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# Working out the stream flow radius for 100% liquidus alloys

## Working out the stream flow radius for 100% liquidus alloys

(OP)
Bit of a weird one, and I thought this is the best place to ask as it is under "fluid mechanics". Just as a note, Fluid mechanic related math goes way over my head so please keep the explanations simple(ish).

I need to work out an approximate inlet radius of a 100% liquidus metal flow when pouring it into a mould so I can accurately setup a casting simulation. Recently I have just been using a fixed value for this radius which I know isn't correct but I would like to get more accurate results.

If I have:
Average fill rate of 1.09 kg/s.
and a Cast Weight of 30kg

is there any way of working out the radius of the flow from this? let me know if you need anymore information.

I found a PDF: (http://www.ans.org/pubs/journals/download/a_28099) of an old paper looked into the viscosity of liquid metals if this is relevant?

Also, Is there a technical term for the stream flow radius that I am looking for so I can research more effectively?

Thanks,

Daniel

### RE: Working out the stream flow radius for 100% liquidus alloys

This is an odd one. I don't know of a field of fluid mechanics that would focus on it, and I think you have to make up your own terms. "Stream-flow radius" is probably as good as any, but I wouldn't expect Google to be much help.

If I was trying to set this problem up, I'd try to determine a stream radius (maybe based on the geometry of the spout?). That would allow converting your mass flow rate into a bulk velocity. Instantaneously, the bulk velocity would be normal to gravity, quickly converting to 100% influenced by gravity. The radius that you want is the rate at which horizontal velocity bleeds to zero. I'm not really sure how to assess that rate of change. Maybe go back to the kinematics equations and make your "particle" a control volume in the flow?

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

### RE: Working out the stream flow radius for 100% liquidus alloys

Not clear if you have a free fluid stream until it hits the mold bottom, like filling a glass with hot wax, or if the fluid flows through the mold, touching all sides, until it reaches the end then backs, like water through a pipe, or like the injection molding of plastic.

Radius of a freely falling liquid flow and the cross sectional area of that flow both change with velocity. Falling fluid velocity accelerates by gravity. Look at water falling from a tap. As a constant flow of water accelerates, falling from the tap due to gravity, the cross section narrows more and more until it hits the sink pan. It narrows because the velocity gets faster and faster.

Velocity is volumetric flow (or fill rate) divided by cross sectional area of the fluid stream.
To get volumetric flow convert your mass flow to volumetric flow, ie. divide mass flow by fluid density.
Once you have the volumetric flow, convert to fluid velocity by dividing by cross sectional area of the fluid stream as it passes through the mold.

Speed of fill will depend on which type of flow you have through the mold, although the time it will take to fill it will be the volume of the mold divided by volumetric flow rate.

### RE: Working out the stream flow radius for 100% liquidus alloys

As ever a diagram or sketch would help but my reading of your query is that, to put it simply, you have a metal version of say a jug of cream which you are pouring into a mould / teacup if you follow the analogy.

Thus you have a small amount of horizontal velocity and vertical velocity starts at zero then accelerates due to gravity. That is unaffected by density.

Thus your curve become a parabola, not a fixed diameter.

You can plot this quite easily if you just use simple equations with small time steps

distance L = Velocity C x time t

For a graph X axis, V is fixed
For the Y axis V1 = V0 + Acceleration x t
Each time step you then substitute V1 back as V0.

See this http://schoolbag.info/physics/ap_physics/6.html and go down to example 21

I think you mean something like the graph below, starting at the top???

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