Bernoullis & Pressure Gradient force

[Timtam]

The more I learn about Bernoulli's the less I feel I understand it

The problem statement

If I had a ball (balloon) filled with fluid at pressure P being acted on by two opposing forces F+ and F-

F+ being larger than F- there would be a net force accelerating the ball to the right but the pressure P would remain the same.

Now if I was to examine the ball as a parcel of fluid in a continuum and have a higher pressure (HP+) ~ F+ acting on one side and a lower pressure (HP-)~ F- on the other side.

Then I would also see the whole ball of fluid being accelerated to the right but the pressure inside the ball would also decrease from HP on the left side to LP on the right side
My question.
What action caused by the unbalanced external forces , is causing the internal pressure of the ball to decrease ?

 

[FactChecker]

The more I learn about Bernoulli's the less I feel I understand it

The problem statement

If I had a ball (balloon) filled with fluid at pressure P being acted on by two opposing forces F+ and F-
View attachment 107778
F+ being larger than F- there would be a net force accelerating the ball to the right but the pressure P would remain the same.

Why would the pressure, P, be the same at all points of the ball? I don't believe that.

 

[Timtam]

Why would the pressure, P, be the same at all points of the ball? I don't believe that.

Ah ok, I guess I was thinking I was thinking of external forces acting on a rigid incompressible ball not considering what's happening as the rigid ball acts on the internal fluid.

So even inside such a ball as it accelerates from the external forces - the force applied internally (on the initially stationary fluid) from the right is greater than the force on the left

(Represented by my over-exaggerated diagram of the rigid ball being displaced before the fluid)

So the ball contains the same total internal energy but it has been redistributed into an internal pressure gradient reflecting the external forces acting on it ?

is this correct ?

 

[FactChecker]

That is what I would think. Another comment I have is that I don't see any connection between the internal pressures and Bernoulli. Bernoulli's equation does apply to the external forces onto the surface of the sphere.