TBR Fluids and Fluid Dynamics

[ImDiene0412]

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My question is more about unit conversion...

Atherosclerosis is the thickening and hardening of the arterial walls. The aorta of a healthy adult has a radius of about 1.3 cm and a blood flow velocity of about 0.5 m/s. An atherosclerosis-stricken bacon epicure (lol) is found to have an effective aortic radius that is 75% of that in a healthy aorta. What is the blood flow velocity through the narrowed section of artery? (Assume that the blood's volumetric flow rate is constant for all adults.)


V1A1 = V2A2 => V2 = (A1/A2)V1 = (pir12/pir22)V1 = (r12/(3/4r12))V1 = (1/(3/4)2)V1 = (16/9)(0.5 m/s)

A: 0.89 m/s

Maybe I've just been studying too long, but I don't understand why there was no conversion between m/s and cm/s?

Thanks!

 

[aldol16]

The actual radius of the aorta never actually enters into the equation because the fact that you know that it's reduced to 75% that of a normal one is enough. We're working with ratios here. Even if you had plugged it in, you could have found that the units actually cancel and that it doesn't matter.