A small hydraulic car jack contains a sealed reservoir of hydraulic oil that is…
MATHEMATICS · Multi-part · A Level · Mathematics · Quantities and units in mechanics · Quantities and units in mechanics
Problem
A small hydraulic car jack contains a sealed reservoir of hydraulic oil that is commonly modeled as an incompressible, non-viscous (ideal) fluid. The jack operates by forcing additional oil from a narrow pump cylinder into a wide lifting cylinder.
Relevant information:
• Density of the hydraulic oil at room temperature: ρ=860kgm−3
• Cross-sectional area of the lifting cylinder: A=0.012m2
• During one pump stroke, the plunger pushes 65cm3 of oil into the lifting cylinder.
Answer the following, showing all reasoning and including units with numerical answers.
(a) Calculate the mass of oil transferred into the lifting cylinder during a single pump stroke.
(b) Assuming the oil is incompressible, determine the vertical displacement of the lifting piston produced by a single pump stroke.
(c) In reality the oil has a small but non-zero compressibility. Explain qualitatively how this compressibility would change the actual vertical displacement calculated in part (b). No numerical answer is required.