Question

prove that p=pgh, p=pressure,p=density,g= gravity, h=height

Answer 1

Answer:

P=pgh

Explanation:

Pressure=Force/area

Force=mg (m=mass , g=acceleration due to gravity)

Density(p)=mass/volume

mass=density(p)*volume(v)

Pressure= (p*v)*g /A   (volume=area*height)

Pressure=p*A*h*g /A  (cancelling A)

Pressure=p*h*g

Answer 2

Answer:

P = ρhg

Explanation:

Pressure is the perpendicular force per unit area.

⇒ P = $\frac{F(Force)}{A(Area)}$ - (1)

where Force is

⇒ F(Force) = m(mass)×a(acceleration) - (2)

also,

ρ (density)= $\frac{M(Mass)}{V(Volume)}$

⇒ M = ρ×V - (3)

Putting equation (3) in equation (2), we've,

⇒ F = ρ×V×a - (4)

Putting equation (4) in equation (1), we finally get,

⇒ P =ρ×a× $\frac{V}{A}$

⇒ P = ρ × a × A × $\frac{h}{A}$  (since, Volume = Area × Height)

⇒ P = ρ × a × h

putting a = g, where g = acceleration due to gravity we've,

P = ρhg

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