Visualizing/Understanding Bernoulli's (TBR Physics Example 7.7a)

[MDminded]

I've been through the explanations of Bernoulli's equation, but I'm having difficulty with a concept and would love your input.

"Example 7.7a: When blood flows through an artery, it exerts pressure on the surrounding arterial wall. Compared to a section of healthy artery of equal size, a narrowed section of diseased artery experiences a:

D. smaller pressure on the surrounding arterial wall, because the flow velocity increases."

I think what I'm having trouble understanding is how flow velocity affects pressure. I understand the mathematics, but the concept is stumping me for whatever reason.

I read this to say that because the flow velocity increases, there is a smaller pressure on the surrounding arterial wall of the diseased artery compared to a normal artery. Why is that?

The explanation goes on to mention atherosclerosis, and I get SO lost in that.

You may have guessed that the pressure should increase because of the high blood pressure associated with artherosclerosis. The heart of one afflicted with atherosclerosis pumps with a greater pressure to keep the blood volumetric flow rate at healthy levels, increasing the total pressure throughout the arteries. However the pressure is lower in an unhealthy section of an artery than it is in a nearby healthy section because of the flow speed increase. This comparison was the thrust of this question. As an aside, the lower pressure in the narrowing cartery can be low enough to do more than offset the increased pumping pressure of the heart, making the arterial pressure lower than that in a healthy individual's artery.

Help?

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[Biebs]

I've been through the explanations of Bernoulli's equation, but I'm having difficulty with a concept and would love your input.

"Example 7.7a: When blood flows through an artery, it exerts pressure on the surrounding arterial wall. Compared to a section of healthy artery of equal size, a narrowed section of diseased artery experiences a:

D. smaller pressure on the surrounding arterial wall, because the flow velocity increases."

I think what I'm having trouble understanding is how flow velocity affects pressure. I understand the mathematics, but the concept is stumping me for whatever reason.

I read this to say that because the flow velocity increases, there is a smaller pressure on the surrounding arterial wall of the diseased artery compared to a normal artery. Why is that?

The explanation goes on to mention atherosclerosis, and I get SO lost in that.

You may have guessed that the pressure should increase because of the high blood pressure associated with artherosclerosis. The heart of one afflicted with atherosclerosis pumps with a greater pressure to keep the blood volumetric flow rate at healthy levels, increasing the total pressure throughout the arteries. However the pressure is lower in an unhealthy section of an artery than it is in a nearby healthy section because of the flow speed increase. This comparison was the thrust of this question. As an aside, the lower pressure in the narrowing cartery can be low enough to do more than offset the increased pumping pressure of the heart, making the arterial pressure lower than that in a healthy individual's artery.

Help?

Ok, so we need to look at two different equations here.


First is the flow rate.
f=AV where A= Area and V= Velocity of fluid

If we narrow the section of the artery, we decrease the area. In order to keep the flow rate the same, the velocity of the blood would have to increase in order to compensate. So, we now know that when we decrease the area in the artery, the blood flows faster.

NOW we can use Bernoulli's equation. You really don't need to do any calculations here. Just know how things relate, just like the change in potential and kinetic energy. When we decrease kinetic energy, we are increasing potential energy. Using the same concepts, INCREASING velocity, should DECREASE the pressure in order to keep the continuity of the equation. P1 + 1/2pv^2 1 + pgy1 = P2 = 1/2pv^2 2 + pgy2

Cross out the pgy1 and pgy2 as they are not relevant. We are only comparing velocity and pressure. If we increase velocity (v1), then the pressure (P1) needs to decrease.

Hopefully this helped. I found if you think about it in the same context as the work energy theorem, it's a lot easier.

Let me know if you need any other clarification.

 

[MDminded]

Ok, so we need to look at two different equations here.


First is the flow rate.
f=AV where A= Area and V= Velocity of fluid

If we narrow the section of the artery, we decrease the area. In order to keep the flow rate the same, the velocity of the blood would have to increase in order to compensate. So, we now know that when we decrease the area in the artery, the blood flows faster.

I understand the math behind it, but I don't get how that is practical. It seems counterintuitive to me. And this is part of where I'm having the issue. I can memorize this concept, but I don't understand it beyond the math. Take away the math, give me arteries, and I have NO idea how speed affects pressure. Could you give me a practical example? A friend of mine tried explaining with pipes - a smaller pipe means the liquid would go faster through it. Why is that? I imagine it like a single-file line, and it taking longer to get through rather than a pipe with a larger diameter. Wouldn't liquid flow faster through a wider pipe? And wouldn't decreasing the pressure cause a decrease in diameter, which would decrease the speed? (I know it's flawed, so tell me how/why I'm wrong)

 

[cartman1980]

try watering plants w/ a garden hose, and covering it up w/ a finger or two and you'll know 😉

 

[MDminded]

try watering plants w/ a garden hose, and covering it up w/ a finger or two and you'll know 😉

Because I'm an idiot (who has been staring at this for six hours), elaborate please?

Covering the hose with my finger = decreasing the cross-sectional area through which the liquid flows.

The pressure increases on the hose end.

Does that make the water spew in my face faster or slower?

 

[Biebs]

I understand the math behind it, but I don't get how that is practical. It seems counterintuitive to me. And this is part of where I'm having the issue. I can memorize this concept, but I don't understand it beyond the math. Take away the math, give me arteries, and I have NO idea how speed affects pressure. Could you give me a practical example? A friend of mine tried explaining with pipes - a smaller pipe means the liquid would go faster through it. Why is that? I imagine it like a single-file line, and it taking longer to get through rather than a pipe with a larger diameter. Wouldn't liquid flow faster through a wider pipe? And wouldn't decreasing the pressure cause a decrease in diameter, which would decrease the speed? (I know it's flawed, so tell me how/why I'm wrong)

Careful, pressure and velocity are different quantities. You might assume that if you were to stick your thumb over the end of the hose, the pressure will increase--but this isn't true. The VELOCITY of the fluid is what is changing, not the pressure. Yes, this is confusing and counter intuitive as you mentioned.

You shouldn't be comparing how an area will change the pressure, instead--compare how the change in the area will effect the velocity of the fluid, then use Bernoulli's equation to see how this change will affect the pressure.

 

[gunj122]

This was confusing to me at first too, but hopefully this'll help you:

What is pressure? Pressure is defined as the quantity of force impacting a given area. Now what is actually exerting the pressure on the walls of the artery? the blood. therefore, if there are greater blood-to-wall interactions, then the exerted pressure will be increased. since you're increasing the velocity of the blood, and consequently reducing the number of collisions/interactions with the walls of the artery, the exerted pressure will be reduced.

heres an analogy: pretend you're running a marathon. you see your friends on the sidelines and they want to say a few words of encouragement to you. the few words here are analogous to pressure. now the faster you run, the less they can say to you because you don't spend as much time near them. the slower you run, they can tell you much more than before because you and your friends are given more time to interact.

hope this helps! lol i know its not the greatest analogy, but its the best i can think of while taking a break from my PS

 

[sibitrum]

I have a follow up question regarding this exact topic. One of the (AAMC #4, question 127) questions claims that vasoconstiction leads to an increased blood pressure. Is this inconsistent with the above discussion?

 

[MDminded]

What is pressure? Pressure is defined as the quantity of force impacting a given area. Now what is actually exerting the pressure on the walls of the artery? the blood. therefore, if there are greater blood-to-wall interactions, then the exerted pressure will be increased. since you're increasing the velocity of the blood, and consequently reducing the number of collisions/interactions with the walls of the artery, the exerted pressure will be reduced.

Thank you!

Careful, pressure and velocity are different quantities. You might assume that if you were to stick your thumb over the end of the hose, the pressure will increase--but this isn't true. The VELOCITY of the fluid is what is changing, not the pressure. Yes, this is confusing and counter intuitive as you mentioned.

You shouldn't be comparing how an area will change the pressure, instead--compare how the change in the area will effect the velocity of the fluid, then use Bernoulli's equation to see how this change will affect the pressure.

Biebs, thanks for this explanation. The 2nd paragraph was SUPER helpful.

I realized that another part of my confusion was due to an inability to differentiate between flow rate and velocity. FLOW RATE is volume/time or velocity*area. VELOCITY is just a component of flow rate.

Then, as the question was asking, I didn't understand how to find a relationship between flow rate and pressure, but now I see. You obtain the velocity from a flow rate equation, and plug that into Bernoulli's.

 

[MDminded]

I have a follow up question regarding this exact topic. One of the (AAMC #4, question 127) questions claims that vasoconstiction leads to an increased blood pressure. Is this inconsistent with the above discussion?

In this case, the blood vessel is exerting pressure, not the blood, as in the previous example. Right?

 

[Biebs]

Thank you!



Biebs, thanks for this explanation. The 2nd paragraph was SUPER helpful.

I realized that another part of my confusion was due to an inability to differentiate between flow rate and velocity. FLOW RATE is volume/time or velocity*area. VELOCITY is just a component of flow rate.

Then, as the question was asking, I didn't understand how to find a relationship between flow rate and pressure, but now I see. You obtain the velocity from a flow rate equation, and plug that into Bernoulli's.

Yup, looks like you got it!

 

[sibitrum]

In this case, the blood vessel is exerting pressure, not the blood, as in the previous example. Right?

Shouldn't these be the same by Newton's 3rd law?

 

[gunj122]

I have a follow up question regarding this exact topic. One of the (AAMC #4, question 127) questions claims that vasoconstiction leads to an increased blood pressure. Is this inconsistent with the above discussion?

the reason BP increases with vasoconstriction is that our cardiovascular system is a dynamic one. it will respond according to the stresses put on it.

BP is determined by two factors: Cardiac output and peripheral resistance.
Vasoconstriction increases the resistance and therefore causes the heart to respond by increasing the blood pressure. without the hearts response to resistance, we would never get blood to tissues affected by the vasoconstriction.

also another note, bernoulli's principle is for ideal fluids so it cannot be completely applied in the cardiovascular system since blood is not an ideal fluid.