I Pressure in Forces on Submerged Surfaces

Why does the pressure we take into account is the gage pressure and not the absolute pressure?

Reading Fundamentals of Momentum Heat and Mass transfer by Welty in chapter 2 it says "the magnitude of the force on the element dA is PgdA ,where Pg is the gage pressure"

my question is why the gage pressure ? it is supposed that the total pressure acting on that element of area dA is the absolute pressure (Patm+Pgage) why we dont take into account Patm?
Think of a thin wall such as a balloon. What keeps the balloon wall from exploding, or collapsing. The force inside pushing out must balance the force outside pushing in. That happens when the pressures inside and outside are equal. In other words, zero gauge pressure.

Now let the balloon float up into the sky. The absolute pressure outside is less. The balloon expands but does not burst. Even up in the sky, the gauge pressure is zero.

Gauge pressure is referenced to ambient air pressure. Zero gauge means ambient. In the balloon example, it is the outside pressure, both on the ground and in the sky.

It is no different for a pipe wall.


Science Advisor
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and not the absolute pressure?
This is not a general principle. It all depends on the situation; when the pressure difference between an experiment and the atmosphere then gauge is relevant. If you are studying how an enclosed gas will behave then it is absolute pressure that counts.

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