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

[hotjohn]

Homework Statement

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

Homework Equations

The Attempt at a Solution

 

[Chestermiller]

Have you drawn a free body diagram and performed a force balance?

 

[hotjohn]

Have you drawn a free body diagram and performed a force balance?

IMO , it should be -P1 - (P1 +ρg ) ... why the ans is = - 2ρg ?

 

[Chestermiller]

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.

 

[hotjohn]

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 ?

 

[Chestermiller]

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.