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## MCAT

### Course: MCAT > Unit 8

Lesson 7: Fluids in motion- Fluids in motion questions
- Volume flow rate and equation of continuity
- Bernoulli's equation derivation part 1
- Bernoulli's equation derivation part 2
- Finding fluid speed exiting hole
- More on finding fluid speed from hole
- Finding flow rate from Bernoulli's equation
- Viscosity and Poiseuille flow
- Turbulence at high velocities and Reynold's number
- Surface Tension and Adhesion
- Venturi effect and Pitot tubes
- Two circulations in the body
- Arteries vs. veins - what's the difference?
- Resistance in a tube
- Putting it all together: Pressure, flow, and resistance

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# Putting it all together: Pressure, flow, and resistance

See how pressure, flow, and resistance relate to one another and how they each affect the human body. Rishi is a pediatric infectious disease physician and works at Khan Academy. Created by Rishi Desai.

## Want to join the conversation?

- This circulatory system equations seem to follow the same rules as an electrical circuit. Is the equation P=Q*R, analogous to Ohm's Law?(56 votes)
- No one answered it for ya- even though it looks like you found the answer already. Yes V=IR is analgous. V = P or some sort change of pressure/charge etc. I = Q or flow. R is resistance. So [P=QR] = [V=IR].(38 votes)

- Why do we actually count the resistance? Does is say something interesting about our health?(15 votes)
- Increased resistance can drastically reduce blood flow, causing problems. For example, Angina Pectoris (symptomatic chest pain) can occur when your coronary arteries are too reduced in size to get proper blood flow; the vessels are just too small and the resistance is too high. You can administer medication to patients with this condition and it will dilate their arteries, decreasing resistance and allowing blood flow to resume.(24 votes)

- Does the standard medical courses of MBBS and MD include the study of all the phenomenon in body through the physical and mathematical point of view or is this just a part of some other course? is physiology really taught based on our understanding and explanation provided ny physics?(5 votes)
- I can't speak with authority on medical school, but as an exercise physiology graduate student, I can say that there is a lot of explanation that kind of goes this way (obviously at a fast pace and without too much time spent on the more basic physics concepts). It is acknowledged that many of the phenomena that we observe in the body can be best explained through principles of physics (electrical conduction, fluid dynamics, pressure/volume relationships, tissue elasticity & plasticity, etc.).

I have found that some of my best teachers have had a pretty good grasp of the physics behind physiology :)(15 votes)

- I'm sort of confused about how to relate the circulatory system with fluid dynamics and resistance. In Bernoulli's Equation (assuming constant height) we found that pressure and velocity where inversely related. In the continuity equation, since volume is constant, we said that area and velocity where also inversely related. Why then, when the arteriole increases in area, does the pressure in the artery decrease?

Intuitively it makes sense, but mathematically I don't get it.(10 votes)- I have had the same question. Elastance is the answer.(2 votes)

- Hi, I'm still unclear why the equation {delta}P = Q x R is as such. In the video he just applies the equation, but does not explain the basis behind the equation.(9 votes)
- it is a way to see fluid as Ohm's law (Ohm’s law is for electricity but it can be analogous to flow)

it comes from the logical postulate that If you lower the resistance or up the flow of fluid/electrons you get a larger potential difference. (that logic is described in the formula)

Like Ohm’s law in terms of:

V = I x R

Change in pressure for blood formula:

P = Q x R

P = change in pressure along vessel [analogous to V = voltage (difference/change of electric potential is like change in pressure)]

Q = blood flow [analogous to I = current as electron flow]

R = resistance of flow [analogous to R = resistance]

Sources:

https://forums.studentdoctor.net/threads/flow-and-resistance.847421/

https://books.google.ca/books?id=Hlk0q8WOxxMC&pg=PA2&lpg=PA2&dq=P+%3D+Q+x+R+blood&source=bl&ots=dSh0F9Q3-O&sig=ACfU3U1KSmW7wjxC9M1-TVzkeT4elART-w&hl=en&sa=X&ved=2ahUKEwiVj9LKgZThAhWMmlkKHeGrBAkQ6AEwDHoECAoQAQ#v=onepage&q=P%20%3D%20Q%20x%20R%20blood&f=false(2 votes)

- At6:00, why does Q stand for blood flow instead of F or something that would be easier to remember?(1 vote)
- You can consider Q as Cardiac Output. Cardiac output is the volume of blood pumped by the heart per minute (mL blood/min). Cardiac output is a function of heart rate and stroke volume. The heart rate is simply the number of heart beats per minute. The stroke volume is the volume of blood, in milliliters (mL), pumped out of the heart with each beat.(2 votes)

- How'd he simplify 4900 mL/min to 5 L/min?(2 votes)
- 5000ml/min=5 L/min, and 4900lm/min=4.9L/min. These numbers are very close.(6 votes)

- I now this is kind of stupid but can somebody tell the differences between resistance and pressure?(3 votes)
- Pressure is how hard fluid is peing pushed along the tube or vessel. It's used to overcome the resistance from the vessel wall.

Resistance is how hard the vessel is trying to stop the flow of fluid. It's made up of how small the vessel is, and the friction along the sides.

Flow is the amount of fluid that's passing through the vessel over an amount of time. It's determined by how much the pressure can push against the resistance.(4 votes)

- @4:50you mentioned the pressure of the blood flow but isnt it that the pressure or blood flow decreases substantialy as it is making it's way to the capillaries but it rises again as soon it leaves the capillaries and enter venules and veins?(2 votes)
- Blood pressure is a difficult concept. Mean arterial pressure virtually stays the same in the large arteries, then goes down drasticly in the arterioles (remember Poiseulle and the radius thingy?), is very low in the capillaries, goes further down in the venules and veins and is almost zero near the heart. But you are right that not ALL blood pressure components go down after the heart. Systolic blood pressure actually goes up untill the arterioles are reached. Look up pulse wave amplification if you are interested.(5 votes)

- Why is the equation not "change is pressure not equal to the
**change**in resistance times the**change**in flow" rather than the "change in pressure is equal to the flow times resistance"?(3 votes)- Because the resistance and flow stay the same.(1 vote)

## Video transcript

And I'm going to talk to you
about pressure, resistance, and flow. We're going to try to make
sure you feel real comfortable with all three of these
things by the time we're done. So we start with the heart, and
off of the heart is the aorta. This is the largest
artery in the body. And this is one
branch of the aorta. I didn't draw a lot
of the other ones. This is the brachial artery. And the blood is
flowing from the aorta into the brachial artery. And let's say that the blood
is trying to make its way out to a fingertip, for example. So on its way out there, it
makes its way to an arterial. And the blood continues
flowing, and it goes into the capillary
bed, and the vessels are too small to draw, so I
just kind of do that thing. And it then goes
into the other half of the capillary bed, where
now the blood is deoxygenated. So I'm going to
draw that as blue. That's the part where now
the blood is without oxygen. And then it continues
to go and get collected into a venule, which sounds a
little bit like the arterial on the other side, right? And we've got a vein over here. And then finally, the
blood gets collected in a large vein
called the vena cava. And there are actually
two vena cavas, so this'll be the
superior vena cava. There's also an
inferior vena cava. And the blood flow through this
half is, as you would guess, continues to go around. And if I was to try to figure
out the pressures, the blood pressures, at different
points along the system, I'm going to choose
some points that I think would be
interesting ones to check. So it would be good
probably to check what the pressure is
right at the beginning. And then maybe at all
the branch points. So what the pressure is as
the blood goes from the aorta to the brachial artery. Maybe as it ends the brachial
artery and enters the arterial. Maybe the beginning and
the end of the capillaries. Also from the venue to a vein,
and also, wrapping it up, what the pressure is at the end. Now, these numbers,
or these pressures, can be represented
as numbers, right? Like what is the
millimeters of mercury that the blood is
exerting on the wall at that particular
point in the system? And earlier, we
talked about systolic versus diastolic
pressure, and there we wanted to use two
numbers, because that's kind of the range, the upper
and the lower range of pressure. But now I'm going to
do it with one number. And the reason I'm using
one number instead of two, is that this is the
average pressure over time. So the average pressure over
time, for me-- keep in mind my blood pressure
is pretty normal. It's somewhere around
120 over 80 in my arm. So the average pressure in
the aorta kind of coming out would be somewhere around 95,
and in the artery in the arm, probably somewhere around 90. Again, that's what you would
expect-- somewhere between 80 and 120. So 90 is the
average, because it's going to be not exactly
100, because remember, it's spending more time in diastole
and relaxation than in systole. So it's going to be closer
to 80 for that reason. And then if you check the
pressure over here by this x, it'd probably be something
like, let's say 80. And then as you
cross the arterial, the pressure falls dramatically. So it's somewhere closer to 30. And then here it's about 20. Here it's about 15. Let's say 10 over here. And then at the very end, it's
going to be close to a 5 or so. So here. Let me just write that again. 10 and 5. And the units here are
millimeters of mercury. So I should just write that. Pressure in
millimeters of mercury. That's the units that
we're talking about. So the pressure falls
dramatically, right? So from 95 all the way
to five, and the heart is a pump, so it's going to
instill a lot of pressure in that blood again and
pump it around and around. And that's what keeps the
blood flowing in one direction. So now let me ask
you a question. Let's see if we can
figure this out. Let's see if we can figure
out what the resistance is in all of the vessels
in our body combined. So we talked about
resistance before, but now I want to
pose this question. See if we can figure it out. So what is total
body resistance? And that's really
the key question I want to try to
figure out with you. We know that there is some
relationship between radius and resistance, and we
talked about vessels and tubes and things like that. But let's really figure this out
and make this a little bit more intuitive for us. So to do that, let's
start with an equation. And this equation
is really going to walk us through this puzzle. So we've got pressure, P,
equals Q times R. Really easy to remember, because
the letters follow each other in the alphabet. And here actually, instead
of P, let me put delta P, which is really
change in pressure. So this is change in pressure. And a little doodle
that I always keep in my mind to remember
what the heck that means is if you have a little tube,
the pressure at the beginning-- let me say start;
S is for start-- and the pressure at the end can
be subtracted from one another. And that gives you PS
minus PE equals delta P. The change in pressure
is really the change from one part of tube
the end of the tube. And that's the first
part of the equation. So next we've got
Q. So what is Q? This is flow, and more
specifically it's blood flow. And this can be thought of
in terms of a volume of blood over time. So let's say minutes. So how much volume--
how many liters of blood are flowing in a minute? Or two minutes? Or whatever number of
minutes you decide? And that's kind of a hard
thing to figure out actually. But what we can figure
out is that Q, the flow, will equal the stroke
volume, and I'll tell you what this is
just after I write it. The stroke volume
times the heart rate. So what that means
is that basically, if you can know how much
blood is in each heartbeat-- so if you know the
volume per heartbeat-- and if you know how many
beats there are per minute, then you can actually figure out
the volume per minute, right? Because the beats would
just cancel each other out. And it just turns
out, it happens to be, that I'm about 70 kilos. That's me. I'm 70 kilos. And for a 70 kilogram
person, the stroke volume is about 70 milliliters. So for a 70 kilo person, you
can expect about 70 milliliters per beat. And as I write this,
let's say my heart rate is about 70
beats per minute. I feel pretty calm, and
so it's not too fast. So the beats cancel
as we said, and I'm left with 70 milliliters
times 70 per minute. So that's about 4,900
milliliters per minute. Or if I was to simplify,
that's a 5, let's say about. So the flow is about
5 liters per minute. So I figured out the blood
flow, and that was simply because I happen
to know my weight, and my weight tells
me the stroke volume. And I know that there's
a change in pressure. We've got to figure
that out soon. And lastly, this last thing
over here is resistance. And know I've said it before. I just want to point
out to you again, the resistance is going to
be proportional to 1 over R to the fourth. And so just remember that
this is an important issue. R is radius. And that's the
radius of the vessel. So let's figure
out this equation. Let's figure out the
variables in this equation and how it's going to help
us solve the question I asked you-- what is the
total body resistance? OK. So if I have to figure out
total body resistance-- let me clear out the board--
I've got, let's say, the heart. I like to do the heart in red. And it's pumping
blood at my aorta. So blood is going
out of the aorta. And then it's going
and branching here. And then it's going
to branch some more. And then it's going
to branch some more. And you can see
where this is going. It's going to keep branching. And eventually every branch kind
of collects on the venous side. All the blood is kind of
filtering back in slowly into venules and veins. And finally into a vena cava. And I should really draw
this going like that. The blood is going to go
back into the vena cava. So that's my system. And I got to figure out what the
total body resistance is here. So if I have a system
drawn out for myself, and I happen to know
that here I said 95. And here I said
the pressure was 5. Then delta P equals 95
minus 5, which is 90. And I know that there are 5
liters of blood flowing through per minute. And that was my
Q. So I could say 90 equals 5 liters per minute. Actually let me take
a step back from that. Instead of 90, let
me write the units. 90 millimeters of mercury
equals 5 liters per minute. That was my flow. That's my Q. And I've
got delta P here. And my resistance
is the unknown. So I'll just leave that as R. So let's just solve
for R. So I'll move my flow to the other side. So R equals-- I'll put it here--
90 divided by 5, which is 18. And the units are
a little funky, but I'll just write
them out anyway. Millimeters of mercury times
minutes divided by meters. So this is the answer
to my question-- what is the total
body resistance? Well, we know what
the pressures are at the beginning and
end of our system. And we know that the flow has to
be around 5 liters per minute, because that's based on my
weight and my heart rate. Therefore, the resistance
must be 18 millimeters of mercury times
minutes over liters. Whatever that set of
units means to you. It's kind of an abstract thing. But basically, I want
to demonstrate to you that this powerful
equation helps us solve for what
would otherwise become a tricky
problem to figure out.