Timeline for If the difference in pressure is zero between two points of a horizontal constant-radius pipe, why isn't flow rate zero?
Current License: CC BY-SA 4.0
11 events
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| Oct 28, 2021 at 23:15 | history | edited | joseph h | CC BY-SA 4.0 |
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| Oct 17, 2021 at 22:16 | history | edited | joseph h | CC BY-SA 4.0 |
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| Oct 10, 2021 at 23:33 | comment | added | electronpusher | I'm sure you can see the resistance would be defined as $R=\frac{8\mu L}{\pi r^4}$. I feel like this conversation is digressing. My goal was to clarify for anyone who reads that the equation the OP presented ($Q=\Delta P/R$) is indeed a valid relationship that I have seen published in textbooks, and that in this equation $R$ represents not the pipe radius but resistance to flow, whose definition can be readily observed by understanding that $Q=\Delta P/R$ is a simplified manifestation of the Hagen-Poiseuille Equation. | |
| Oct 10, 2021 at 22:49 | comment | added | joseph h | So what would be the appropriate definition and units of R in this case where Q=P/R given Q is the flow rate and P is the pressure? The equation is still incorrect unless there is a dimensionally correct definition of R. | |
| Oct 10, 2021 at 21:19 | comment | added | electronpusher | The Hagen-Poiseuille Equation can be viewed as analogous to Ohm's Law (∆V=IR), which are both special cases of the more general relationship (driving force) = (flow rate) × (resistance). In this context (common in physiology/biology), the HP Equation takes the form ∆P=QR, where R is the resistance to flow, as I previously stated (of course depending on viscosity, pipe length and pipe radius). I assume this abbreviated version of the HP Equation is what OP was presenting when the mentioned Q=∆P/R. It is dimensionally consistent with appropriate definition of R. | |
| Oct 9, 2021 at 21:00 | history | edited | joseph h | CC BY-SA 4.0 |
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| Oct 9, 2021 at 20:00 | comment | added | joseph h | The Hagen-Poiseuillie equation is $$\Delta P=\frac{8\mu LQ}{\pi R^4}$$ where $R$ is the pipe radius and $\mu$ is the dynamic viscosity. The above equation $Q=dp/R$ is still dimensionally incorrect. | |
| Oct 9, 2021 at 14:00 | comment | added | electronpusher | I believe the final "incorrect" equation is a form of the Hagen-Pouseulle Equation, where $R$ is meant to be the de facto resistance (not radius). | |
| Oct 9, 2021 at 8:42 | history | edited | joseph h | CC BY-SA 4.0 |
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| Oct 9, 2021 at 5:49 | history | edited | joseph h | CC BY-SA 4.0 |
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| Oct 9, 2021 at 3:54 | history | answered | joseph h | CC BY-SA 4.0 |