Mechatronics · Module 5 of 10

Hydraulic and Pneumatic Actuation

Fluid power turns pressure into large, controllable force. A cylinder's force is pressure times piston area, and its speed is flow divided by that area, whether the fluid is stiff oil or springy air.

01

Readiness check

This module opens the actuation half of the course. Tick only what you can do closed-notes.

  • Compute a circle area from its diameter.
  • Recall that pressure is force per unit area.
  • Convert litres per minute to cubic metres per second.
  • Recall that liquids are nearly incompressible and gases are not.
  • Rearrange force equals pressure times area.
0 or 1 weak itemsContinue with this module.
2 weak itemsRevisit pressure in Fluid Mechanics, Module 3.
3 or more weak itemsRevisit the fundamentals in Fluid Mechanics.
02

The core idea

A fluid-power cylinder makes force by applying pressure over the piston area, so F = P × A with A = πd2/4. It extends at a speed set by the supplied flow divided by that area, v = Q/A. Hydraulics use stiff oil for high force; pneumatics use compressible air for speed and compliance.

A = πd2/4F = P × Av = Q / A

Fluid power actuation converts the pressure of a fluid into mechanical force and motion. The heart of it is the cylinder: pressure P acting on a piston of area A produces a force F = P × A, and because the piston is circular its area is πd2/4, so the bore diameter sets how much force a given pressure delivers. The same cylinder's extension speed comes from continuity: a volumetric flow Q into the cylinder fills it at v = Q/A, so a bigger bore is stronger but slower for the same pump. The choice of fluid divides the field. Hydraulic systems use nearly incompressible oil at high pressure, giving large, stiff, precisely held forces, ideal for presses and heavy machinery. Pneumatic systems use compressible air at lower pressure, giving fast, springy, and inherently compliant motion that is clean and cheap, ideal for light, repetitive tasks. Directional control valves route the fluid to extend, retract, or hold, and a solenoid on the valve is where the electronic controller meets the fluid power.

The skill works when: you compute the piston area from the bore and use F = PA and v = Q/A.
The skill breaks down when: diameter is used in place of area, or air is treated as stiff like oil.
The concept. Pressure acting over the piston area makes the force; the flow into the cylinder sets the speed. Bore diameter controls both through the area.
03

The skills, taught in order

Five skills size and control a fluid-power actuator.

5.1 Fluid power and the two families

Hydraulic systems move nearly incompressible oil at high pressure for large, stiff forces; pneumatic systems move compressible air at lower pressure for fast, compliant motion. Compressibility is the key difference: air stores energy like a spring, oil does not.

5.2 Cylinder force

A cylinder converts pressure to force through F = P × A, with the piston area A = πd2/4. A double-acting cylinder is driven both ways; on the rod side the area is reduced by the rod, so the retract force is a little smaller than the extend force.

5.3 Cylinder speed

By continuity the extension speed is v = Q/A: the pump's flow fills the bore. For a fixed pump, a larger bore gives more force but less speed, the fundamental force-speed trade of a cylinder.

QuantityRelationSet by
Piston areaA = πd2/4bore diameter
ForceF = P × Apressure and area
Speedv = Q/Aflow and area

The three cylinder relations. The area appears in all of them, which is why bore choice is central.

5.4 Directional control valves

A valve is described by its ports and positions, such as a 4/3 valve with four ports and three positions. A solenoid shifts the spool, so a digital output can extend, retract, or centre a cylinder, connecting the controller to the fluid.

5.5 The rest of the circuit

A pump and prime mover supply flow; a relief valve caps pressure for safety; an accumulator stores energy; and in pneumatics a filter, regulator, and lubricator condition the air. These support the actuator and keep it safe.

Engineering connection: an injection-moulding clamp uses a large-bore hydraulic cylinder for stiff tonnage, while the parts are ejected by fast, compliant pneumatic cylinders.

04

Worked example 1: cylinder force

A hydraulic cylinder has a 40 mm bore and runs at 12 MPa. Find the piston area and the extend force.

Figure 1. The 40 mm bore gives a piston area of 1.257 × 10−3 m2; at 12 MPa this produces about 15.1 kN of force.
  1. ProblemFind the piston area and extend force for the cylinder in Figure 1.
  2. Given / findd = 40 mm = 0.040 m, P = 12 MPa. Find A and F.
  3. AssumptionsForce on the full bore (extend stroke), pressure acts uniformly, friction neglected.
  4. ModelA = πd2/4; F = P × A.
  5. EquationsA = π(0.040)2/4F = 12×106 × A
  6. SolveA = 1.257 × 10−3 m2; F = 12×106 × 1.257×10−3 = 15080 N ≈ 15.1 kN.
  7. Check12 MPa is 12 N per mm2; the bore is π(20)2 = 1257 mm2; 12 × 1257 = 15080 N, matching.
  8. ConclusionA modest 40 mm cylinder at 12 MPa lifts about 1.5 tonnes, showing why hydraulics dominate heavy force.
Result. A = 1.257 × 10−3 m2; F ≈ 15.1 kN.
05

Worked example 2: cylinder speed

The same 40 mm cylinder is fed 15 litres per minute. Find its extension speed.

Figure 2. The 15 L/min flow is 2.5 × 10−4 m3/s; dividing by the piston area gives an extension speed of about 0.20 m/s.
  1. ProblemFind the extension speed for the cylinder in Figure 2.
  2. Given / findQ = 15 L/min, A = 1.257 × 10−3 m2. Find v.
  3. AssumptionsIncompressible flow, no leakage past the piston.
  4. ModelContinuity: v = Q/A, with Q in m3/s.
  5. EquationsQ = 15/60000 = 2.5×10−4 m3/sv = Q/A
  6. Solvev = 2.5×10−4 / 1.257×10−3 = 0.20 m/s.
  7. CheckA 0.2 m/s speed over the 1.257×10−3 m2 bore returns 2.5×10−4 m3/s, the given flow.
  8. ConclusionThe cylinder extends at about 0.2 m/s; doubling the bore for more force would quarter the area's speed for the same flow.
Result. Extension speed v ≈ 0.20 m/s.
06

Misconceptions and diagnostics

MistakeSymptomDiagnostic questionCorrection
Using diameter as areaForce off by a large factor"Did I compute πd2/4?"Force uses the area, not the diameter.
Radius and diameter mixedArea four times wrong"Is d the bore or the radius?"Use d in πd2/4, or πr2 with the radius.
Flow units left as L/minSpeed 60000 times off"Is Q in m3/s?"Convert L/min to m3/s before v = Q/A.
Treating air as stiffPneumatic position drifts under load"Is the fluid compressible?"Air springs; hold precise force with hydraulics.
07

Practice ladder

Level 1 · Direct skill

A cylinder has a 50 mm bore at 10 MPa. Find the force.

Show answer

A = π(0.05)2/4 = 1.963 × 10−3 m2; F = 10×106 × A = 19.6 kN.

Level 2 · Mixed concept

A 40 mm bore cylinder is fed 20 L/min. Find its speed.

Show answer

Q = 20/60000 = 3.33 × 10−4 m3/s; v = Q/(1.257×10−3) = 0.265 m/s.

Level 3 · Independent problem

You need 20 kN at 16 MPa. What bore diameter is required?

Show answer

A = F/P = 20000/16×106 = 1.25 × 10−3 m2; d = √(4A/π) = 39.9 mm, so a 40 mm bore.

Transfer task | Real engineering

Choose hydraulic or pneumatic actuation for (a) a 60 kN press that must hold position and (b) a fast, light pick-and-place gripper. Justify each.

What good work looks like

(a) Hydraulic: high, stiff force held precisely, since oil is incompressible; (b) pneumatic: fast, clean, compliant, and cheap for light repetitive motion where exact position under load is not critical.

08

Working with AI, and proving it yourself

Use AI as an examiner, not a solver

"Check that I used the piston area, not the diameter, in this force."
"Give me three cylinders; I will compute force and speed for each."
"Size my hydraulic system." Choosing bore and pressure is the skill.
"Hydraulic or pneumatic?" Reason from force, speed, and compliance yourself.

Portfolio task

Specify a cylinder for one task: choose a bore and pressure for the force, then check the speed at your pump's flow.

Must include: a piston area, a force, a speed, and a hydraulic-versus-pneumatic choice with reasons.
09

Retrieval and spaced review

Closed notes. Answer out loud, then reveal.

1. Write the cylinder force.

F = P × A, with A = πd2/4.

2. Write the cylinder speed.

v = Q/A, with Q in m3/s.

3. Why is hydraulic force stiff?

Oil is nearly incompressible, so it holds position and force precisely.

4. What describes a directional valve?

Its ports and positions, such as a 4/3 valve, shifted by a solenoid.

5. Why choose pneumatics?

Fast, clean, compliant, and cheap motion for light repetitive tasks.

TodayFinish this quiz and Levels 1 and 2 of the ladder.
+1 dayRe-derive force and speed for a new bore.
+3 daysSize a cylinder for one real task.
+7 daysMove on to mechanical actuation in Module 6.
+30 daysReuse F = PA and v = Q/A on any cylinder.
10

Textbook mapping

This module follows William Bolton, Mechatronics, 6th edition. Use these references to read further.

Topic in this moduleWhere to read more
Hydraulic and pneumatic systemsBolton, Chapter 7, Actuation systems
Cylinders and forceBolton, Chapter 7, Cylinders
Directional control valvesBolton, Chapter 7, Directional control valves

Chapter numbers refer to Bolton's Mechatronics, 6th edition. Any edition with the same chapter titles is equivalent for study.