Why does reduced diameter decrease flow?

[seratia]

Textbooks say it decreases flow. But, when I think about it...

If you blow through a small straw, you are blowing out less volume. But wouldn't the speed of flow be higher, therefore making up for the decrease in volume?

Like this:
Lower volume squeezed out faster = higher volume squeezed out slower?

After all, when you squeeze the open end of a hose, it's not like you deliver less water. You deliver less water but faster, and therefore the same amount of water.

Is my assumption flawed?
Maybe I am assuming constant pressure where I shouldn't? Maybe the hose is responding to the reduced diameter by increasing the pressure, thus overcoming the increase in resistance with increase in pressure?

 

[DaveC426913]

1] Answers may be different depending on whether you're talking gas or liquid.

2] A garden hose might be considered a rigid tube. So the flow will remain constant. A bodily vessel is not rigid, so it can expand before the constriction, slowing flow.

I don't think these are definitive answers to your question, just factors.

 

[seratia]

1) I'm talking about fluids.

2) So does pressure increase in the rigid tube if constricted?

My whole point of asking this is to understand the body's circulatory system. For example, why do vasoconstrictors increase blood pressure when used for shock?

 

[russ_watters]

Textbooks say it decreases flow. But, when I think about it...

If you blow through a small straw, you are blowing out less volume. But wouldn't the speed of flow be higher, therefore making up for the decrease in volume?

The word "flow" in this context means volumetric flow rate. So as you say: you are blowing out less volume (volumetric flow).

After all, when you squeeze the open end of a hose, it's not like you deliver less water. You deliver less water but faster, and therefore the same amount of water.

These are contradictions. You deliver less water so you deliver less water. The fact that you deliver less water faster doesn't mean it isn't still less water; it is still less water.

Maybe the hose is responding to the reduced diameter by increasing the pressure, thus overcoming the increase in resistance with increase in pressure?

It is.

 

[BillTre]

Flow of water behaves in a similar manner to current in a wire.
Smaller pipes have greater resistance to flow. This is like a resister in a circuit.
The pressure pushing the water through is like voltage (electromotive force).
Water flow is roughly described by flow = pressure/resistance; similar to I = V/R in circuits.

The flow of water (my fluid of choice) through a tube will not increase when being pushed through a tube by the same pressure.
The resistance will go up for water going through a smaller tube.
The pressure will not go up unless something else is increasing it.

Water flow is somewhat different in that has to deal with that the viscosity of the fluid and shear from its interaction with the walls of the tube it is going through.
A pipe's resistance to water flow is not linear with the cross sectional area because a greater proportion of the cross-sectional area of the pipe will be more affected by closer adjacency to the walls.

Since this is in the biol/med forum, I am guessing you are interested in blood flow.
As mentioned above, blood vessels can also have compliance where (especially veins) can expand as blood flows into them, so that for a while there can be more flow in than comes out.
This is like capacitance in a circuit.

You might get more technical details if this were posted in an engineering section.
Engineering analysis of biological functions have a long history: bio-physics, bio-engineering, bio-mechanics.

 

[DaveC426913]

These are contradictions. You deliver less water so you deliver less water. The fact that you deliver less water faster doesn't mean it isn't still less water; it is still less water.

I meant to mention this too.

When you constrict a garden hose - say, to clean gunk off your car - you are indeed reducing the flow.

Fill a bucket with the nozzle wide open and then fill it again with the nozzle constricted so you get the power wash effect. The latter will take longer to fill the bucket. i.e. less overall delivery.

 

[Tom.G]

When two 'things' rub against each other there is resistance to their movement from friction. In your case you seem to be referring to Blood and the Blood vessels it flows in. There is also a characterisitic of fluids called Viscosity, that could be called a measure of how much they 'stick to themselves'. For instance water has a fairly low viscosity and it flows easily when poured. Honey or Corn syrup have a higher viscosity and they flow more slowly when you pour them.

A liquid such as blood, when flowing thru a blood vessel, will have some friction against the walls of the vessel. This causes the blood in contact with the vessel wall to slow down a little. In a large vessel, the blood in the center of the vessel is not much affected by this layer of slower-moving blood against the wall because it is further away. In a small vessel, the slow layer against the wall takes up a larger percentage of the area available for flow.

So with a given pressure, between the friction against the vessel wall slowing the blood, and the viscosity of the blood trying to keep it flowing at the same rate as at the wall, you end up with decreased blood flow thru the smaller vessel.

Addendum:
A smaller blood vessel has a larger wall area relative to its cross sectional flow area than does a larger blood vessel. (the wall surface is proportional to 2⋅π⋅R but the cross sectional area (called the Lumen) is proportional to π⋅R², so the lumen area changes faster than the wall area.)

Hope this helps.

Cheers,
Tom

 

[seratia]

These are contradictions. You deliver less water so you deliver less water. The fact that you deliver less water faster doesn't mean it isn't still less water; it is still less water.

Q = P / R

If you increase resistance, and pressure increases, doesn't that keep Q the same? Unless maybe P increases less than R does.

 

[russ_watters]

Q = P / R

If you increase resistance, and pressure increases, doesn't that keep Q the same? Unless maybe P increases less than R does.

P increases less than R does.

 

[CWatters]

The nature of the source and how it responds to changes may matter. Is it designed to provide a constant pressure or constant flow rate? Not quite either?

 

[seratia]

The nature of the source and how it responds to changes may matter. Is it designed to provide a constant pressure or constant flow rate? Not quite either?

A. The human body (CV system)
B. Is there any educational source that breaks down these complexities individually?

 

[jim mcnamara]

@Choppy - I believe can provide some resources. It seems you want Medical Physics references, elementary textbooks maybe.

 

[BillTre]

I believe that we used an older version of this medical physiology textbook (Guyton and Hall) when we covered this in a physiology class I was a teaching assistant in.
On the other hand, one of the guys teaching the course was a former physicist turned biophysicist and he really loved this stuff. So he might have provided most of the material himself.
I would expect you could find decent medical texts on this subject in a university biology research library, certainly in a medical school.

On the third hand, here is the results of googling for "cardio vascular flow textbooks".

 

[russ_watters]

We get this question a lot, so I feel like maybe medical schools or physiology classes are teaching it in a way that is confusing/misleading.

A. The human body (CV system)
B. Is there any educational source that breaks down these complexities individually?

• From an engineering/fluid dynamic standpoint, the piping system and pump are separate components.
• The system has a performance curve where pressure loss (or requirement) is a square function of flow rate. If you add/increase a restriction, it increases the constant on that function.
• The pump has its own performance curve of pressure vs flow rate.
• Where the system curve and pump curve intersect is what the flow and pressure will be.
• The heart is essentially a positive displacement pump, which means it produces an essentially constant flow rate at a wide range of pressures.

You can learn the fluid dynamics of this from a fluid dynamics textbook or internet resource. For the specific performance of the heart, search for various permutations of: human heart positive displacement pump curve pressure flow

 

[ZapperZ]

I often teach General Physics for Life Sciences and PreMed majors, and we tailor the course so that it has applications and relevances in the bio and medical fields. Certainly, topics in fluid flow, Archimedes Principle, Bernoulli Principle, etc... are part of what we teach, with direct examples from blood flow in the human body, etc.

The issue here is whether in this situation, the continuity equation is valid, and that you treat this as a straight-forward fluid flow, or whether the situation is more complex than that. If the continuity equation is valid, then the volumetric flow rate is a constant. However, this is not always the case when we consider real situations, especially in blood flow. This is because when a blood vessel becomes constricted, there are other "channels" for blood to flow through instead, and the constricted channel may not get the same volumetric flow rate as before, i.e. the continuity equation is no longer valid there.

So in this question, the exact "phase space" of complexity needs to be clarified. What are the assumptions here? What parameters can we approximate as constants?

Zz.