5 replies to this topic

[djack77494]

Paraq,
I would think that you would be more successful at controlling the speed at which the plunger travels rather than the force you apply. Actually, you have some degree of control over both of these parameters, but I think speed/position are more easily controlled. Thus, the smaller the diameter of the plunger, the greater control you will have over the rate of fluid expression AND therefore the better control you would have over limiting the pressure built up in the surrounding tissue. As fluid enters the injection point, it will attempt to diffuse into the surrounding tissue. The tissue itself presents a resistance to the movement of fluid. So the lower the rate of delivery, the more time the fluid has to diffuse, the lower the pressure buildup.
Doug

[Art Montemayor]

Bravo! What an excellent and articulate response from Doug. All that he has said is precisely correct and to the point (pardon the pun …). The system (the surrounding tissue) sets up the ultimate, highest pressure realized by the injection of an external fluid – and it does this due to the fixed resistance nature that it has in its make-up (here I am assuming, as a non-medic, that the tissue won’t dilate or open up upon stimulation by the fluid). Since the resistance is fixed, the pressure in the syringe builds up with the flow rate of fluid injected. If the injection rate is increased, so will the required pressure.

In order to keep the driving force (the syringe pressure) as low as possible in order to alleviate pain or discomfort, the thing to do is to lengthen the time that it takes to administer a specific dose of fluid – which is another way of saying: inject the fluid at a relatively slow flow rate, nice and easy.

Doug is also correct with respect to the second question. It is the long (or “tall”) syringe that contributes better and more precise control over the desired injection flow rate – simply because it administers less fluid per length of stroke and, thereby, allows better manual control over the amount of pressure being impressed on the fluid.

However, from practical and actual experience I can state that having said the above is easier than doing it. But this is to be expected – if you are a Chemical Engineer – because one is always on the wary side, looking for Trade Offs in any operation. I have been administering growth hormone injections to one of my beautiful, courageous, and outstanding granddaughters every night for some years now and so you can imagine that I have studied and researched this subject very deeply because it involves someone that I dearly love and treasure and couldn’t bear to subject to any pain or discomfort. I have found the following Trade Offs:

• The long, slow, and drawn-out injection is less painful but it presents additional potential pain in that it lasts longer and offers the opportunity for the needle (or patient) to move or “jerk” and cause a hurt or a jagged wound;
• The longer, “taller” syringe is more prone to slight movement while the injection is being administered simply because it is awkward and presents a “leverage effect” due to its length; it unfortunately is more clumsy to handle for those with small hands or fingers.

I try to have the fluid dose as close to body temperature as I can to minimize the viscosity (and consequently, the required pressure) of a refrigerated dose. The warmer fluid also presents less body “shock” as it enters the tissues. However, this means that I have to warm up the refrigerated dose and this takes organization and time.

I have my granddaughters for the entire summer every year and I am their caretaker during this time. My daughter, who is a physician, prefers to take the minimum time and simply inject hard and quick – taking the time that it takes me to wink an eye. I can’t do that. I try to transfer the fluid in as efficiently - but painless way that I can possibly do it.

This thread is a great seminar on the practicality of applying basic fluid mechanics knowledge in a meaningful and profitable way. Thank you Doug for a great response.

[Art Montemayor]

Parag:

Yes, you are correct in judging that the Darcy-Weisbach equation applies to your application of fluid mechanics. However, the Darcy-Weisbach equation applies only in defining the related pressure drop with regards to the involved flow rate and fluid viscosity:

h_l = f*L/D * V²/2g

where,

h_l = the head loss (or pressure drop);
L = is the pipe length;
D = the diameter of the fluid’s conduit;
V = is the average velocity;
g = the acceleration of gravity; and,
f = a friction factor, dependent on viscosity (the Reynolds Number)

In your specific application, as Doug has stated, it is the system that sets the pressure drop because its resistance to flow (a measure of the pressure drop) is fixed. In order to overcome that fixed resistance, you must increase the pressure of the injected fluid in order to overcome the pressure caused by that resistance. The resultant fluid flow rate is related to the fluid velocity which, in turn, is a variable in the above Darcy equation.

The syringe body is NOT part of the fluid’s conduit (or “D”) in the Darcy equation. The resistance to flow that the fluid confronts are the hypodermic needle, the outlet of the needle, and the rigorous path through the human tissue that the fluid must overcome. That is why the diameter (or the height) of the syringe plunger (or reservoir) has no influence on the downstream pressure. True, in static hydraulics the force imposed on the surface of the fluid is the initial pressure imposed on the syringe plunger. And it is also true (according to Pascal) that for a given imposed force, the larger-diameter syringe will yield a smaller pressure (lbs force divided by cross-sectional area of syringe). However, all that means is that you have to put more force on a larger diameter to get the same pressure as you would with a smaller force and a smaller diameter. Static hydraulics doesn’t help us in relating dynamic fluid flow – which is Darcy’s relationship.

I believe you are being side-tracked with the concept of the force being applied. It would be, I believe, easier to understand the hydraulics model if you thought of the PRESSURE imposed on the fluid as it enters the hypodermic needle and tries to enter the cavity in the human tissue (which exists at a different, lower pressure). The difference between these two pressures is the driving force that is creating the ability of the fluid to flow from a high pressure source to a lower pressure. And that represents the model that Darcy-Weisbach paints.

Your application is very similar to a deep well disposal method. In this method we drill a hole in the earth and dispose of liquid wastes by using a pump to force the liquid down through a pipe and into the well where the liquid “disappears into the subsoil. If our well has a very porous substructure – such as gravel or sand – we don’t have to generate much pressure with our pump to force a given quantity of liquid down and into the well. However, if the internal walls of the well are coated with clay or other non-porous material, our disposal pump will have to work harder to generate a higher pressure so that the well will “take” the disposed liquid. However, our well will “take” the liquid if we lower the flow rate at which we feed the well – simply because the RATE at which we have disposal now is much lower – and consequently takes a lot of more time to carry out the job. That is the trade off: we have to work the pump longer (at a lower flow rate) to get by with less pressure drop.

I hope I have succeeded in explaining what I believe is happening in your application. Please do no hestitate to complain if I have failed. I consider this subject far too important to allow it to go by without everyone clearly understanding the underlying principles. If I can't describe it efficiently (or correctly) there are certainly others on the Forum (like Doug) who probably can.