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I'm a nurse, so my physics background is about that of a lay person. Please explain on that level. Ordinarily an Intravenous (IV) fluid bag is one liter. An IV piggyback is usually 2500ml. usually the fluid in each is the same 0.45% NaCl. The piggyback may also get medication mixed in with it. such as a Gm of Rocephin. But the effect is the same without it.

The main one has a small gauge tube that is spiked into the port at the bottom of the bag that continues to the patient's arm, infused into the vein with, commonly a 18 Ga catheter. That tube will have a port, there the same gauge tube can be connected to the piggy back bag. The Main bag is on a pole, about 1.5 meters above the infusion site. the piggyback is placed just higher than the main bag. The accepted explanation for why the piggyback flows and runs out before the main one starts (intentional) is gravity. To say the higher one has higher gravity. I tend to disbelieve this explanation. Does anyone know what the real reason for this effect is? assume all settings are equal and there is no pump, and is gravity fed.

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The bags are essentially connected because none of the joints are 1-way only. So they will seek a common level. That common level reaches the bottom of the higher bag before it reaches the bottom of the lower bag.

Another way to put it is, at the Y joint where tubes A and B join into tube C, there is a "head" of pressure in A and B. That "head" is the density of water times the vertical distance between the joint and the top surface of the liquid. Thus the "head" will be greater in the tube connecting to the bag with the higher surface.

That pressure difference between A and B will cause one of them to flow faster and even quite possibly back up into the other bag.

Aside: In pharmacokinetics, there is such a thing as a "two-compartment model" that works the same way (except gravity is not the driver, but concentration).

Further aside: In a high-wing airplane such as a Cessna 172, there are two fuel tanks, one in each wing, joined at a selector valve on the floor of the cabin. If the pilot makes the mistake of leaving the selector in the "both" position, and the plane is parked on a slope with one wing lower than the other, the fuel in the higher wing will drain, through the valve, and enter the slightly lower wing, causing it to fill up and overflow via its vent.

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A nice keyword to drop here (so that wolf can look this up easily) is "Communicating vessels", the name this phenomenon is often called. – Christoph Aug 8 '12 at 18:21

The flow in a IV is very slow and can therefore be assumed to be laminar and uniform which simplifies the analysis.

You should think of trying to push something soft through a tube--marshmallow through a straw, perhaps. In that case it would not surprise you that the speed would depend on how hard you press.

Well, the flow of a liquid through a narrow aperture depends on the pressure-difference of the fluid between the two ends, and that depends on the height of the liquid surface above the aperture.

So, the higher bag develops more pressure causing it to flow faster and empty sooner.

Now this analysis isn't perfect because I haven't discussed what happens when you bring two different flows together. The short--short version is that the higher pressure bag (which is the upper one) displaces some of the flow from the lower pressure one. But a full analysis is complicated.

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It's actually not too complicated--- it's the zero velocity limit of viscous flow, and it's exactly like resistors, with pressure playing the role of voltage, and flow playing the role of current. – Ron Maimon Aug 7 '12 at 22:01

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