please solve question with full working steps and include assumption in beginnin
ID: 1860301 • Letter: P
Question
please solve question with full working steps and include assumption in beginning.
The hydraulic jack shown below consists of a master cylinder with a diameter of 60mm and a lifting (or slave) cylinder with a diameter of 150mm. The two cylinders are connected by a flexible high pressure hose with a diameter of 10mm.The density of the hydraulic fluid that fills the jack is 15,000kg/m3.
The jack is being used to lift a 5 tonne mass through a vertical distance of 50mm. Initially the hydraulic fluid heights are hA=150mm and hB=400mm.
What is initial force that is required to be applied at location B to lift the weight off the ground?
Develop and expression for the force at B that varies with the lift height at location A Hint: From the conservation of mass and the fact that the hydraulic fluid is incompressible, the volume of fluid displaced at locations A and B must be the same.
What is percentage increase in the force that is required to be applied at location B when the mass is 50mm off the ground compared to the initial force?
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The hydraulic jack shown below consists of a master cylinder with a diameter of 60mm and a lifting (or slave) cylinder with a diameter of 150mm. The two cylinders are connected by a flexible high pressure hose with a diameter of 10mm.The density of the hydraulic fluid that fills the jack is 15,000kg/m3. The jack is being used to lift a 5 tonne mass through a vertical distance of 50mm. Initially the hydraulic fluid heights are hA=150mm and hB=400mm. What is initial force that is required to be applied at location B to lift the weight off the ground? Develop and expression for the force at B that varies with the lift height at location A Hint: From the conservation of mass and the fact that the hydraulic fluid is incompressible, the volume of fluid displaced at locations A and B must be the same. What is percentage increase in the force that is required to be applied at location B when the mass is 50mm off the ground compared to the initial force?Explanation / Answer
the pressure on both sides will be the same and as the pressure is force / area
thus as area at B is smaller than that at B thus the force required at B will be lesser than that requred at A
work done in both the vessels will be same
Force at A x displacement at A = force at B x displacement at B
weight at A = 5000 x 9.8 = 49000N
lifted thru = 50mm = 0.05m
work = force x displacement = 49000 x 0.05 = 2450 Nm
so at B
work = 2450 Nm
volume of liquid that flows from B to A = area of cross section of A x height
= 3.14 x .15^2/4 x .05 = 0.00088 m^3
volume at B = area x height = 3.14 x 0.06^2/4 x h
as both volumes are equal
thus height moves by B
0.00282 x hb = 0.00088
hb = 0.31123 m
so
work done at B = force at B x height
2450 = Fb x .31123
Fb = 7871.83 N
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