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February 12, 2002, 17:19 
Fluid flow through a nozzle

#1 
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I hope this is the right board. I am trying to determine the effects of nozzle length on the flow and pressure through a cone shaped nozzle. Here is the situation: A cone shaped adapter is placed at the end of an open bore (open ended) syringe. A cannula (thin tube) is attached to the cone adapter (see crude drawing below). The material being injected has the viscosity of wet cement. If the cone adapter is made longer, will this have a signficant effect on the flow and pressure? How can I calculate this? Any help is appreciated. Thanks.
\ cone adapter \ \ Syringe Cannula / / / 

February 12, 2002, 17:20 
Re: Fluid flow through a nozzle

#2 
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OK the drawing got completely screwed up so use your imagination instead.


February 13, 2002, 02:43 
Re: Fluid flow through a nozzle

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I am not quite sure I understand the question.
Is there something that says that you cannot use the normal equations for a convergent/divergent nozzle? Or maybe you are looking to calculate for a nonisentropic nozzle. In case of an analytical approach, can you not use a simple expression for the Reynolds stresses to calculate the momentum and pressure drop? Christian 

February 13, 2002, 03:58 
Re: Fluid flow through a nozzle

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I'm not sure I understand the geometry correctly  but if the device you are describing first has a wide "bore" and then a cone and a thin "cannula" then the length of the bore will not have much effect on the flow or pressure drop  the section which is much thinner will govern the flow & pressure drop. If you want to estimate the change in pressure drop this should be quite easy to do either analytically or with a very quick CFD computation.
One questions  the fluid that you are describing sounds a bit tricky  is it Newtonian or can it "thicken" if it is flowing slowly?  this might change my conclusion above. 

February 13, 2002, 12:43 
Re: Fluid flow through a nozzle

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You have the setup right (a large tube attched to a cone attached to a thin tube). The cone gadually reduces the inner diameter to the size of the smaller tube. I am interested in changing the length of the cone not the tube. If the diameter change is severe (i.e. no longer a cone but a direct transition from large to small bore) the material will not flow. This is the case with a typical syringe. By removing the end of a syringe and attaching a cone shaped adapter, the gradual change in diameter (from large to small) provided by the cone allows a thick cement to flow into the small tube (the cannula).
With a longer cone and more gradual change in diameter, will this have a tangible effect on flow and/or pressure? I hope this clarifies the question. 

February 19, 2002, 13:08 
Re: Fluid flow through a nozzle

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I suggest you to read some book about hydraulics. I think it should be enough for you. The topic you have to look for is "dynamic head loss in ducts". DarcyWeisbach or Fanning formula should work quite well. In this case: p_inp_out= beta*rho*w^2/2 where beta is a coefficient depending on the type of geometrical discontinuity in the duct (valve, filtering grids, severe diameter change ...). This should be correct if you work with an incompressible medium (wet cement) or with gases at low mach number. Hope it helps


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