I have a question about fluids ok...

I've been told that
Pressure = (density of fluid) (gravity) (height)

ok that's great in all but I don't see how it works...

Pressure = (Force perinduclar to area force is acting on)/(Area force is acting on)

ok this great and all but leads me to several questions ok the force perpendicular to area it acts on is gravity

1.) WHY NOT THE BOUYANCY FORCE?

assuming that the force is gravity then

Force of gravity = (mass)(gravity)

for objects near surface of planet

so plug into our pressure equation

Pressure = ( (mass of object)(gravity) )/(Area the force is acting on)

my book then goes on to say

density of an object = (mass of object)/(volume of object)
ok rearaning for mass

(density of an object)(volume of object) = objects mass

plug and chug into our Pressure equation...

Pressure = ( (density of an object)(volume of object)(gravity) )/(Area the force of gravity is acting on)

Volume of uniform solid = (area of bottom)(height of object)

pluging into our Pressure equation

Pressure = ( (density of mass)(gravity)(area force of gravity is acting on)(height of object) )/(area force of gravity is acting on)

area cancels out

Pressure = (density of mass)(gravity)(height of ojbect)

ok I followed this derivation step by step but it's wrong WHY???

my book gives me this equation

Pressure = (density of fluid object is in)(gravity) (how far submerged the object is in the fluid, the depth i believe the term is like how far under the surface the object is)

this does not match my equation

2.) The density of the object changed to the denisty of the fluid it's in

3.) The height of the object changed to how far under the surface the object is

4.) How do I use this equation when it's not a uniformed block? I couldn't right? Like if it were a person...

THANK YOU
Please I need to understand this... I don't see how such a simple derivation just changes variables around and such...

I HAVE FIGURED IT OUT

I understand your confusion, and I'll try my best to help you understand the derivation and the changes that occur in the equation.

Let's start with the derivation of the equation:

1. The pressure is defined as the force perpendicular to the area divided by the area the force is acting on. In fluid mechanics, this force is usually gravity, so the equation becomes Pressure = (Force of gravity)/(Area).

2. The force of gravity acting on an object near the surface of the Earth is given by the equation Force of gravity = (mass)(gravity).

3. Next, we can rearrange the equation for density, which is defined as mass divided by volume, to get mass = (density)(volume).

4. Substituting the expression for mass into the equation for the force of gravity, we get Force of gravity = (density)(volume)(gravity).

5. Finally, substituting the expression for the force of gravity into the equation for pressure, we get Pressure = (density)(volume)(gravity)/(Area).

Now, let's address the changes that occur in the equation:

1. The density in the equation changes from the density of the object to the density of the fluid it's in. This change reflects the fact that pressure in a fluid is caused by the weight of the fluid above an object, so the density of the fluid becomes relevant.

2. The height in the equation changes to the depth, which is the distance the object is submerged under the surface of the fluid. This change is necessary because, in fluids, the pressure increases with depth due to the weight of the fluid above.

3. For objects that aren't uniform blocks, the equation may not directly apply. The equation assumes a constant density and uniform height. However, you can still use the equation by considering an infinitesimally small volume element within the object and summing up the pressure contributions from all these elements. This process is known as integration and is commonly done in more complex fluid mechanics problems.

In summary, the equation you derived is valid for objects near the surface of the Earth with a constant density and uniform height. The changes in variables reflect the specific considerations needed for fluid mechanics, such as the density of the fluid and the depth of the object. When dealing with non-uniform objects, you may need to use integration to account for variations in density or shape.