Why does liquid rise vertically in an accelerating tank?

[hotjohn]

Homework Statement

why the vertical rise of the surface is given by the formula as shown in the notes ? shouldn't it = Δs =
(g +az ) Δx / ax ?

Homework Equations

The Attempt at a Solution

 

[haruspex]

(g +az ) Δx / ax ?

No, it can't be that. Consider a_x=0.
How did you arrive at that?

 

[gleem]

Another issue is that your expression is dimensionally inconsistent.

 

[haruspex]

Another issue is that your expression is dimensionally inconsistent.

No, I don't think so. az is supposed to be a_z, an acceleration, etc.