Fluid Mechanics?? A simple hydraulic jack can be built that docs not need a pump

Question

Fluid Mechanics??

A simple hydraulic jack can be built that docs not need a pump. As shown in the sketch, the jack consists of a large - diameter cylinder/piston on the right side that lifts the heavy weight, W, and nothing but a tall tube on the left side into which oil can be poured. The idea is to use the hydrostatic pressure force ("head") of the oil in the tube on the left side to lift the wight on the right side. Ignoring friction in the piston/cylinder, ignoring the weight of the piston compared to W. and assuming no oil leakage, generate an expression for the oil heigh*, h required to just start lifting the weight Your expression should be h as a function of the other variables as needed To sum lifting a car that has a mass of 900 kg. calculate h in m if pd = 653 kg/m3. Df = 0.725 m. and Dt = 1.04 cm.

Explanation / Answer

equate the pressure at the level where load is applied

since pressure of a liquid is same at the same height

assume datum as level of loading

Area on which load is applied=pi*D2^2/4

pressure at that level=Poil*g*h

pressure due to weight W*g=W*g/area

W*g/(pi*D2^2/4)=Poil*g*h

so, h=W/Poil/(pi*D^2/4)

now coming to part 2

h=900/653/(pi*.725^2/4)

h=3.338 m

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