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

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Homework Help Overview

The discussion revolves around the appearance of the factor of 1/2 in dynamic pressure calculations, particularly in the context of fluid dynamics and calculus. Participants are exploring the mathematical foundations and implications of this factor within the framework of pressure equations.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the origin of the factor of 1/2 in dynamic pressure equations and discussing the relevance of calculus concepts such as derivatives and integrals. There is an exploration of different methods for integrating equations and the implications of including constants of integration.

Discussion Status

The discussion is active, with participants offering insights into calculus techniques and questioning the appropriateness of various methods. Some guidance has been provided regarding the necessity of constants of integration, indicating a productive direction in understanding the mathematical framework.

Contextual Notes

Participants are navigating the complexities of applying calculus to physics problems, with specific reference to the need for initial conditions in integration. There is an acknowledgment of the differences between mathematical approaches in physics and other fields.

malindenmoyer
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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!
 
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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?
 
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?
 
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.
 
Last edited:

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