1. H & P Formulas Engineering II – August 2016

2. The parts and values of concern…. D 1 = diameter of cylinder (in) D 2 = diameter of piston rod (in) P 1 = pressure on face of piston (PSI) P 2 = pressure on rod side of (PSI) Q 1 = fluid flow face side (gal/min) Q 2 = fluid flow rod side (gal/min) F 1 = force of extending piston (lbs) F 2 = force of retracting piston (lbs) V 1 = velocity of extension (ft/s) V 1 = velocity of retraction (ft/s) Cylinder Bore Piston Rod

3. Basic (Single Acting)Cylinder Force Formula: Extension Force (lbs) = Fluid Pressure (PSI) X Cylinder Area (in 2 )

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 (in 2 ) Extension Force (lbs) = 11,575.3 lbs. Extension Force (lbs) = 640 PSI X  (4.8 in /2) 2

5. Retraction Force of a Double Acting Cylinder Retraction Force (lbs) = (Piston Area [in 2 ] - Rod Area [in 2 ]) 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 [in 2 ] - Rod Area [in 2 ]) x Fluid Pressure (PSI) Retraction Force (lbs) = 9.6 lbs. Retraction Force (lbs) = 100 PSI X  (0.39/2) 2 -  (0.17/2) 2

7. Cylinder Speed Cylinder Speed* (ft/s) =.3208* X Pump Flow Rate (GPM) / Cylinder Area (in 2 ) *Also called “velocity” in H&P literature **For retraction speed of a double acting cylinder, use the annulus area as the cylinder area in the formula.

8. Example Cylinder Speed (ft/s) =.3208 X Pump Flow Rate (GPM) / *Cylinder Area (in 2 ) 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  ) *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 (in 2 ) Cylinder Area (in 2 ) =  r 2

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.