Pascal`s Law
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Transcript Pascal`s Law
Larry’s New truck
1
Larry’s Truck Improvements
GIT-R-DONE
• Larry put a 6” lift kit on his
Ford F-150 and a set of
33’s Super Swamper
Thornbird Tires
• The Suspension System
has been modified but the
Brake System has not.
• Do You See Any
Problems?
2
What Parts Control the Stopping of
the Truck?
•
•
•
•
Master Cylinder
Brake Hoses/Lines
Wheel Cylinders
Brake Calipers
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Larry has a Problem!
• What changes could you make to fix the
problem?
– Bigger parts
• Such as: Master Cylinder, Brake lines, Wheel
Cylinders, and/or Brake Calipers
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Pascal’s Law
Unlock the mechanics of the
Hydraulic Braking System
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Before we apply Pascal’s Law
We must first review and be familiar with…
Diameter of a Piston
Radius of the Piston
Area of the top surface of the Piston
Mathematically speaking…
Diameter: The width of a circular or cylindrical object.
Radius: The radius of a circle is half the diameter
Area: Any particular extent of space or surface
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Math – Hands on Practice
Measure across the top
of the piston, through
the center and record
the diameter (inches)
Calculate the radius of
the piston
Calculate the area of
the top of the piston
A = π · r · r or
A = πr2
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Area Example
Diameter = 7 inches
Radius = 3 1/2 inches
Area = ?
A= π·r2
3.14 · (3 ½ in)2 = 38.465 in2
Area = 38.465 in2
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Homework
Practice skill work
Read article: Effect of Oversize Tires on
Braking Characteristics
– www.aamva.org/Documents/
vehStudyEffectOfOversizedTiresOnAlteredHei
ghtVehicles.pdf -
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Pascal’s Law
In the 1600's, the French scientist Blaise
Pascal discovered a fact now known as
Pascal's Law. It states that pressure at any
point in a body of fluid is the same in every
direction, exerting equal force on equal
areas. This works for gases and liquids
(both are fluids).
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Pascal’s Formula
This brings us to a very important formula:
F
P
A
P = Pressure, F = Force and A = Area
This expresses that Pressure is Force per Unit Area.
This is why pressure is usually expressed in
pounds per square inch (psi).
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Variations of Pascal’s Law
Pressure = Force
divided by area
F
P
A
Force = Pressure times
area
F P A
Area = Force divided
by pressure
F
A
P
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F =Force
F
P
P = Pressure
A
A = Area
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Have you used formulas like
Pascal’s Law? Where are they used?
Generic Inverse Variation
Problem
used in Algebra
Time = Distance / Rate
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y
x
Ohm’s Law
used in science class
with electrical components
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Using Pascal’s Law
Pascal's Law - gives us the
mechanics to do a great deal
of work with hydraulics. The
drawing on the left shows that
we can lift a large amount of
weight with a small amount of
effort. We can lift 100 pounds
by applying just 10 pounds of
force to the piston measuring
1 square inch
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Basic automotive braking system
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50 lbs force
.5 sq in area of top of piston
F
P
A
50lb
P
2
.5in
P 100lb / in
2
50 lbs divided by .5 = 100 psi
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Where might Pascal’s Law be used?
A twenty ton floor
jack has a hydraulic
piston with a 7 in
diameter.
60 pounds of force is
being applied to the
piston.
Calculate the line
pressure being exerted
on the piston.
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Solving a Pascal’s Law problem
Which version of Pascal’s Law will you use?
Pressure = Force divided by area
F
P
A
Recall from earlier…..
A= π·r2
3.14 · (3 ½ in)2 = 38.465 in2
Area = 38.465 in2
P = (60pounds) / (38.465 in2)
P = 1.56 pounds/ in2
P = 1.56 psi
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Using Pascal’s Law
A caliper piston has a
diameter = 1.5 in
The Master cylinder
has 50 pounds per
square inch (psi) line
pressure applied to it.
Determine the force
exerted on the caliper
piston.
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Solving a Pascal’s Law problem
Which version of Pascal’s Law will you use?
Force = Pressure times area
F P A
Recall how to find area…..
A= π·r2
3.14 · (3/4 in)2 = 1.77 in2
Area = 1.77 in2
F = (50pounds/ in2) (1.77 in2)
F = 88.5 pounds
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Did Larry have brake failure?
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Remember Larry’s Truck ……..
The truck has a major
GIT-R-DONE
braking problem.
You suggested earlier
that we replace it with
bigger brake parts…
What do we need to
know about the
original braking
system?
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Facts about Larry’s Truck
¼ in brake lines
½ in bore master cylinder
7/8 in bore wheel cylinders
2 in caliper pistons
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Can you fix Larry’s truck?
Devise a plan to fix Larry’s truck based on
Pascal’s Law and your knowledge of
automotive systems that will remedy
Larry’s braking problems.
– Be sure to show all calculations and justify your
solution plan in a written paragraph.
Remember Larry doubled the size of the original
tire size…..
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Be thorough..Larry is depending on
you…
How would you
–“Git-R-Done”?
GIT-R-DONE
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