TBR: Steady Fluid Flow

[justadream]

TBR page 88 #24

“As blood flows steadily through a pipe of uniform cross-section and length L, its speed___”

Answer: remains unchanged, as long as the pressure difference between the ends of the pipe is constant.

Wrong Answer Choices:
"must decrease to counteract losses to viscosity"
"must increase to counteract losses to viscosity"

Can someone explain (intuitively) why the speed remains constant for a fluid with a nonnegligible viscosity?

In addition, I assume there is a distinction between the viscosity of the fluid and any resistance in the pipe/vessel. Does only the resistance in the pipe/vessel slow down speed (whereas, the viscosity doesn’t)? If that is true, is it because viscosity is “accounted for” when determining initial (and constant) speed of the fluid but forces like resistance in the vessel/tube are not?

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[DrknoSDN]

If you measure the flow at the start of the pipe and it ends up being say, 1L/min... You would expect that the other end would also have 1L/min exiting.

If that wasn't true you would either have air pockets forming if flow out is greater than flow in, or if (flow in > flow out) you would have extreme pressure buildup in the pipe because the mass of fluid in the pipe would be increasing while volume is constant (fluids are not very compressible).

For a completely rigid pipe and an incompressible fluid, flow in must equal flow out.
In this question cross sectional area is constant, so flow is proportional to speed. Therefore speed must be equal at both ends.

 

[justadream]

@DrknoSDN

So no matter the resistance/viscosity, as long as the pressure difference remains the same, the velocity is constant?

If so, what exactly do resistance/viscosity do in terms of affecting the fluid flow? Do they just slow down the fluid flow "initially" (as in, the constant rate at which the fluid flows is just less if the fluid is more viscous)?

 

[DrknoSDN]

@DrknoSDN

So no matter the resistance/viscosity, as long as the pressure difference remains the same, the velocity is constant?

If so, what exactly do resistance/viscosity do in terms of affecting the fluid flow? Do they just slow down the fluid flow "initially" (as in, the constant rate at which the fluid flows is just less if the fluid is more viscous)?

Yes, a more viscous fluid would flow slower in and out, but the speed at both ends should always be the same to avoid pressure gradient formation.
The velocity/speed is altered by resistance/viscosity but the question is asking about a change in speed from the beginning to end of the pipe, which should always be zero.

Also, this is all MCAT style interpretation and without giving examples, it is important to remember that it does not apply to real world scenarios. That is why the answer choice included the caveat, "as long as the pressure difference between the ends of the pipe is constant".

 

[justadream]

@DrknoSDN

So why does hydrostatic pressure in blood capillaries decrease across the length of the capillary?

Shouldn't it flow at a constant (slow) rate?

 

[Cawolf]

@DrknoSDN

So why does hydrostatic pressure in blood capillaries decrease across the length of the capillary?

Shouldn't it flow at a constant (slow) rate?

The volume in the capillary is not constant, fluid is forced out into the interstitial space along the vessel.

 

[justadream]

@Cawolf

I got this quote from Silverthorn's Physio book

"Capillary hydrostatic pressure (PH), by contrast, decreases along the length of the capillary as energy is lost to friction."

So I guess that's wrong?

 

[Cawolf]

I don't think I know more than a textbook, go with what that says.

 

[justadream]

@Cawolf

I mean it's plausible that the textbook writers are biologists and not fluids-specializing physicists like you

 

[Cawolf]

Haha! My only accolades are in my signature, and I don't see physicist down there!

 

[Cawolf]

I did reference a bio textbook I have ("Principles of Life" by Heller) and it focuses on velocity decreasing due to the vast cross sectional area of the capillaries.

 

[justadream]

@Cawolf

That is a plausible explanation.

Now bringing in Pouiselle's law (however you spell it), I remember that wikipremed's physics flashcards said that

"the pressure drop per unit length in narrow vessels is much greater than in larger vessels"

So is it possible that pressure is decreasing?

 

[Cawolf]

The pressure is definitely decreasing.

The capillary gets down to a diameter just greater than that of an RBC. The hydrostatic pressure decreases along the length of the vessel as fluid is forced into the interstitial space. The hydrostatic pressure actually drops below the osmotic pressure of the tissues near the venule end, resulting in the re uptake of fluid.

I guess that is aligned with what the flashcard said.

 

[justadream]

@Cawolf

So what's the explanation for WHY the pressure is decreasing in the capillaries?

If you bring in area, the area at the beginning portion of the capillaries should be the same as the area of the middle portion of the capillaries (or however small you want the difference to be).

It just seems weird to me that in fluids with viscosity, the speed doesn't go down gradually (whereas if you are talking about box sliding on a road, it slows down due to friction) but rather just starts at the slower velocity and continues at the constant rate.

 

[Cawolf]

The fluid is leaving the capillary as the hydrostatic pressure (greater than the tissue osmotic pressure) forces fluid through the highly porous capillary. Less fluid = less pressure.

The fluid reverses directions and the pressure goes back up once you start approaching the venule.

It is not constant volume, so none of the area formulas mean anything.

 

[justadream]

@Cawolf

So it's not constant volume, even within the capillaries (like take point_1 to be point just inside the capillaries and take point_2 to be the point .000001m farther along but still in the capillaries)?

"The fluid reverses directions and the pressure goes back up once you start approaching the venule."
Yes, I read that fluid reverses at the end (since osmotic pressure exceeds hydrostatic pressure at the end) but my question was: why is it that hydrostatic pressure decreases within the capillaries (from point_1 to point_2 in my hypothetical above)?

 

[Cawolf]

The fluid is leaving the capillary as the hydrostatic pressure (greater than the tissue osmotic pressure) forces fluid through the highly porous capillary.

Less fluid = less pressure.

 

[justadream]

@Cawolf

Okay I think I get it. And the reason osmotic pressure is constant (despite fluid leaving) is because osmotic pressure just depends on the amount of solute/proteins? (so like 5 units of solute + 5 units of water would have the same osmotic pressure as 5 units of solute + 5000000000 units of water).

 

[Cawolf]

Right. The osmotic pressure differential is relatively constant.