An automotive repair shop uses a single-piston hydraulic lift to raise cars for maintenance. The lift piston is level with the shop floor, while the hydraulic fluid surface in the reservoir is located 0.40m below the piston’s underside. The hydraulic fluid has density 850kgm−3, and the maximum gauge pressure that the pump is rated to deliver safely is 1.2×106Pa. When designing the lift, the engineer chooses a safety factor of 1.5; that is, the maximum operating gauge pressure must not exceed two-thirds of the pump’s safe limit.
A typical automobile to be lifted has mass 1.4×103kg.
(a) Calculate the weight of the automobile in newtons.
(b) Determine the minimum gauge pressure that must act on the underside of the piston in order to raise the car at constant speed. Neglect the piston’s own mass.
(c) Because the fluid surface is lower than the piston, hydrostatic effects contribute additional pressure at the pump outlet. Compute the hydrostatic gauge pressure due solely to the 0.40m fluid column.
(d) Using your results from parts (b) and (c), find the minimum piston cross-sectional area that satisfies both the weight-support requirement and the safety-factor operating limit. Then state the corresponding minimum piston diameter.
(e) Explain qualitatively how changing the piston diameter would affect the hydraulic pressure required and discuss one practical limitation of simply making the piston arbitrarily large.