14.3 Pascal's principle and hydraulics (Page 3/6)

University physics volume 1 Page 3 / 6

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.

Strategy

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}

\frac{F_{1}}{A_{1}} = \frac{F_{2}}{A_{2}} .

Manipulate this algebraically to get $F_{2}$ on one side and substitute known values.

Solution

Pascal’s principle applied to hydraulic systems is given by

\frac{F_{1}}{A_{1}} = \frac{F_{2}}{A_{2}} :

\begin{matrix} F_{2} & = \frac{A_{2}}{A_{1}} F_{1} = \frac{π r_{2}^{2}}{π r_{1}^{2}} F_{1} \\ = \frac{{(1.25 cm)}^{2}}{{(0.250 cm)}^{2}} \times 500 N = 1.25 \times 10^{4} N . \end{matrix}

Significance

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 \times 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.

Got questions? Get instant answers now!

Summary

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.

Got questions? Get instant answers now!

Problems

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

251 atm

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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.

$5.76 \times 10^{3} N extra force$

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

<< Chapter < Page Page > Chapter >>

Practice Key Terms 3

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

100% Free Mobile Applications
Receive real-time job alerts and never miss the right job again

Source: OpenStax, University physics volume 1. OpenStax CNX. Sep 19, 2016 Download for free at http://cnx.org/content/col12031/1.5

Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'University physics volume 1' conversation and receive update notifications?

Ask

	1 Pharmacology Nervous System MCQ By Rohini Ajay Start Quiz
©flickr: Gareth	Resume Writing MCQ By Abby Sharp Start Quiz
	2 Gastrointestinal Pathophysiology Self-Assessment By Laurence Bailen Start Assessment
©flickr: Miguel	Protozoal and Parasitic Infections By Cath Yu Start Quiz
	Corporate Communication BUS210 By P. Wynn Norman Start Quiz
	45 Biology 45 Population and Community Ecology MCQ By OpenStax Start Quiz
	Principles of economics By OpenStax Read Online Course
	2 Sociology 02 Sociological Research MCQ By OpenStax Start Quiz
	8 Physiotherapy MMT Review By Rhodes Start Flashcards
	Basic Of Computer Exam By Naveen Tomar Start Quiz