Deriving Bernoulli's Equation Using Euler's Law of Motion

[yjl]

Hi all,

I have attached an image of a page out of the book I am using for context. The blue arrow in Figure 12-3 describes the motion of the particle. I figured the net force would need to be in the same direction, but apparently the net force opposes the motion. So, in Figure 12-3 the pressure at the top of the particle is higher than the pressure at the bottom (P + dP versus P). I am wondering why this is the case.

 

[BvU]

Hello yjl, !

Where does it say $dp > 0$ ?

 

[yjl]

Hello yjl, !

Where does it say $dp > 0$ ?

Thank you :-)

Nowhere explicitly. But surely there must be a good reason for assuming the top part of the particle to have a greater pressure.

Is it not true that the net force in Figure 12-3 would make the particle accelerate towards the x-axis?

 

[BvU]

What net force ?

 

[yjl]

What net force ?

The net force due to the pressure difference when dP > 0.

 

[Chestermiller]

The expression $(P+dP)$ does not mean that dP is positive. It only means that pressure changes from one end of the free body to the other. But dP can also be negative.

 

[yjl]

The expression $(P+dP)$ does not mean that dP is positive. It only means that pressure changes from one end of the free body to the other. But dP can also be negative.

Ah.
Well, thank you :-).
I see now that that was what BvU was hinting at.