I'm reading a textbook, chapter entitled "Fluid Mechanics".
This section is entirely devoted to fluid statics.
Assuming an element of fluid in equilibrium,
Consider a thin element of fluid with thickness dy. and density & gravity constant.
let p be pressure upward on the bottom of the surface, then total pressure on bottom of the surface is pA (pressure * Area).
Then, the pressure on the top surface is p+dp, and the total pressure on top of the surface is (p + dp) * A.
I have been looking into the web, but I am quite not sure what dp is meant when finding the top surface pressure.
My only guess is that dP is the difference of pressure due to change in altitude.
If my guess is right, is it notable to include such small change in altitude (considering the material has small dy).
Best Answer
Take for example, a submarine. The pressure against the walls of the submarine increments as this goes deeper.
For another example, take an airplane, as it goes higher the pressure against the walls decrease.
So yes, the pressure changes as the altitude (or depth) changes (if you are submerged on a fluid in a gravitational field). Even small amounts of change in altitude (or depth) will make a change in the pressure of the fluid against a real or imaginary wall.
dP is not a physicall quantity but a mathematical expression of something that changes an infinitesimal. In this particular case, dP is a small change (infinitesimal) in the pressure. And pressure is a dependant variable of 'w' (the weight of the fluid element), 'y' (the altitude or depth), and 'A' (the area of an horizontal plane).
Just another comment; take a look at the force diagram, you will see that all horizontal forces are counteracting forces, but the upper force is slightly smaller than the force pushing from below (The difference is F2-F1=dF, a very small amount of change in the force). As the system is in equilibrium, the vector sum of all forces must be zero. So the small force that you need to add is exactly A * dP.