# Hydraulic Advantage by qingyunliuliu

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```									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

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