Question

prove that p = dgh in mathematical way

Answer 1

Let's finding the force at the bottom of the container.

Let,
mass of the container = m
Volume of the container = V
density of the container = d
Area of the bottom = A
Height of the container = h

F = mg

Now,

Pressure = Force / Area
P = F/A
P = m g / A

dividing h on denometer and numerator,

P = mgh / Ah
P = mgh / V ( V = Ah )
P = d g h ( d = m/V)

Answer 2

From, what is pressure: Pressure = Force/Area

From, what is Force: Force = mass xacceleration = m x g (acceleration in gravity)

So: Pressure = F/A = mg/A

From What is Density: Density = Mass/Volume ; Mass= Density x Volume

We now have Pressure = (density x volume x acceleration)/area.