Verify Rationale: Decreasing Blood Density to Reduce Turbulent Flow

AI Thread Summary
The discussion centers on verifying the rationale for reducing turbulent blood flow in veins, with the correct answer identified as lowering blood density without thinning it. The Reynolds number (NR) is crucial in determining flow type, where values below 2000 indicate laminar flow. The participant initially questions whether narrowing the vein would also decrease turbulence but realizes that reducing the radius increases velocity, thus raising NR. The equations provided confirm that maintaining a constant flow rate means that decreasing the radius does not help in reducing turbulence. Overall, the focus is on understanding how density and radius affect turbulent flow in blood vessels.
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Homework Statement



This time I'd like someone to verify that my rationale behind the correct answer is accurate...

Which of the following will decrease the chance of turbulent blood flow in a vein?

A. Narrowing the vein.
B. Thinning the blood without changing its density.
C. Increasing the absolute pressure on each end of the vein by the same amount.
D. Lowering the blood density without thinning it.

Correct Answer: D.

Homework Equations


Reynolds number (NR): NR = (2ρvR)/η
where ρ is density, v is the average velocity, R is the vessel's radius, and η is viscosity.


The Attempt at a Solution




Okay... I know a fluid with Reynold's number less than 2000 is results in laminar and non-turbulent flow. Of course I see why D is absolutely correct because a drop in density without changing it's viscosity will decrease NR, but what about choice A as well?! if I decrease the radius I should get the same effect right?

...OR! (I just had an epiphany) because flow rate *must* remain the same (Q=Av), decreasing the radius would only increase the velocity, thus there would be no change.

What do you think?
 
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Oh Sorry I wasn't more descriptive in the title - I clicked submit before realizing that.
 
lets see ...

Q is volume which flows per second ... which is constant.

Q = πR2v

lets substitute for v

N_R = \frac{2\rho}{\eta} \frac{QR}{\pi R^2}

N_R = \frac{2\rho Q}{\eta \pi R}

so yes decreasing R should inc. NR
 
cupid.callin said:
lets see ...

Q is volume which flows per second ... which is constant.

Q = πR2v

lets substitute for v

N_R = \frac{2\rho}{\eta} \frac{QR}{\pi R^2}

N_R = \frac{2\rho Q}{\eta \pi R}

so yes decreasing R should inc. NR

Great - thanks for showing me the equations as well!
 
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