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3.4 Pascal Principle

Introduction

The molecules in a liquid are close and in contact with each other. As a result ,liquids are practically in compressible.

Pascal’s Principle

 

Pascal’s principle states that  when pressure is applied to an enclosed fluid, the pressure will  be transmitted equally throughout the whole enclosed fluid.

Eperiment to verify the Pascal’s Principle

clip_image002

When the piston is pushed into the glass sphere the jet of water is shot out from the holes in the glass sphere with the same speed.

This is because the pressure acting on the water is transferred uniformly throughout  the water.

 

Pascal’s Principle in Mathematic Expression

Output force = output piston area

Input force      input piston area

        

  F2      = A2

           F1         A1

 

Example 1

To produce a 2 500 N force over a 20 m2 area of a hydraulic system, calculate the magnitude of the force that must be applied to a 50 cm2 area.

 

Solution

 

 

Applications of Pascal’s Principle

(1)Automobile hydraulic lift

 

Automobile hydraulic lift is used to lift a vehicle in a workshop.

The system uses Pascal’s Principle to produce a larger force to lift a heavy vehicle.

clip_image004

 

When incompressible fluid is moved through a hydraulic system, the volume through which the input system moved must be the same as the volume through which the output system,

Hence

                                A1d1  =  A2d2

 

Based on the Pascal’s Principle,the pressure is transmitted throughout all points in the fluid and acts in all directions,

                                F1  =  F2

                                A1       A2  

Example 2

The figure shows a basic hydraulic system has small and large pistons with cross-sectional area of 0.005 m2 and 0.1 m2 respectively. A force of 20 N is applied to the small piston.

 

clip_image006

Determine

(a)    The pressure  transmitted in the hydraulic fluid.

(b)    The mass of the load.

(c)     If  the small piston is pushed down  at  a depth a 0.04 m, what is the distance moved by the large piston.

 

Solution

 

 

 

(2) Hydraulic Jack

clip_image008

 

When the handle is pulled, valve P is still closed and valve Q opens so the pressure can be sent to the larger piston. The large piston will rise.

While the small piston is pulled out, valve Q closes and valve P opens so that  the oil in the tank enter into the hydraulic cylinder as a result of atmospheric pressure.

By moving the push-pull handle a number of times , the large piston can be raised carrying a heavy load.

(3)  Hydraulic Brake

clip_image010

 

A small force acting at the pedal can transmit a large force to all wheels simultaneously to stop the car.

It is because the  pressure will be transferred through the pedal brake liquid to car’s tyre .

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