any math experts out there?

I think flow is proportional to radius to the 4th power, so if we had radius=r before, and radius=3r now, flow should increase by a factor of (3^4), or 3*3*3*3, or 81. IE flow has increased by a factor of 81. So flow should be 4 L/min * 81, or 324 L/min. I think. Linky:

http://www.fas.harvard.edu/~scdiroff/lds/NewtonianMechanics/PoiseuillesLaw/PoiseuillesLaw.html

You need to remember that when youu increae the radius or diameter of a tube or pipe, you ware increasing the cross sectional area by the square of the radius. pie r squared. The volume the pipe will carry goes up very fast.

I feel sorry for the patient he's pumping 324 liters a minute of ANYTHING through.

Unless it's like, chocolate milk.

Just so you know, that's a physics/fluid dynamics question more than a math question. The math part is easy. Knowing the "laminar flow rate" goes up with the fourth power of the radius is, uh, priceless.

Kitty Pryde said:

I think flow is proportional to radius to the 4th power, so if we had radius=r before, and radius=3r now, flow should increase by a factor of (3^4), or 3*3*3*3, or 81. IE flow has increased by a factor of 81. So flow should be 4 L/min * 81, or 324 L/min. I think. Linky:

http://www.fas.harvard.edu/~scdiroff/lds/NewtonianMechanics/PoiseuillesLaw/PoiseuillesLaw.html

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Good stuff! I know enough about this to be dangerous, and I was thinking flow rate might be proportional to the cross sectional area. Obviously I should do less thinking and more studying when it comes to this...

sheadakota said:

Thank you Kitty!!! MR Dakato is slapping the side of his head and going DOH!

Apparently he read the answer key wrong - the question was #10 and in the key it read like this

10,324L/min


he mistook this as ten thousand... Hahahahaha

I 'm not laughing at him, but he is so rarely wrong about anything I love it when he makes a mistake-

NOW I can get back to my Nano !

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Wanna have some fun? Send him to http://collegeboard.com and have him sign up for the SAT Question of The Day. It only takes a minute or so out of your day, and it's often fun and sometimes(!) even challenging. I kick myself just about every time I miss a question, as I know I "should have" got it.

dclary said:

I feel sorry for the patient he's pumping 324 liters a minute of ANYTHING through.

Unless it's like, chocolate milk.

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I used to prefer Baccardi rum, then moved up to Meyer's. But wow, the cost per minute... the tightwad in me is suggesting Ronrico...

At least it's not ten thousand three hundred and twenty four liters per minute.

This thread makes my brain 'splode.

Hmm, a question of pie are squared. My pies are round, so count me out. Just a thought, how long before the patient explodes from the increased flow?

Smiles
Bob

sheadakota said:

SAT question of the day? He does the Anesthesia question of the day- he hasn't gotten one wrong yet- the guy is scary smart!

Click to expand...

I had to look:

Disodium edetate or sodium metabisulfite is added to formulations of propofol to:

enhance drug solubility
adjust pH
inhibit bacterial growth
increase drug potency
​

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UNCLE!

MagicMan said:

Hmm, a question of pie are squared. My pies are round, so count me out. Just a thought, how long before the patient explodes from the increased flow?

Smiles
Bob

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12.8 milliseconds.

Geez, I would have gotten it wrong.

I would have assumed that the flow rate would be directly proportional to the area of the tube. Since the area of the cylinder is (Pi) r squared, wouldn't the area (and therefore the flow) increase by 9?

What am I doing wrong?

BarbaraKE said:

Geez, I would have gotten it wrong.

I would have assumed that the flow rate would be directly proportional to the area of the tube. Since the area of the cylinder is (Pi) r squared, wouldn't the area (and therefore the flow) increase by 9?

What am I doing wrong?

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It makes reasonable sense that it would increase by r squared with the area, but it actually follows a law called Poiseuille's Law:

so flow increases proportional to r^4. If you click the link in my original post it explains how that is derived.

Kitty - Things like this frustrate me no end.

I followed your link. It talked about the equation but didn't really explain why it worked the way it does.

(By the way, I'm not saying you're wrong. Far from it. Obviously you're right and the original poster's husband agreed. I'm just frustrated that I don't understand why.)

Can you explain (in simple English <smile>) why the flow is 81 times higher when the cross-sectional area is only 9 times higher?

(I realize I'm getting away from the original poster's question - sorry. I drive my teachers crazy too.)

<GEEK WARNING> (where's that magnetic ink font...)
As is common thesedays, Wikipedia has an explanation:
http://en.wikipedia.org/wiki/Poiseuille's_Law

Look under "Liquid flow through a pipe" and the diagram, the fluid near the pipe walls is slowed down because it tends to 'stick' to the walls which aren't moving, but in the middle it flows faster, since it's surrounded by other fluid that's already flowing. With a larger pipe, the middle part is even further from the walls, so it flows even easier.

That doesn't tell me why it's the fourth power of radius (apparently those calculus equations do, but I didn't check those...), but at least it gives an intuitive explanation of why the flow rate goes up at a rate faster than being proportional to the area as the radius is increased.
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BarbaraKE said:

Can you explain (in simple English <smile>) why the flow is 81 times higher when the cross-sectional area is only 9 times higher?

Click to expand...

I had to look it up last night because I had exactly the same question!

Visualize the liquid flowing through the tube as tube-shaped concentric layers. The layer of liquid that is next to the outer tube has friction against the tube so it can't flow very fast. The second layer of liquid has friction with the first layer, so it flows only a little bit faster than the first layer. The third layer flows a little faster than the second, and so on. The center part of the liquid is the fastest of all. The larger the tube, the more layers there are, so the faster the center part can flow. So there two effects at work: a larger tube has a larger cross-sectional area and a larger tube also has faster flow in the center.

ETA: Ah, Ben beat me to it.

Ben & Fennel - Thanks for the explanation. I did try to figure it out before posting my question and found that same Wikipedia entry. But if you notice - about 4/5's of the way down the page, it says (I hope this works)...

For an ideal gas in the isothermal case, where the temperature of the fluid is permitted to equilibrate with its surroundings, and when the pressure difference between ends of the pipe is small, the volumetric flow rate at the pipe outlet is given by



Where:

Pi inlet pressure
Po outlet pressure
L is the length of tube
η is the viscosity
R is the radius
V is the volume of the fluid at outlet pressure
v is the velocity of the fluid at outlet pressure

See the 'velocity' times 'pi' times 'r squared'? So assuming that the velocity of the fluid/gas coming out remains the same, the flow rate varies as r squared.

In theory, I can understand why friction against the walls could make the gas/fluid slow down. That does make a certain amount of sense to me. I just don't intuitively understand why it makes that much difference.

(I realize that I've totally gotten away from the original poster's question. My apologies.)