Pressure Vs velocity

inaccensa · Jul 21, 2009

please confirm the following

In ideal fluids
Velocity increases with a decrease in area.
Velocity increases with a decrease in pressure.
Velocity increases with decrease in resistance.
Velocity increases with a decrease in temperature?

In real fluids such as the cardiovascular system

Aorta has smallest (cross-sectional) area, high pressure and low velocity? Since deviating from ideal fluids, the velocity is not as low as predicted by ideal fluids?

Capillaries have the largest cross-sectional area, lowest velocity and low pressure. However, the pressure is not as low as predicted, but slightly higher.

Veins have the lowest pressure & slightly high velocity?

Omni · Jul 21, 2009

just remember it like this:
Pressure and velocity are inversely related to each other.
P= F/A, and V=m/s
(P=pressure, F= force, A= area, V=velocity)

-if A is decreasing, P is increasing, and hence V is decreasing
-if A is increasing, P is decreasing, and hence V is increasing

Also, keep in mind that ideal fluid is not the same as real fluid.

inaccensa · Jul 21, 2009

Omni said:
just remember it like this:
Pressure and velocity are inversely related to each other.
P= F/A, and V=m/s
(P=pressure, F= force, A= area, V=velocity)

-if A is decreasing, P is increasing, and hence V is decreasing
-if A is increasing, P is decreasing, and hence V is increasing

Also, keep in mind that ideal fluid is not the same as real fluid.

But i'm trying to related these equations to real phenomenon. i think that the velocity decreases with increasing area. So if we follow the equations, the area of the capillaries is quite large & thus must have the lowest velocity. & lowest pressure? I'm totally confused. I thought pressure and velocity with inversely related. if the same force is applied over a larger area, the pressure increases. Thus the pressure in the capillaries must be high...please help my thought process.

Charles_Carmichael · Jul 21, 2009

inaccensa said:
But i'm trying to related these equations to real phenomenon. i think that the velocity decreases with increasing area. So if we follow the equations, the area of the capillaries is quite large & thus must have the lowest velocity. & lowest pressure? I'm totally confused. I thought pressure and velocity with inversely related. if the same force is applied over a larger area, the pressure increases. Thus the pressure in the capillaries must be high...please help my thought process.

The equation you want to think of when thinking of blood velocity is:

v = Q/A

where v is velocity, Q is the cardiac output (or blood flow), and A is the total cross-sectional area. The cardiac output is pretty constant (at resting conditions) at 5 liters/min. So the equation simplifies to v = 1/A. The capillaries have the largest total cross-sectional area, so they have the lowest velocity.

If you want to think of the relationship between pressure and velocity, you can use the following equation:

dP = Q x R

where dP is the change in pressure (or you can think of it as the mean arterial pressure), Q is the cardiac output, and R is the total peripheral resistance. If you rearrange the velocity equation, you get Q = vA...if you plug this in to this previous equation, you get dP = vAR. So, based on this equation, the pressure and blood velocity are directly related, not inversely.

Hope this helps.

inaccensa · Jul 21, 2009

Kaushik said:
The equation you want to think of when thinking of blood velocity is:

v = Q/A

where v is velocity, Q is the cardiac output (or blood flow), and A is the total cross-sectional area. The cardiac output is pretty constant (at resting conditions) at 5 liters/min. So the equation simplifies to v = 1/A. The capillaries have the largest total cross-sectional area, so they have the lowest velocity.

If you want to think of the relationship between pressure and velocity, you can use the following equation:

dP = Q x R

where dP is the change in pressure (or you can think of it as the mean arterial pressure), Q is the cardiac output, and R is the total peripheral resistance. If you rearrange the velocity equation, you get Q = vA...if you plug this in to this previous equation, you get dP = vAR. So, based on this equation, the pressure and blood velocity are directly related, not inversely.

Hope this helps.

Thanks that definitely explains a lot. I guess I shouldn't think of P=f/a for blood flow. Can you just clarify the relationship in ideal fluids

Omni · Jul 21, 2009

You have to keep in mind. This is for IDEAL fluids only. This will not apply to blood. For blood, you will need a different equation that encompasses all of the factors related to blood.

These are some of the factors that must be in order for you to use that logic b/w pressure and velocity (Bernoulli's Principle)
1) Must be NON-VISCOUS
2) Pressure must only have one source (blood has multiple pressure sources, such as the heart or the venus pump)
3) Steady Flow
4) No friction
5) Ideal fluid

You cannot apply that principle to blood...you won't see it happening that way.

Use another analogy. Try using a pipe for an analogy that has a smaller area in on part and then a bigger area in another.

For blood, you need a completely different formula.

Omni · Jul 21, 2009

my computer didn't refresh this page so I didn't see the post Kaushik made. My last post was made without knowing what was there.

inaccensa · Jul 22, 2009

Omni said:
You have to keep in mind. This is for IDEAL fluids only. This will not apply to blood. For blood, you will need a different equation that encompasses all of the factors related to blood.

These are some of the factors that must be in order for you to use that logic b/w pressure and velocity (Bernoulli's Principle)
1) Must be NON-VISCOUS
2) Pressure must only have one source (blood has multiple pressure sources, such as the heart or the venus pump)
3) Steady Flow
4) No friction
5) Ideal fluid

You cannot apply that principle to blood...you won't see it happening that way.

Use another analogy. Try using a pipe for an analogy that has a smaller area in on part and then a bigger area in another.

For blood, you need a completely different formula.

So for Blood which is a non-deal fluid, with increase in resistance, both the pressure and velocity will increase simultaneously? ( but if u look at the equation dP= AvR, velocity and resistance are inversely related and pressure and velocty are directly proportional) Decrease in resistance will decrease the velocity and pressure. Increase in area, decrease both the velocity and pressure. But in real fluids, the change in pressure and velocity will be greater than predicted by the non-ideal fluids?

Pressure Vs velocity

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