# Blood flow and pressure ( and velocity)

• kay
In summary, the flow of blood in this region (the region inside the artery) is raised which lower the pressure inside the artery and it may collapse due to external pressure.

#### kay

so i was reading on some applications of bernoulli's principle and i encountered a paragraph in which it was stated that 'the speed of the flow of blood in this region ( the region inside the artery) is raised which lower the pressure inside the artery and it may collapse due to external pressure. '
Now my doubt is that why does pressure decrease? When the velocity of blood flow increases inside the artery?

Bernoulli's principle is basically conservation of energy, and says that the total pressure remains constant on a streamline. The total pressure is the static pressure plus the dynamic pressure. Dynamic pressure is 'velocity pressure': $P=p_s + \frac{1}{2}\rho V^2=\textrm{const}$.
So if the velocity goes up (because for instance the flow-through area of the artery is decreasing), the dynamic pressure goes up and therefore the static pressure goes down.

There is a derivation based on conservation of energy here:
http://en.wikipedia.org/wiki/Bernoulli's_principle#Derivations_of_Bernoulli_equation

Can you give me the theoretical reason for it?

Imagine billions of particles with velocity vectors. Each velocity vector is the sum of a velocity component toward the artery wall and a velocity component parallel to the wall. The component that is pushing into the wall contributes to the pressure against the artery wall. The component parallel to the wall contributes to the flow of the fluid. The Pythagorean theorem tells how to divide the vector (hypotenuse) between velocity toward the wall and velocity in the direction of flow. As the fluid flow increases, the velocity vectors are tilting more in the direction of flow and less toward the artery wall. So more flow velocity => less pressure against the artery wall.

FactChecker said:
Imagine billions of particles with velocity vectors. Each velocity vector is the sum of a velocity component toward the artery wall and a velocity component parallel to the wall. The component that is pushing into the wall contributes to the pressure against the artery wall. The component parallel to the wall contributes to the flow of the fluid. The Pythagorean theorem tells how to divide the vector (hypotenuse) between velocity toward the wall and velocity in the direction of flow. As the fluid flow increases, the velocity vectors are tilting more in the direction of flow and less toward the artery wall. So more flow velocity => less pressure against the artery wall.
If you have a literature reference for this explanation, please provide it.

Chestermiller said:
If you have a literature reference for this explanation, please provide it.
I don't know a reference. I just wanted to give some intuition as to why there was a trade off between pressure and flow velocity squared.
constant energy =~ Vtotal2 = Vtoward wall2 + Vparallel to wall2 =~ Pressure + 1/2 ρ Vparallel to wall2
The references I have seen seemed more rigorous, but less intuitive to me.

FactChecker said:
I don't know a reference. I just wanted to give some intuition as to why there was a trade off between pressure and flow velocity squared.
constant energy =~ Vtotal2 = Vtoward wall2 + Vparallel to wall2 =~ Pressure + 1/2 ρ Vparallel to wall2
The references I have seen seemed more rigorous, but less intuitive to me.
The reason I asked for a reference is that this doesn't seem correct (to me). The Bernoulli equation, which is what Bigfoot was alluding to in post #2 and you were alluding to in this quote, is based on Newton's 2nd law. If the velocity is higher downstream than upstream, the pressure must be higher upstream than downstream in order to accelerate the fluid. (This, of course, neglects viscous drag).

Chet

FactChecker
Chestermiller said:
If the velocity is higher downstream than upstream, the pressure must be higher upstream than downstream in order to accelerate the fluid.
I agree. I must have said something confusing in my earlier post if I implied the opposite. And your way of looking at it may be the most intuitive of all.
To continue your logic: If the velocity slows down farther downstream, there must be some higher pressure downstream that slowed it down. So the trade-off between flow velocity and pressure is intuitive in all cases.

Chestermiller

## What is blood flow?

Blood flow refers to the movement of blood through the blood vessels of the body. It is a vital process that delivers oxygen and nutrients to cells and removes waste products from the body.

## What factors affect blood flow?

The main factors that affect blood flow are blood pressure and blood velocity. Other factors include the diameter and elasticity of blood vessels, the viscosity of blood, and the activity of the heart.

## What is blood pressure?

Blood pressure is the force exerted by the blood against the walls of the blood vessels. It is measured in millimeters of mercury (mmHg) and consists of two values: systolic pressure (when the heart contracts) and diastolic pressure (when the heart relaxes).

## What is the relationship between blood flow and blood pressure?

Blood flow and blood pressure are directly related. When blood pressure increases, blood flow also increases. This is because the increased pressure pushes more blood through the blood vessels. Conversely, when blood pressure decreases, blood flow also decreases.

## How does blood velocity vary in different parts of the body?

Blood velocity varies in different parts of the body based on the size and type of blood vessel. Blood moves slower in smaller blood vessels, such as capillaries, due to their narrow diameter. In larger vessels, such as arteries and veins, blood moves faster due to their larger diameter and higher pressure.