VIEWS: 10 PAGES: 20 POSTED ON: 6/24/2011
Hydraulic Advantage What is the advantage of Hydraulics Calculating MA, SR, and E Calculating Hydraulic Advantage There is a mechanical advantage when using hydraulics to lift a load We calculate this advantage using the same formulas that we have used in the past MA = Foutput SR = dinput E = MA x 100 F input doutput SR Hydraulic Lifting Devices Input Output piston… piston… Input Output Force and Force and Distance Distance Hydraulic Lifting Devices Hydraulic lifting devices have an input piston for the input force and output piston for the output force Calculating MA, SR and E all depend on the Surface Area Ratio (SAR) The ratio in size difference between the two pistons will determine the MA and SR Hydraulic Lifting Devices If we have a small area making up the input piston which has an area of 1 unit of area (1 m²) The output piston has an area made up of 9 of the same units (9 m²)… Therefore the SAR is 9 because the output piston is times larger than the input piston Small Area for the input piston Large Area for the output piston Hydraulic Lifting Devices Surface Area Ratio = Area of Large Piston (output) Area of Small Piston (input) SAR = Area large piston Area small piston SAR = 9 m² 1 m² SAR = 9 Hydraulic Lifting Devices Here we have a small 10 N force applied to the input piston (1 unit of area or 1 m²) The output piston has an area made up of 9 of the same units (9 m²)… Therefore we multiply the input force by 9 to find out what the output force will be 10 N Hydraulic Lifting Devices Example If we apply 10 N of force to the input piston, then we need to multiply that by 9 to know what the output force is Therefore… Output Force = Input force x Surface Area Ratio Output Force = Input force x SAR Output Force = 10 N x 9 90 N Output Force = 90 N 10 N Hydraulic Lifting Devices Example If we were given the output force and we needed to calculate the input force, We would now divide rather than multiply because the input force is smaller than the output force Therefore… Input Force = Output force x Surface Area Ratio Input Force = Output force x SAR 90 N Input Force = 90 N ÷ 9 Input Force = 10 N 10 N Calculating Mechanical Advantage Example We now know that the input force is 10 N and the output force is 90N Therefore we can now calculate Mechanical Advantage MA = Foutput Finput MA = 90 N 10 N MA = 9 Hydraulic Lifting Devices The disadvantage is that the output distance will only be 1/9th our input distance We gain Mechanical Advantage, but we lose when it comes to Speed Ratio Hydraulic Lifting Devices Example If we push down on the input piston for a total distance of 18 cm, then the output distance will be 1/9th of 18 cm Therefore… Output distance = Input distance Speed Ratio 2 cm Output distance = 18 cm 9 cm 18 cm Output distance = 2 cm Calculating Speed Ratio Example We now know that the input Distance is 18 cm and the output Distance is 2 cm Therefore we can now calculate Speed Ratio SR = dinput doutput SR = 18 cm 2 cm SR = 9 Surface Area Ratio is the Key! As we have now calculated, the MA, SAR and SR are all the same If you can calculate the surface area of both pistons and figure out what the ratio is between them, then you automatically know what the MA and SR will be Should we x or ÷ When deciding whether to multiply or divide by the SR for MA or SAR… you need to visualize the system and decide if the value you are calculating will be less than your starting value, or more If it should be less, you ÷ If it should be more, you x Example Question (on the board) The person exerts a force of 40 N, the car exerts a force of 1200 N How many times heavier is the car than the person? (This is the same as asking what is MA) How large would the area of the output piston have to be if the in put piston is 0.5 m² N N Example Question (on the board) What is the Mechanical Advantage of this hydraulic system? What is the Speed ratio of the System? If the Output distance was 0.5 m, then what would the input distance be? N N Example Question (on the board) What will the pressure in the system be as the person is applying her 40 N of force to an area of 0.5 m² N N Hydraulic Demo Take a look at the two syringes at the front of the room Make your predictions as to what will happen in terms of input/output force and distance What will the efficiency of this set up be (theoretically) Home Work Take some time to look at the worksheet and practice some of the example questions This sheet will be marked in class so if you are having troubles, make sure you ask for help or come in after school