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Figure is a schematic drawing of a hydraulic brake system. A foot is applied to the brake pedal with the force F1. It is transmitted to the pedal cylinder with the area A1 of 0.5 cm. The Pedal cylinder is connected to the hydraulic system with two wheel cylinders with an area A2 of 2.5 cm. Wheel cylinders create output force F2.
Hydraulic brakes use Pascal’s principle. The driver pushes the brake pedal, exerting a force that is increased by the simple lever and again by the hydraulic system. Each of the identical wheel cylinders receives the same pressure and, therefore, creates the same force output F 2 . The circular cross-sectional areas of the pedal and wheel cylinders are represented by A 1 and A 2 , respectively.


We are given the force F 1 applied to the pedal cylinder. The cross-sectional areas A 1 and A 2 can be calculated from their given diameters. Then we can use the following relationship to find the force F 2 :

F 1 A 1 = F 2 A 2 .

Manipulate this algebraically to get F 2 on one side and substitute known values.


Pascal’s principle applied to hydraulic systems is given by F 1 A 1 = F 2 A 2 :

F 2 = A 2 A 1 F 1 = π r 2 2 π r 1 2 F 1 = ( 1.25 cm ) 2 ( 0.250 cm ) 2 × 500 N = 1.25 × 10 4 N .


This value is the force exerted by each of the four wheel cylinders. Note that we can add as many wheel cylinders as we wish. If each has a 2.50-cm diameter, each will exert 1.25 × 10 4 N . A simple hydraulic system, as an example of a simple machine, can increase force but cannot do more work than is done on it. Work is force times distance moved, and the wheel cylinder moves through a smaller distance than the pedal cylinder. Furthermore, the more wheels added, the smaller the distance each one moves. Many hydraulic systems—such as power brakes and those in bulldozers—have a motorized pump that actually does most of the work in the system.

Check Your Understanding Would a hydraulic press still operate properly if a gas is used instead of a liquid?

Yes, it would still work, but since a gas is compressible, it would not operate as efficiently. When the force is applied, the gas would first compress and warm. Hence, the air in the brake lines must be bled out in order for the brakes to work properly.

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  • Pressure is force per unit area.
  • A change in pressure applied to an enclosed fluid is transmitted undiminished to all portions of the fluid and to the walls of its container.
  • A hydraulic system is an enclosed fluid system used to exert forces.

Conceptual questions

Suppose the master cylinder in a hydraulic system is at a greater height than the cylinder it is controlling. Explain how this will affect the force produced at the cylinder that is being controlled.

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How much pressure is transmitted in the hydraulic system considered in [link] ? Express your answer in atmospheres.

251 atm

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What force must be exerted on the master cylinder of a hydraulic lift to support the weight of a 2000-kg car (a large car) resting on a second cylinder? The master cylinder has a 2.00-cm diameter and the second cylinder has a 24.0-cm diameter.

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A host pours the remnants of several bottles of wine into a jug after a party. The host then inserts a cork with a 2.00-cm diameter into the bottle, placing it in direct contact with the wine. The host is amazed when the host pounds the cork into place and the bottom of the jug (with a 14.0-cm diameter) breaks away. Calculate the extra force exerted against the bottom if he pounded the cork with a 120-N force.

5.76 × 10 3 N extra force

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A certain hydraulic system is designed to exert a force 100 times as large as the one put into it. (a) What must be the ratio of the area of the cylinder that is being controlled to the area of the master cylinder? (b) What must be the ratio of their diameters? (c) By what factor is the distance through which the output force moves reduced relative to the distance through which the input force moves? Assume no losses due to friction.

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Verify that work input equals work output for a hydraulic system assuming no losses due to friction. Do this by showing that the distance the output force moves is reduced by the same factor that the output force is increased. Assume the volume of the fluid is constant. What effect would friction within the fluid and between components in the system have on the output force? How would this depend on whether or not the fluid is moving?

If the system is not moving, the friction would not play a role. With friction, we know there are losses, so that W o = W i W f ; therefore, the work output is less than the work input. In other words, to account for friction, you would need to push harder on the input piston than was calculated.

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Questions & Answers

What is concept associated with linear motion
Adeoye Reply
what will happen to vapor pressure when you add solute to a solution?
shane Reply
how is freezing point depression different from boiling point elevation?
how is the osmotic pressure affect the blood serum?
what is the example of colligative properties that seen in everyday living?
What is motion
Adeoye Reply
moving place to place
change position with respect to surrounding
to which
to where ?
the phenomenon of an object to changes its position with respect to the reference point with passage of time then it is called as motion
it's just a change in position
reference point -it is a fixed point respect to which can say that a object is at rest or motion
Is there any calculation for line integral in scalar feild?
Sadia Reply
yes I'm available
what is thrust
Aarti Reply
when an object is immersed in liquid, it experiences an upward force which is called as upthrust.
@Phanindra Thapa No, that is buoyancy that you're talking about...
thrust is simply a push
it is a force that is exerted by liquid.
what is the difference between upthrust and buoyancy?
The force exerted by a liquid is called buoyancy. not thrust. there are many different types of thrust and I think you should Google it instead of asking here.
hey Kumar, don't discourage somebody like that. I think this conversation is all about discussion...remember that the more we discuss the more we know...
thrust is an upward force acting on an object immersed in a liquid.
uptrust and buoyancy are the same
the question isn't asking about up thrust. he simply asked what is thrust
a Thrust is simply a push
the perpendicular force applied on the body
how did astromers neasure the mass of earth and sun
papillas Reply
wats the simplest and shortest formula to calc. for order of magnitude
Distinguish between steamline and turbulent flow with at least one example of each
Aarti Reply
what is newtons first law
Theodore Reply
It state that an object in rest will continue to remain in rest or an object in motion will continue to remain in motion except resultant(unbalanced force) force act on it
Thanks Gerald Fokumla
Your welcome
it states that a body remains in its state of rest or uniform motion unless acted upon by resultant external force.
it that a body continues to be in a state of rest or in straight line in a motion unless there is an external force acting on it
derive the relation above
jeba Reply
formula for find angular velocity
Mark Reply
Why satellites don't fall on earth? Reason?
Abdur Reply
because space doesn't have gravity
satellites technically fall to earth but they travel parallel to earth so fast that they orbit instead if falling(plus the gravity is also weaker in the orbit). its a circular motion where the centripetal force is the weight due to gravity
Exactly everyone what is gravity?
Tebogo Reply
the force that attrats a body towards the center of earth,or towards any other physical body having mass
That force which attracts or pulls two objects to each other. A body having mass has gravitational pull. If the object is bigger in mass then it's gravitational pull would be stronger.For Example earth have gravitational pull on other objects that is why we are pulled by earth.
Gravity is the force that act on a on body to the center of the earth.
what are the application of 2nd law
Sana Reply
It's applicable when determining the amount of force needed to make a body to move or to stop a moving body
coplanar force system
Alex Reply
how did you get 7.50times
Cole Reply
Practice Key Terms 3

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