Why is the pressure gradient equal to -2ρg instead of ρg in physics?

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Homework Help Overview

The discussion revolves around understanding why the pressure gradient is expressed as -2ρg instead of ρg in a physics context, specifically related to fluid mechanics and pressure calculations.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants are examining the formulation of the pressure gradient and questioning the signs and terms used in the equations. There are references to free body diagrams and force balance as methods to clarify the situation.

Discussion Status

The discussion is ongoing, with participants providing hints and prompting each other to consider free body diagrams and force balance equations. There is an emphasis on guiding the original poster to explore their understanding rather than providing direct answers.

Contextual Notes

Participants note the importance of correctly identifying pressure terms and their signs in the equations, indicating potential misunderstandings in the original poster's approach. There is a suggestion that the original poster may need to revisit foundational concepts related to free body diagrams.

hotjohn
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Homework Statement


why the pressure gradient is = - 2ρg ? why not ρg ?

Homework Equations

The Attempt at a Solution

 

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Have you drawn a free body diagram and performed a force balance?
 
Chestermiller said:
Have you drawn a free body diagram and performed a force balance?
IMO , it should be -P1 - (P1 +ρg ) ... why the ans is = - 2ρg ?
 
hotjohn said:
IMO , it should be -P1 - (P1 +hρg ) ... why the ans is = - 2ρg ?
I don't see a right hand side to this equation, and one of your two pressure terms is of the wrong sign. Next time you respond, please respond with a complete force balance equation, based on a proper free body diagram, and including a mass times acceleration term.
 
Chestermiller said:
I don't see a right hand side to this equation, and one of your two pressure terms is of the wrong sign. Next time you respond, please respond with a complete force balance equation, based on a proper free body diagram, and including a mass times acceleration term.
so , what is the correct one ?
 
hotjohn said:
so , what is the correct one ?
No, no. That's not how we work here. We can only help you to help yourself by giving you hints and asking you leading questions. So my first hint for you was to draw a free body diagram showing the forces acting on the water (do you feel that you have progressed beyond the need to use free body diagrams any more?), and my second hint was to write a force balance equation based on the free body diagram. So, the ball is in your court now.
 

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