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newSchoolWorks.com › VoTechWorks › Building & Construction › Elevator Mechanic (pre-apprentice) › Hydraulic Elevator Systems › Lesson 1
BLD-ELEV10-02 · Lesson 1 · 10 clock hours · theory

Fluid Power Fundamentals and Pascal's Law

Objective. Students will explain Pascal's Law and calculate pressure, force, and area relationships in hydraulic circuits using trade-relevant examples.

⚠ Pending professional review

This lesson, its worked examples and its practice questions has not yet been verified by a licensed professional engineer or master tradesperson or by a certification or approval body. It is a study draft and may contain errors. Do not use it as instructions for work on a job site or on live equipment. Always follow your instructor, your supervising professional, and current official references and regulations.

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What Is Fluid Power?

Hydraulic elevator systems move the car by pushing fluid — almost always a petroleum-based or biodegradable hydraulic oil — through a sealed circuit under pressure. Understanding how that pressure is created, transmitted, and controlled is the foundation of every hydraulic elevator task you will perform as an apprentice and throughout your career.

Pascal's Law

Blaise Pascal, a seventeenth-century French mathematician, established the principle that governs every hydraulic system: pressure applied to a confined fluid is transmitted equally and undiminished in all directions throughout the fluid and acts with equal force on equal areas.

In plain trade language: squeeze oil in one place and the same squeeze shows up everywhere in the circuit at the same time. This is why a relatively small pump can lift a fully loaded elevator car weighing several thousand pounds — the pump builds pressure throughout the oil, and that pressure pushes on the full cross-sectional area of the jack cylinder.

Key Relationships: Pressure, Force, and Area

Three quantities are linked by a simple formula you will use constantly:

P = F ÷ A

Rearrange the formula to solve for any unknown:

To find the area of a circular cylinder bore, use:

A = π × r² (where r = radius = bore diameter ÷ 2, and π ≈ 3.1416)

Flow Rate and Car Speed

Pressure determines whether the car can lift the load. Flow rate — measured in gallons per minute (GPM) — determines how fast the car moves. More GPM from the pump means faster upward travel. The control valve regulates GPM during leveling and stopping to give passengers a smooth ride. Pressure and flow rate work together: you need adequate pressure to overcome the load, and the right flow rate to control speed.

How a Hydraulic Elevator Works

Up Travel

The electric motor drives the pump, which draws oil from the reservoir (tank) and forces it through the control valve into the bottom of the jack cylinder. As oil enters, it pushes the plunger (piston rod) upward, raising the car. Pressure must be high enough to support the total load: car weight plus rated passenger or freight capacity plus the weight of the plunger itself.

Down Travel

The motor stops. The control valve opens a metered path back to the tank. Gravity and the weight of the car push the plunger down, forcing oil back through the valve to the reservoir. The valve controls the rate of descent so the car lowers smoothly and levels accurately at each floor.

In-Ground vs. Holeless Hydraulic Elevators

In-ground (conventional) hydraulic elevators have the jack cylinder buried in a casing below the pit floor. The plunger rises directly from the ground, giving a clean, single-stage lift. Concern about underground oil leaks led to the development of double-bottom cylinders and PVC liners required by modern codes.

Holeless hydraulic elevators eliminate the in-ground cylinder entirely. Two common configurations exist:

Both designs keep all hydraulic components above the pit floor, removing the underground leak risk.

Safety Considerations

Lockout/Tagout (LOTO): Before working on any hydraulic component, de-energize the pump motor at the disconnect, verify zero energy, and apply your personal lock and tag per your employer's written LOTO program and OSHA requirements. Hydraulic systems store energy under pressure even after the motor stops — always verify pressure is relieved before opening any fitting or line.

PPE: Wear safety glasses or a face shield when working near hydraulic lines. A pinhole leak in a pressurized line can inject fluid through skin — this is a medical emergency. Wear chemical-resistant gloves when handling hydraulic oil.

Pit Safety: The elevator pit must be entered only when the car is secured and cannot move. Use pit stop switches and follow your employer's confined-space and pit-entry procedures.

Spill Control: Hydraulic oil is a slip and environmental hazard. Have absorbent material available and dispose of used oil according to local regulations.

Connecting Theory to the Trade

When you troubleshoot a hydraulic elevator that will not lift its rated load, Pascal's Law points you directly to the variables: Is the pump building adequate pressure? Is the relief valve set correctly and not bypassing oil? Is the cylinder bore the right size for the design pressure? Every diagnostic step traces back to P = F ÷ A and the fundamentals you learn in this lesson.

Key terms8

Pascal's LawThe principle that pressure applied to a confined, incompressible fluid is transmitted equally and undiminished in all directions throughout the fluid.
Pressure (PSI)Force per unit area, expressed in pounds per square inch; the driving quantity that determines whether a hydraulic jack can lift a given load.
Flow Rate (GPM)The volume of hydraulic fluid moving through the system per minute, measured in gallons per minute; governs the speed of elevator car travel.
Jack (Hydraulic Cylinder)The assembly of cylinder and plunger (or piston and rod) that converts hydraulic pressure into the mechanical force that raises the elevator car.
PlungerThe solid, round steel rod that extends out of a single-acting hydraulic cylinder; its upward movement lifts the elevator car or its crosshead.
Relief ValveA safety valve set to open at a defined maximum pressure, returning oil to the tank if system pressure exceeds the safe design limit.
Holeless Hydraulic ElevatorA hydraulic elevator design that uses above-ground jacks (telescoping or roped) so no cylinder casing needs to be buried below the pit floor.
BoreThe inside diameter of a hydraulic cylinder; combined with system pressure, the bore area determines the maximum force the jack can produce.

Worked examples4

1. A hydraulic elevator car plus its rated load has a total weight of 12,000 lb. The jack cylinder has an inside bore diameter of 6 inches. What working pressure (PSI) is required to lift the load?
  1. Find the cross-sectional area of the cylinder bore. Radius = 6 ÷ 2 = 3 inches. Area = π × r² = 3.1416 × (3)² = 3.1416 × 9 = 28.27 in².
  2. Apply the pressure formula: P = F ÷ A = 12,000 lb ÷ 28.27 in².
  3. Calculate: 12,000 ÷ 28.27 = 424.5 PSI.
Answer: Approximately 424.5 PSI is required.
2. A hydraulic jack operates at 500 PSI. The cylinder bore diameter is 5 inches. What maximum force (in pounds) can the jack produce?
  1. Find the bore area. Radius = 5 ÷ 2 = 2.5 inches. Area = π × r² = 3.1416 × (2.5)² = 3.1416 × 6.25 = 19.635 in².
  2. Apply the force formula: F = P × A = 500 PSI × 19.635 in².
  3. Calculate: 500 × 19.635 = 9,817.5 lb.
Answer: The jack can produce approximately 9,817.5 lb of force.
3. An elevator system must lift a total load of 8,500 lb. The pump is rated to deliver a maximum of 400 PSI. What minimum cylinder bore area (in²) is needed, and what bore diameter does that correspond to?
  1. Solve for the required area: A = F ÷ P = 8,500 lb ÷ 400 PSI = 21.25 in².
  2. Find the corresponding bore diameter using A = π × r², so r² = A ÷ π = 21.25 ÷ 3.1416 = 6.763. Then r = √6.763 = 2.60 inches.
  3. Bore diameter = 2 × r = 2 × 2.60 = 5.20 inches.
Answer: Minimum bore area is 21.25 in², requiring a bore diameter of approximately 5.20 inches.
4. A technician measures working pressure at 380 PSI. The cylinder bore diameter is 4.5 inches. What is the upward force being applied to the plunger?
  1. Find the bore area. Radius = 4.5 ÷ 2 = 2.25 inches. Area = π × r² = 3.1416 × (2.25)² = 3.1416 × 5.0625 = 15.90 in².
  2. Apply the force formula: F = P × A = 380 PSI × 15.90 in².
  3. Calculate: 380 × 15.90 = 6,042 lb.
Answer: The upward force on the plunger is approximately 6,042 lb.

The math in this lesson2

Learners compute cylinder bore area from diameter using πr² before applying Pascal's law.
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Brush up in the math halls at newSchoolWorks.com:
In class: Lecture and guided notes on Pascal's Law, pressure (PSI), flow rate (GPM), and how these govern elevator car movement; students complete a worksheet calculating jack load, required pressure, and cylinder bore for three sample car/capacity scenarios. · Small-group analysis of a cross-section diagram of a holeless in-ground and above-ground hydraulic elevator, labeling fluid path from tank through pump, valve, and jack during up and down travel, then presenting findings to the class. · Paired problem-solving activity: given a set of elevator load and cylinder data cards, students calculate working pressure and verify results against an instructor answer key, identifying any calculation errors and correcting them.
Materials: Whiteboard, Pascal's Law reference handout, trade math worksheets, hydraulic elevator cross-section diagrams (in-ground and holeless), scientific calculators, NEIEP Hydraulics Study Guide (student edition)
Check: Graded worksheet: student correctly solves at least 8 of 10 pressure/force/area problems; pass mark 80%.

Practice check8

Answer each question, then check it. Nothing is recorded; this is your own practice.

Hydraulic Systems Theory
1. Pascal's Law states that pressure applied to a confined fluid is transmitted:
Trade Mathematics / Hydraulic Calculations
2. A hydraulic jack cylinder has a bore area of 25 in² and the system operates at 450 PSI. What is the lifting force produced by the jack?
Trade Mathematics / Hydraulic Calculations
3. A total elevator load of 10,000 lb must be lifted by a jack operating at 400 PSI. What bore area is required?
Hydraulic Systems Theory
4. In a hydraulic elevator during down travel, what causes the car to descend?
Hydraulic Systems Theory
5. What is the primary difference between an in-ground and a holeless hydraulic elevator?
Safety / Lockout-Tagout
6. Before opening a hydraulic fitting to replace a seal, a technician must first:
Trade Mathematics / Hydraulic Calculations
7. A cylinder bore has a diameter of 4 inches. What is the cross-sectional area of the bore? (Use π ≈ 3.1416)
Hydraulic Systems Theory
8. In a hydraulic elevator circuit, flow rate measured in GPM primarily controls:
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