The diameter of the large cylinder of the hydraulic machine is 50 cm, and the diameter of the small
| May 8, 2021 | education
The diameter of the large cylinder of the hydraulic machine is 50 cm, and the diameter of the small one is 4 cm. What is the advantage in power of this machine?
Let’s translate all the values from given to the SI system:
Sb = 50 cm2 = 0.005 m2
Sm = 4 cm2 = 0.0004 m2
An external force acting on the small piston creates pressure:
Pm = Fm / Sm
According to Pascal’s law, it is transmitted by the liquid in all directions without change. Therefore, from the side of the liquid, a force acts on the second piston:
Fb = Pm * Sb
Pm = Fb / Sb
Equating the pressure, we get:
Fm / Sm = Fb / Sb
From this expression, we find the gain in strength by dividing Fb by Fm:
Fb / Fm = Sb / Sm = 0.005 / 0.0004 = 12.5
Answer: Strength wins 12.5 times.
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