Problem Statement
A hydraulic lift is required to lift a load of 98.1 kN through a height of 12 m, once in every 100 seconds. The speed of the lift is 600 mm/s. Determine : (a) power required to drive the lift, (b) working period of lift in seconds, and (c) idle period of the lift in seconds.
Given Data & Constants
- Load to be lifted, \(W = 98.1 \, \text{kN} = 98100 \, \text{N}\)
- Height of lift, \(h = 12 \, \text{m}\)
- Total cycle time, \(T = 100 \, \text{s}\)
- Speed of lift, \(v = 600 \, \text{mm/s} = 0.6 \, \text{m/s}\)
Solution
(b) Working Period of the Lift
The working period is the time the lift is actually moving upwards to lift the load.
(c) Idle Period of the Lift
The idle period is the remainder of the total cycle time when the lift is not working (e.g., being lowered, loaded, or waiting).
(a) Power Required to Drive the Lift
The power required is the work done to lift the load, divided by the time it takes to do that work (the working period).
(a) Power required to drive the lift: \( 58.86 \, \text{kW} \)
(b) Working period of the lift: \( 20 \, \text{s} \)
(c) Idle period of the lift: \( 80 \, \text{s} \)
Explanation of the Lift Cycle
This problem analyzes the operational cycle of a lift. The total time for one complete operation (e.g., from starting one lift to starting the next) is 100 seconds.
- Working Period: This is the phase where the lift is actively performing its primary function—moving the load upwards. The power calculation is based on this period because this is when the energy is being expended to lift the weight.
- Idle Period: This phase includes all other parts of the cycle. The lift might be descending (which often requires little power), being loaded or unloaded, or simply waiting for the next cycle to begin.
- Power Required: The power of 58.86 kW represents the rate of energy transfer required *during the lift*. If this power were supplied by a hydraulic accumulator, the accumulator would discharge during the 20-second working period and would be recharged by a smaller pump during the 80-second idle period.
