Question

What is the meaning of the "-" signs in this equation of the vertical pressure variation in a static fluid?

-(∂P/∂z)-ρ*g=0

Answer 1

The -ve sign is there , bcoz you have taken the +ve z direction opposite to the direction of acceleration due to gravity, i.e. g

Answer 2

we can rewrite such equation, as below:
\[\Large \frac{{\partial P}}{{\partial z}} = - \rho g\]
now, at the right side we have a product of two positive quantities, which gives a positive quantity, as result, so that ODE, tells us that the pressure changes are opposite to the changes of z-coordinate

Answer 3

more precisely we have:
\[\Large \frac{{\partial P}}{{\partial z}} = - \rho g < 0\]

Answer 4

I agree with the posts above ; I will simply have a different viewpoint.

I will talk about the negative sign before (dP/dz) :
It means that pressure increases in the direction of the other applied forces.

This equation can be written independently of the coordinate system by:

\(\color {red}-\vec {grad} \;P+\rho \vec g=\vec 0\) that is: \(\vec {grad} \;P=\rho \vec g\)

Hence P increases in the direction of vector \(\vec g\)

Answer 5

Thank you all for your answers! I think now I understand it much better