Verify Rationale: Decreasing Blood Density to Reduce Turbulent Flow

[tenbee]

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 (N_R): N_R = (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 N_R, 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?

 

[tenbee]

Oh Sorry I wasn't more descriptive in the title - I clicked submit before realizing that.

 

[cupid.callin]

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. N_R

 

[tenbee]

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. N_R

Great - thanks for showing me the equations as well!