Model:
A vertical thin Tube_a of water (or any fluid) linked (at the bottom only) to a larger vertical Tube_b of water
One equation for hydraulic fluids for the above model is:
(For visual of 1st model below see "Fluid Pressure Calculations" at :
P_a = density * g * h + P_b
(Where P_a & P_b are the pressures applied downward at the surface of thin Tube_a & wider Tube_b)
Let say A_a (Area of Tube_a) = 1 and A_b = 3 and F_a = 2 and F_b = 3
P_a = F_a / A_a = 2 /1 = 2
P_b = 3 / 3 = 1
Thus P_a = density * g * h + P_b
2 = density * g * h + 1************** therefore h = 1 / density * g (PARTAA)
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But then another equation for Hydraulic Press (to lift up a car) says Work_a = Work_b therefore F_a * D_a = F_b * D_b
(For visual of 2nd model below see:
(F is the force and D is the distance of vertical travel ....similar to h in the previous equation) (in fact I believe h = D_b - D_a)
Thus F_a * D_a = F_b * D_b
(replacing Force with P * A in the previous equation)
(2 * 1) * D_a = (1 * 3) * D_b
****************** Therefore D_a = 3/2 * D_b (PARTBB)Since h in the previous equation is a vertical distance that is in some way related to D_a - D_b but then PARTAA does not match with PARTBB????
since h is related to the density of the fluid (h = 1/ density * g)?
So where did I make a mistake??