prove that pressure at depth h from the free surface of a liquid (P) in a container is P=Po +hpg, where Po is the atmosphere pressure
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Consider a liquid of the density p contained in a vessel in equilibrium of rest . Let C and D be two most points the liquid at a vertical distance h. Imagine a consider of liquid with axis CD, cross-sectional area A and Length h, such that the points C and D lie on the flat faces of the cylinder see in image
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M= VOLUME X DENSITY
M= Ah x p
I) force F1= P1A , acting vertical downwards on the top face of the cylinder ,
2) force F2=P2A , acting vertical upwards on the lower face of the cylinder ,
3) Weight , Mg= A x h x p x g of the liquid cylinder acting vertically downwards .
F1 + Mg- F2 = 0
P1A+Ahpg - P2A=0
P2-P1= h x p x g
This shows that the pressure is same at all points inside the liquid lying at the same depth in a horizontal plane .
h= 0
P2 - P1 = 0
P-Po= h x p x g
P = Po + h x p x g
-----------------------------------------------------------#Aion-13 -------------------------------
.
M= VOLUME X DENSITY
M= Ah x p
I) force F1= P1A , acting vertical downwards on the top face of the cylinder ,
2) force F2=P2A , acting vertical upwards on the lower face of the cylinder ,
3) Weight , Mg= A x h x p x g of the liquid cylinder acting vertically downwards .
F1 + Mg- F2 = 0
P1A+Ahpg - P2A=0
P2-P1= h x p x g
This shows that the pressure is same at all points inside the liquid lying at the same depth in a horizontal plane .
h= 0
P2 - P1 = 0
P-Po= h x p x g
P = Po + h x p x g
-----------------------------------------------------------#Aion-13 -------------------------------
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