Stent math puzzle

Here is an easier problem on fluid dynamics to get us in the mood for the "difficult math problem."

A doctor places a stent in an artery that doubles the blood flow through that section of the artery. The artery before and the stent was perfectly circular. The pressure either way is the same (I know probably not realistic, but let's keep this simple).

Hint: The flow of liquid through a circular pipe is faster in the middle of the pipe than the edges. To be more specific, the rate of flow at any given location is proportional to the distance to the nearest edge.

How much did the stent increase the radius of the artery at the point of the stent?

Quote: Wizard

Here is an easier problem on fluid dynamics to get us in the mood for the "difficult math problem."

A doctor places a stent in an artery that doubles the blood flow through that section of the artery. The artery before and the stent was perfectly circular. The pressure either way is the same (I know probably not realistic, but let's keep this simple).

Hint: The flow of liquid through a circular pipe is faster in the middle of the pipe than the edges. To be more specific, the rate of flow at any given location is proportional to the distance to the nearest edge.

How much did the stent increase the radius of the artery at the point of the stent?

By a factor of 2^.25 or about a 19% increase

Quote: Ace2

By a factor of 2^.25 or about a 19% increase

I agree.

Quote: Ace2

By a factor of 2^.25 or about a 19% increase

So I did this quick but I got a different answer.

v = velocity
q = volumetric flow rate
d = internal pipe diameter
r = internal pipe radius

The velocity of a fluid in a cylindrical pipe is defined by the equation v = 4q/d²π
1st we find the equation with radius which is v = 4q/(2r)²π = q/r²π
Then we isolate our constants (since velocity & pie won't change) and we get vπ = q/r²
So for every variable (x) change of flow rate, we get a variable change of xr for our radius.
Therefore our radius should increase by a factor of 2r to obtain twice the flow rate.
Therefore if both equations are to increase by 2 then the equation becomes vπ = (2)q/(2)r*r
Therefore the increase of twice the flow rate will have a √2 increase to r

So the answer is by a factor of √2 or 41.42%

I think the problem is you guys combined velocity & volumetric flow rate as 1 variable or either I messed up in the interpretation of the question :/

I used the Hagen-Poiseuille law.

Volume flow rate = π X pressure difference X pipe radius^ 4 X liquid viscosity / 8 X viscosity X pipe length.

F = πPr^4 / 8nl

For full credit, I'd like to see a calculus solution to the problem, not an off-the-shelf equation.

Quote: Wizard

For full credit, I'd like to see a calculus solution to the problem, not an off-the-shelf equation.

Wow, for full credit I'd like all the variables defined and not just some half-ass question for the intellectual. Those "off the shelf" equations as you like to call them are some of the best models for reality that we have and usually, someone spent a portion of their life on proofing them so let's show some respect & not dismiss them as if they are just fictitious gibberish.

Btw, I'm already relearning calculus because of you and you don't want that because then I'm going to probably lose interest in game design and start applying calculus to work that will make me no money. It's so easy to forget things you don't use daily, which is why college is a waste of time for most people.

Quote: Wizard

For full credit, I'd like to see a calculus solution to the problem, not an off-the-shelf equation.

I've never dealt with another mathematician that only accepts the branch of calculus as the only true form of mathematics. It's almost as if your discriminating against each language of math as if their is a superior lol. And the sad thing is that as powerful as calculus is, it has so many limitations in that soooo many math problems can't be solved using it, including how we define reality like the microverse.

I purposefully choose this question because calculus can't help you solve this and more importantly it's actually a probability question that you can't even comprehend since your lost in the translation. So either change your name to the Wizard of Cal or start looking at the question from a different perspective since it's a geography question disguised as a physics question but actually takes a considerable amount of statistics to figure out ;)

P.S. I don't appreciate you just creating a different question and taking the attention away from my question when your question isn't even remotely related other than fluid flow. Also, I'm sure there is a lot of bogus Cal functions on the web also, a good mathematician knows which equations are credible & how to test them for accuracy.

Quote: USpapergames

I've never dealt with another mathematician that only accepts the branch of calculus as the only true form of mathematics. It's almost as if your discriminating against each language of math as if their is a superior lol. And the sad thing is that as powerful as calculus is, it has so many limitations in that soooo many math problems can't be solved using it, including how we define reality like the microverse.

I purposefully choose this question because calculus can't help you solve this and more importantly it's actually a probability question that you can't even comprehend since your lost in the translation. So either change your name to the Wizard of Cal or start looking at the question from a different perspective since it's a geography question disguised as a physics question but actually takes a considerable amount of statistics to figure out ;)

P.S. I don't appreciate you just creating a different question and taking the attention away from my question when your question isn't even remotely related other than fluid flow. Also, I'm sure there is a lot of bogus Cal functions on the web also, a good mathematician knows which equations are credible & how to test them for accuracy.

That was one of the best rants I've ever heard!

I fully admit I'm a calculus snob. Being called one I take as a badge of honor.

As to asking a different question in your thread, I apologize. Would you like me to split if off to a separate thread?

Please & thank you

Quote: Ace2

I used the Hagen-Poiseuille law.

Volume flow rate = π X pressure difference X pipe radius^ 4 X liquid viscosity / 8 X viscosity X pipe length.

F = πPr^4 / 8nl

So after reviewing the equation your using I think 1 of use is using the wrong equation but my understanding of the question might be off. I don't fully understand the medical procedure, so is the blood discharging out of the cylinder into an open area, or is it within constant cylindrical shape equal to the radius?

You don't have velocity in the equation but instead your using pressure differential??? Velocity and flow rate are differently related. I think I've used this equation in the past to explain the liquid discharge rate where the cylinder ends and the liquid is poured into an open space.

Oh wow, I was way off in the interpretation of the question! So I was right your equation does explain the discharge of a liquid into a larger volume of space! I thought for some reason they cut a tube of the artery and replace it with a tube of stent lol I didn't know the stent goes inside the artery I swear!

Quote: Wizard

Here is an easier problem on fluid dynamics to get us in the mood for the "difficult math problem."

A doctor places a stent in an artery that doubles the blood flow through that section of the artery. The artery before and the stent was perfectly circular. The pressure either way is the same (I know probably not realistic, but let's keep this simple).

Hint: The flow of liquid through a circular pipe is faster in the middle of the pipe than the edges. To be more specific, the rate of flow at any given location is proportional to the distance to the nearest edge.

How much did the stent increase the radius of the artery at the point of the stent?

So does the stent discharge at both ends or just 1?