged in). The flow is 5-10L/min.
What equation would you recommend to figure:
- The length of the spray?
- The effect of the spray(on a surface) if it has a distance to a surface of i.e. 10mm?

Sounds like a jet cleaning system to clean underwater surfaces.

I see if I can find an example. I would imagine one wants some equation that is a function of distance and angle to surface, both of which will effect the momentum of the fluid at the surface.

For seawater, I'd recommend a 6 Moly SS, like ALX-6N or 254 SMO or the more recent Avesta 654 SMO.

http://www.alleghenyludlum.com/Ludlum/documents/AL_6XN_SourceBook.pdf

http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VJK-4HHNH42-10&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=9dd3da25daa1eb3ce445a059bfc85b76

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Oh man, you are lucky I'm in the middle of a numerical run right now.

From Viscous Fluid Flow(3rd ed.), Frank White, Chapter 4, Section 10.6.

If a round jet emerges from a circular hole with sufficient momentum, it remains narrow and grows slowly, the radial changes $$\partial /\partial r$$ being much larger than axial changes $$\partial / \partial x$$
Continuity:
$$\frac{\partial u}{\partial x} + \frac{1}{r}\frac{\partial}{\partial r}(rv) = 0$$
x momentum
$$u\frac{\partial u}{\partial x} + v\frac{\partial u}{\partial y} = \frac{v}{r}\frac{\partial}{\partial r}\left(r\frac{\partial u}{\partial r}\right)$$

Schlichting reasoned that the jet thickness grew linearly, so the similarity variable is $$r/x$$. he defined the stream function
$$\psi(r,x) = \nu x F(\eta)\,\, \eta = \frac{r}{x}$$
From which the axisymmetrical velocity components are:
$$u = \frac{1}{r}\frac{\partial \psi}{\partial r} = \frac{\nu F'}{r}$$
$$v = -\frac{1}{r}\frac{\partial \psi}{\partial x} = \frac{\nu}{r}(\eta F' - F)$$
Substitution into the x-momentum equation gives the following third-order non-linear differential equation.
$$\frac{d}{d\eta}\left( F'' - \frac{F'}{\eta}\right) = \frac{1}{\eta^2} (FF'' - \eta F'^2 - \eta FF'')$$
The boundary conditions are F(0) = F'(0) = F'(infinity) = 0. The exact solution is:
$$F = \frac{(C\eta)^2}{1 + (C\eta /2)^2}$$
Where C is a constant determined from the momentum of the jet
$$J = \rho \int^\infty_0 u^2 2\pi r\,dr = \frac{16\pi}{3}\rho C^2 \nu^2$$
$$C = \left( \frac{3J}{16\pi \rho \nu^2}\right)^{1/2}$$
The axial jet velocity is then:
$$u = \frac{3J}{8\pi \mu x}\left( 1 + \frac{C^2 \eta^2}{4}\right)^{-2}$$
The term in parenthesis is the shape of the jet profile. The jet centerline velocity drops off as $$x^{-1}$$. The mass flow rate across any axial section of the jet is:
$$\dot{m} = \rho \int^{\infty}_0 u2\pi r\,dr = 8\pi \mu x$$

IF the jet is laminar, and we assume a simple plane laminar jet, we find that the velocity distribution is:
$$u(x,y) = u_{max} \sech^2 a\eta$$ Or:

$$u(x,y) = u_{max}\sech^2 \left[ 0.2752 \left(\frac{J\rho}{\mu^2 x^2}\right)^{1/3} y \right]$$

Where J is the momentum flux. At this point, if we define width of the jet as twice the distance y where $$u = 0.001u_{max}$$ then:
$$\mbox{Width} = 21.8 \left(\frac{x^2 \mu^2}{J \rho}\right)^{1/3}$$

That may be slightly more helpful on the width of the jet question. On the effect of the surface...no idea.

Last edited: Thanks a lot Minger and Astronuc! This were of great help!

## 1. What is the purpose of a jet nozzle in seawater?

A jet nozzle is a device used to direct the flow of seawater in a specific direction with high velocity. It is typically used in applications such as ship propulsion, marine construction, and dredging to create a powerful jet of water that can move objects or clear debris from an area.

## 2. How does a jet nozzle create propulsion in seawater?

A jet nozzle creates propulsion by compressing the seawater and forcing it out at a high velocity through a small opening. This creates a reaction force in the opposite direction, propelling the vessel or object forward. The shape and design of the nozzle also play a role in the efficiency of propulsion.

## 3. What factors affect the performance of a jet nozzle in seawater?

The performance of a jet nozzle in seawater can be affected by several factors, including the shape and design of the nozzle, the pressure and flow rate of the seawater, the angle at which the nozzle is directed, and the surrounding water conditions such as waves and currents.

## 4. What are the advantages of using a jet nozzle in seawater over traditional propellers?

Jet nozzles offer several advantages over traditional propellers in seawater, such as higher efficiency and maneuverability, reduced risk of damage to marine life and the environment, and the ability to operate in shallow or debris-filled waters. They also tend to be more compact and have a lower noise level.

## 5. How does the use of jet nozzles in seawater impact the environment?

The use of jet nozzles in seawater can have both positive and negative impacts on the environment. On one hand, they can reduce the risk of damage to marine life and habitats compared to traditional propellers. However, they can also create noise pollution and disturb sediment on the seafloor, potentially affecting marine ecosystems. Proper design and use of jet nozzles can minimize these negative impacts.