Why Does the Factor of 1/2 Appear in Dynamic Pressure Calculations?

[malindenmoyer]

Please refer to this website: http://www.grc.nasa.gov/WWW/K-12/airplane/dynpress.html"

In the "Simplify" step, where does the factor of 1/2 come from? I must be missing something simple...

Thanks for the help!

 

[Gyro]

What is the derivative of d(u^2)/dx? How does that differ from the second term in the 'algebra step'?
This relates to the concept of anti-derivative and integration. Have you studied that yet?

 

[malindenmoyer]

I get it now--I'm not used to a 'physicist's' calculus. Would it be proper to simply multiply each side of the original equation by 'dx' and integrate each side with the respective variables? This leaves (r*u^2)/2=-p -> (r*u^2)/2+p=0

Is there a reason why this method is not preferable?

 

[Gyro]

Maybe to re-inforce that a constant of integration is required to specify an initial condition? The method you used does not account for the 'constant' as you have the static + dynamic pressure equal to zero instead of the 'total pressure".

Remember, indefinite integrals require a constant of integration.