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# How to calculate orifice diameter for laminar flow from a nozzle

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# How to calculate orifice diameter for laminar flow from a nozzle

May 31, 2010 12:44 PM Subscribe

How to calculate nozzle orifice diameter for a given fluid flow rate to have a laminar output stream rather drips (orifice too large/ flow rate too small) or turbulent flow (orifice to small / flow rate too large)?

Think how a faucet acts as you increase the flow rate, initially it drips, then you get a laminar flow and lastly it becomes turbulent. I have a small range of flow rates centered around 10ml/min. I need to design a nozzle whose output is a nice laminar flow but I'm at a loss to know how to calculate it.

Think how a faucet acts as you increase the flow rate, initially it drips, then you get a laminar flow and lastly it becomes turbulent. I have a small range of flow rates centered around 10ml/min. I need to design a nozzle whose output is a nice laminar flow but I'm at a loss to know how to calculate it.

You need to know the viscosity and density of the fluid, then calculate the Reynolds number for your system.

posted by TedW at 1:16 PM on May 31, 2010 [1 favorite]

posted by TedW at 1:16 PM on May 31, 2010 [1 favorite]

Assuming you don't need exact specifications, here is the engineering approach to it.

If a flow is laminar, it will have a parabolic profile, maximum at the centerline, and dropping off as the square of the radius to the walls where it is zero. For such a parabolic profile, the mean velocity will be 2/3 the centerline velocity. You are welcome to calculate it to confirm.

Required flow rate = Q = mean velocity * area.

Reynolds number = characteristic velocity * characterstic length/kinematic viscosity (nu)

char. length = diameter = D

char. velocity = centerline velocity = 1.5 x mean velocity = 1.5Q/A = 1.5Q/(pi*D^2/4) = 6Q/(piD^2)

Re = 6Q/pi*nu*D

You want this to be less than 2100 for a smooth pipe, and smaller if your pipe is rough, or has bends or other features that can trigger transition to turbulence.

posted by hariya at 1:29 PM on May 31, 2010 [2 favorites]

If a flow is laminar, it will have a parabolic profile, maximum at the centerline, and dropping off as the square of the radius to the walls where it is zero. For such a parabolic profile, the mean velocity will be 2/3 the centerline velocity. You are welcome to calculate it to confirm.

Required flow rate = Q = mean velocity * area.

Reynolds number = characteristic velocity * characterstic length/kinematic viscosity (nu)

char. length = diameter = D

char. velocity = centerline velocity = 1.5 x mean velocity = 1.5Q/A = 1.5Q/(pi*D^2/4) = 6Q/(piD^2)

Re = 6Q/pi*nu*D

You want this to be less than 2100 for a smooth pipe, and smaller if your pipe is rough, or has bends or other features that can trigger transition to turbulence.

posted by hariya at 1:29 PM on May 31, 2010 [2 favorites]

In addition to bare tubing, there are various high tech nozzles that might be applied.

posted by StickyCarpet at 2:26 PM on May 31, 2010

posted by StickyCarpet at 2:26 PM on May 31, 2010

What is your source? I'm asking because this system will be sensitive to upstream pressure changes, and a single orifice may not do what is required, a variable pressure drop (i.e. valve) may actually be better suited.

Another issue, your flow rate is really low, surface tension may start giving you trouble assuming you're using water. (I'm not sure what the threshold is, I haven't worked with flows this small)

posted by defcom1 at 5:28 PM on May 31, 2010

Another issue, your flow rate is really low, surface tension may start giving you trouble assuming you're using water. (I'm not sure what the threshold is, I haven't worked with flows this small)

posted by defcom1 at 5:28 PM on May 31, 2010

You could make yourself a little laminar jet nozzle.

posted by ctmf at 5:32 PM on May 31, 2010 [1 favorite]

posted by ctmf at 5:32 PM on May 31, 2010 [1 favorite]

Thanks for all the great suggestions. The source is a syringe pump so it provides a pretty constant and precise flow rate. The system works more or less at ambient pressure, except for whatever increase in pressure is caused by the restriction of the nozzle opening. Our material is about 95% Isopropyl Alcohol and 5% water, so surface tension is quite a bit less than pure water.

As I understand it, there are a number of flow transitions that occur as flow rate increases. At really low flow rates a single drop forms at the nozzle and grows until gravity overcomes the surface tension of the liquid and the drop detaches and falls. Increasing flow rate speeds up this process but it remains periodic and pretty simple. As flow rate increases beyond that there is a transition to chaotic regime where the period between drops changes chaotically. With a further increase there is a sudden transition where the separation boundary (i.e. where the drops separate from each other) suddenly moves downstream of the nozzle opening and a laminar stream emerges that at some distant point (> 10 diameter of nozzle) breaks up into drops. This is the area of operation I need to work in. I have found this paper [pdf] which seems relevant, but its slow going.

posted by Long Way To Go at 9:20 PM on May 31, 2010

As I understand it, there are a number of flow transitions that occur as flow rate increases. At really low flow rates a single drop forms at the nozzle and grows until gravity overcomes the surface tension of the liquid and the drop detaches and falls. Increasing flow rate speeds up this process but it remains periodic and pretty simple. As flow rate increases beyond that there is a transition to chaotic regime where the period between drops changes chaotically. With a further increase there is a sudden transition where the separation boundary (i.e. where the drops separate from each other) suddenly moves downstream of the nozzle opening and a laminar stream emerges that at some distant point (> 10 diameter of nozzle) breaks up into drops. This is the area of operation I need to work in. I have found this paper [pdf] which seems relevant, but its slow going.

posted by Long Way To Go at 9:20 PM on May 31, 2010

(Masters in Mechanical Engineering) I suspect you may be making this harder than it needs to be.

Do you have control/input over the pump? Does the pump already operate at the flow rate you want? Are you working with that fixed flow rate and just want the right fluid regime? How are you going to fabricate/procure the nozzle? How durable does this need to be.

3 possibly easier solutions come to mind: pick a nozzle/diameter and adjust the pump to give you the flow characteristics you want, pick a flow and try a few nozzles/diameters until you get what you want; install some sort of regulator between the pump and the nozzle and adjust it until you get the flow characteristics you want.

Put a small/relatively restrictive plastic nozzle on the output, slowly work the opening larger until you get the flow you want. Tada. No numerical solution required.

posted by kenbennedy at 12:12 PM on June 2, 2010

Do you have control/input over the pump? Does the pump already operate at the flow rate you want? Are you working with that fixed flow rate and just want the right fluid regime? How are you going to fabricate/procure the nozzle? How durable does this need to be.

3 possibly easier solutions come to mind: pick a nozzle/diameter and adjust the pump to give you the flow characteristics you want, pick a flow and try a few nozzles/diameters until you get what you want; install some sort of regulator between the pump and the nozzle and adjust it until you get the flow characteristics you want.

Put a small/relatively restrictive plastic nozzle on the output, slowly work the opening larger until you get the flow you want. Tada. No numerical solution required.

posted by kenbennedy at 12:12 PM on June 2, 2010

Yes, we have full control over the pump and it's adjustable over a wide range. We're also following the purely empirical route - trying a bunch of different nozzle diameters and seeing what works.

The reason to look for the numerical solution is we'd like to be able to calculate the optimal nozzle diameter for a given range of flow rates. We have other process constraints on flow rates so we want to build the best nozzle possible for the process. That all said in the short term I think we'll just take a bunch of data on transition points and see if we can fit a curve to it.

posted by Long Way To Go at 11:55 PM on June 3, 2010

The reason to look for the numerical solution is we'd like to be able to calculate the optimal nozzle diameter for a given range of flow rates. We have other process constraints on flow rates so we want to build the best nozzle possible for the process. That all said in the short term I think we'll just take a bunch of data on transition points and see if we can fit a curve to it.

posted by Long Way To Go at 11:55 PM on June 3, 2010

This thread is closed to new comments.

posted by makethemost at 1:12 PM on May 31, 2010