Pressure diagram labelled incorrectly?

[needingtoknow]

Homework Statement

At the point specified in the diagram, isn't pressure coming from all directions, namely gauge pressure. So wouldn't some of the gauge pressure be used to counteract the effects from the atmospheric pressure. Doesn't this mean the equation Ptotal = Patsurface + Pgauge is wrong?

 

[Doc Al]

You are correct that at any point, the pressure is the same in all directions. But I believe you are misinterpreting the diagram. What they are calling P_gauge is just that portion of the pressure due to the weight of the fluid itself. So the equation holds.

 

[needingtoknow]

So but if it's only due to weight then by that saying wouldn't water at the bottom of the container have the greatest Pgauge because it is under the most fluid and the weight of a fluid is F = Pvg right so more volume = larger weight?

 

[Doc Al]

So but if it's only due to weight then by that saying wouldn't water at the bottom of the container have the greatest Pgauge because it is under the most fluid and the weight of a fluid is F = Pvg right so more volume = larger weight?

It's the pressure of the fluid, not the volume, that counts. But yes, at the bottom of the container the pressure due to the fluid is greatest. The pressure at any point below the surface is given by ρgh, regardless of volume.

 

[needingtoknow]

All right great then that makes sense! Thank you very much!

 

[Chestermiller]

Gage pressure is defined as total pressure minus ambient atmospheric air pressure.

Chet