I've seen the standard derivation of the expression for liquid pressure
P = dgh where,
d = density of the liquid;
g = acceleration due to gravity;
h = height of liquid column
in many text books has been done by using a specific example of a cylindrical vessel.
In such a case, the geometry of the cylinder allows us to write Volume = Base Area x Height
So, the above result is trivial.
But in many cases where such a direct link between volume of the vessel and its area and the other dimension doesn't exist, like for a cone, its volume is V = [itex]\pi[/itex] r[itex]^{2}[/itex] x h x (1/3) , we get that extra constant 1/3 and liquid pressure is no more dgh I think.
How then can a specific example be used to speak for the general?
I've seen this kind of easy generalization in many other parts of physics such as torque on a plane coil in a magnetic field([itex]\tau[/itex]=BINAcosx), where the actual derivation has been performed using a simple rectangular coil and said that the result is true for any shape of plane coil with the same area.
I understand that this has been done for simplifying things but is there some law in physics that I do not know of that allows for such bold assumptions to be made even just by watching patterns?
P = dgh where,
d = density of the liquid;
g = acceleration due to gravity;
h = height of liquid column
in many text books has been done by using a specific example of a cylindrical vessel.
In such a case, the geometry of the cylinder allows us to write Volume = Base Area x Height
So, the above result is trivial.
But in many cases where such a direct link between volume of the vessel and its area and the other dimension doesn't exist, like for a cone, its volume is V = [itex]\pi[/itex] r[itex]^{2}[/itex] x h x (1/3) , we get that extra constant 1/3 and liquid pressure is no more dgh I think.
How then can a specific example be used to speak for the general?
I've seen this kind of easy generalization in many other parts of physics such as torque on a plane coil in a magnetic field([itex]\tau[/itex]=BINAcosx), where the actual derivation has been performed using a simple rectangular coil and said that the result is true for any shape of plane coil with the same area.
I understand that this has been done for simplifying things but is there some law in physics that I do not know of that allows for such bold assumptions to be made even just by watching patterns?