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Last modified: January 26, 2018
Pascal's Principle
------------------
Pressure is transmitted undiminished in an enclosed non-compressible fluid.
Consider a bottle:
| |
|--| F1 = A1P1
| |
/ \
| |
| |||| |
| vvvv |
------ F2 = A2P2
P2 = P1 + hρg
Hydraulic Jack:
P1 = A1F1 P2 = A2F2
| | | |
|--| ^ |..........| P2
d1 | | h | | d2
P1 |..| v |----------|
| |_________| |
| |
-----------------------
P1 = P2 + hρg
F1/A1 = F2/A2 + hρg
conservation of energy: F1d1 = F2d2
d1 = (F2/F1)d2
= (A2P2/A1P1)d2
= (A2P2/A1(P2 + hρg))d2
= {A2(F2/A2)d2}/{A1((F2/A2) + hρg)}
= F2d2/{A1((F2/A2) + hρg)}
If we negelect the weight of the fluid (ρ = 0) so that the pressure
throughout the enclosed volume will be the same then:
d1 = F2d2/{A1(F2/A2)}
= d2/{A1(1/A2)}
= d2(A2/A1)