If you have a fluid with with pressure field p what is the physical significance of the the volume integral of the pressure int_V dV

Holzkeulecz

Holzkeulecz

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2022-08-16

If you have a fluid with with pressure field p what is the physical significance of the the volume integral of the pressure V p d V ?

Answer & Explanation

Gillian Howell

Gillian Howell

Beginner2022-08-17Added 17 answers

The equation for work W that you have written comes from the relationship we learned in freshman physics, W = F d x . If A the area over which the force acts, then the pressure is p = F / A, and the differential change in volume is dV=Adx. So,
W = F d x = ( F A ) A d x = p d V
In terms of interpretation of the integral as an average, we can define the average pressure as p ¯ = W / Δ V. So, the average pressure during the volume change is given by:
p ¯ = p d V Δ V

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