Converting velocity to pressure

[ssavader]

I am trying to work with the simplified Bernoulli equation to determine how to convert a drop in flow velocity across a stenosis (narrowing) into a change in hemodynamic pressure. Radiologists often use Doppler ultrasound to measure flow velocity change in a blood vessel with a stenosis- but I would like to make a conversion to a pressure differential.

Equation: P2-P1 = (V2^2 - V1^2)/2 (assuming frictionless system, blood density ~ 1.0 gm/cm^3, and no change in height)

P2-P1 = [(126 cm/sec)^2 - (90 cm/sec)^2]/2 (^ symbol= raise to power of)

Can someone show me how to convert the units of (cm/sec)^2 to mmHg? Or show me where my error in thinking is?

Thank you kindly,
Scott

 

[boneh3ad]

Convert to m/s and then carry out the computation and your answer will come out in Pascals. Then convert Pascals to mmHg using whatever Google says the conversion factor is.

 

[ssavader]

Help me out please: Is 126 cm/sec x 126 cm/sec = 15826 cm/sec or cm squared/sec squared? I know this is basic but its been a few decades since my last physics class!

Also, I am unsure if you are implying that m/sec x m/sec can be converted to pascals. I can't find a calculator to do this conversion?

 

[cjl]

If you do everything in standard SI, your answer will come out in Pa. You're forgetting to include the units of density (which will need to be in kg/m³, so you should use 1000 rather than 1 for that). As for the units of V²? It should be m²/s². So, for your specific numbers, it should be:

P2-P1 = [(1.26 m/s)² - (0.90 m/s)²]*1000 kg/m³/2

If you work through the units, you will find that it does in fact come to be pressure (specifically pascals) when done this way.

(Specifically, the units are m²/s²*kg/m³, which can be rearranged into (kg*m/s²)/m², which becomes N/m², which is a pascal)

 

[ssavader]

cjl, thank you so much. Now it all makes sense.Ii really appreciate the time you invested in my question. Once I get the answer in Pascals, I can then use a converter to change to Torr, or "mmHg", which is how blood pressure is measured.