Converting velocity to pressure

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Discussion Overview

The discussion revolves around the application of the Bernoulli equation to convert changes in flow velocity across a stenosis into corresponding changes in hemodynamic pressure. The context includes theoretical and practical aspects of fluid dynamics as applied to medical imaging techniques like Doppler ultrasound.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • Scott seeks assistance in converting a drop in flow velocity into a pressure differential using the Bernoulli equation, specifically asking for help with unit conversion from (cm/sec)2 to mmHg.
  • One participant suggests converting the velocity to m/s and performing the calculation to obtain the result in Pascals, followed by a conversion to mmHg.
  • Another participant questions the multiplication of velocities and seeks clarification on unit conversions, expressing uncertainty about the calculations involved.
  • A further reply emphasizes the importance of using standard SI units, noting that density must be expressed in kg/m3 and clarifying the units involved in the calculations leading to pressure in Pascals.
  • Scott expresses gratitude for the clarification and notes the intention to convert the final result from Pascals to Torr or mmHg.

Areas of Agreement / Disagreement

Participants generally agree on the approach of using the Bernoulli equation and the necessity of unit conversions, but there are varying levels of understanding regarding the calculations and unit transformations involved. The discussion does not reach a consensus on the specifics of the conversion process.

Contextual Notes

Some participants highlight the need for careful attention to unit conversions and the importance of using consistent units throughout the calculations. There is an acknowledgment of potential confusion regarding the relationship between different units of measurement.

Who May Find This Useful

This discussion may be useful for individuals interested in fluid dynamics, medical imaging techniques, or those seeking to understand the application of the Bernoulli equation in practical scenarios.

ssavader
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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
 
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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.
 
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?
 
Last edited:
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)
 
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.
 

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