# Converting velocity to pressure

In summary, the conversation discusses the use of the simplified Bernoulli equation to convert flow velocity into pressure differential in a blood vessel with a stenosis. The equation is P2-P1 = (V2^2 - V1^2)/2, with the units of (cm/sec)^2. The conversation includes a discussion on converting the units to m/s and then to Pascals, as well as the inclusion of density units. The final step is to convert from Pascals to mmHg, the unit used to measure blood pressure. The conversation concludes with gratitude for the help given.
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

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.

## What is the equation for converting velocity to pressure?

The equation for converting velocity to pressure is P = 1/2 ρv2, where P is pressure, ρ is density, and v is velocity.

## How do I convert velocity to pressure for a gas?

To convert velocity to pressure for a gas, you will need to know the density of the gas. Then, use the equation P = 1/2 ρv2 to calculate the pressure.

## Can velocity and pressure be directly converted without an equation?

No, velocity and pressure cannot be directly converted without an equation. The equation P = 1/2 ρv2 is necessary to accurately convert between the two units.

## What is the unit of measurement for velocity and pressure?

Velocity is typically measured in meters per second (m/s) and pressure is measured in pascals (Pa) or newtons per square meter (N/m2).

## How does converting velocity to pressure relate to Bernoulli's principle?

Converting velocity to pressure is a key component of Bernoulli's principle, which states that as the speed of a fluid (such as air or water) increases, the pressure exerted by that fluid decreases. This principle is important in understanding the flow of fluids and can be applied in many scientific and engineering applications.

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