1. Engineering II – August 2016
H & P Formulas
Engineering II – August 2016

2. The parts and values of concern….
Piston Rod
Cylinder Bore
D1 = diameter of cylinder (in)
D2 = diameter of piston rod (in)
P1 = pressure on face of piston (PSI)
P2 = pressure on rod side of (PSI)
Q1 = fluid flow face side (gal/min)
Q2 = fluid flow rod side (gal/min)
F1 = force of extending piston (lbs)
F2 = force of retracting piston (lbs)
V1 = velocity of extension (ft/s)
V1 = velocity of retraction (ft/s)

3. Basic (Single Acting)Cylinder Force Formula:
Extension Force (lbs) = Fluid Pressure (PSI) X Cylinder Area (in2)

4. Example
A single acting pneumatic cylinder used to compress garbage has a bore of 4.8 inches, and operates under a pressure upon extension of 640 psi. What force does it generate? (round answer to one decimal place; use 3.14 for value of )
Extension Force (lbs) = Fluid Pressure (PSI) X Cylinder Area (in2)
Extension Force (lbs) = 640 PSI X  (4.8 in /2)2
Extension Force (lbs) = 11,575.3 lbs.

5. Retraction Force of a Double Acting Cylinder
Retraction Force (lbs) = (Piston Area [in2] - Rod Area [in2]) x Fluid Pressure (PSI)
Defines the annulus area

6. Example
A VEX double-acting pneumatic cylinder has a bore (diameter) of 0.39 inches and has a normal operating pressure of 100 psi. If the cylinder has a rod with a diameter of 0.17 inches, what is the force generated by this cylinder when it is retracted? (round answer to one decimal place; use 3.14 for value of )
Retraction Force (lbs) = (Piston Area [in2] - Rod Area [in2]) x Fluid Pressure (PSI)
Retraction Force (lbs) = 100 PSI X  (0.39/2)2 -  (0.17/2)2
Retraction Force (lbs) = 9.6 lbs.

7. Cylinder Speed
Cylinder Speed (ft/s) = .3208* X Pump Flow Rate (GPM) / Cylinder Area (in2)
*For retraction speed of a double acting cylinder, use the annulus area as the cylinder area in the formula.

8. Example
At what speed would a hydraulic piston with a 4 inch bore cylinder extend with an oil flow rate of 12 GPM? (round answer to two decimal place; use 3.14 for value of )
Cylinder Speed (ft/s) = X Pump Flow Rate (GPM) / *Cylinder Area (in2)
*For retraction speed of a double acting cylinder, use the annulus area as the cylinder area in the formula.
Cylinder Speed (ft/s) = 0.31 ft/s

9. Other Formulas You Might Need….
Fluid Pressure (PSI) = Force (Pounds) / Unit Area (in2)
Cylinder Area (in2) =  r2

10. H & P Vocabulary
absolute pressure: The total pressure exerted on a system, including atmospheric pressure.
annulus: the ring-shaped space between the two circles that define it.
atmospheric pressure: The pressure exerted by the weight of the atmosphere above the point of measurement.
Boyle's law: The volume of a gas at constant temperature varies inversely with the pressure exerted on it.
Charles' law: The volume of a confined gas is proportional to its temperature, provided its pressure remains constant.
check valve: A valve that allows flow in one direction but prevents flow in the opposite direction.
compressor: An air pump that compresses air into a receiver tank.
crank: A part of an axle or shaft bent out at right angles, for converting reciprocal to circular motion and vice versa.

11. H & P Vocabulary (…continued)
cylinder: A device used to convert fluid power into mechanical power in the form of linear motion.
directional-control valve: Used to control which path fluid takes in a circuit.
double-acting cylinder: A cylinder that can act under pressure in both directions (extend and retract) to move a load.
filter: A device used to remove contamination from a fluid.
flow meter: A device used to measure flow rate.
flow rate: The volume of fluid that moves through a system in a given period of time.
flow velocity: The distance the fluid travels through a system in a given period of time.
flow-control valve: Used to start and stop flow in a circuit.
fluid power: The use of a fluid (liquid or gas) to transmit power from one location to another.

12. H & P Vocabulary (…continued)
Gay-Lussac's law: The absolute pressure of a confined gas is proportional to its temperature, provided its volume stays constant.
hydraulics: The use of a liquid flowing under pressure to transmit power from one location to another.
lubricator: A device used to spray an oil mist into the stream of a pneumatic system.
Pascal's law: Pressure exerted by a confined fluid acts undiminished equally in all directions.
piston: A sliding piece moved by or moving against fluid pressure, which usually consists of a short cylindrical body fitting within a cylindrical chamber or vessel along which it moves back and forth.
pneumatics: The use of gas flowing under pressure to transmit power from one location to another.

13. H & P Vocabulary (…continued)
pressure: The force per unit area exerted by a fluid against a surface.
pressure regulator: A type of pneumatic pressure control valve that controls the maximum pressure in a branch of a circuit.
pressure relief valve: A type of pressure control valve that limits the maximum pressure in a hydraulic or pneumatic circuit.
pump: A device used to create flow in a hydraulic system.
receiver tank: A device that holds the compressed air in a pneumatic system.
reservoir: The tank that holds the fluid in a hydraulic system.
single-acting cylinder: A cylinder that acts under pressure in one direction only and returns automatically when the pressure is released.
solenoid: A switching device that uses the magnetic field generated by an electrical current for actuation.

14. H & P Vocabulary (…continued)
transmission Lines: Used to transport fluid in a circuit.
valve: Any device that controls, either automatically or manually, the flow of a fluid.
viscosity: A measure of a fluid's thickness or resistance to flow.
volume: The amount or quantity of something measured in cubic units.