Properties of fluids related to pressure

Properties of fluids related to pressure

(i) A liquid finds its own level:
Pressure in liquids does not depend on cross sectional area and shape of vessel containing the liquid.
This can be illustrated by an experiment using a communicating tube as shown below.

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A liquid is poured into the communicating tubes of different cross-sectional areas.

The liquid is found to stand at the same level in each tube. This shows that pressure at same level is the same.
This is because the same atmospheric pressure acts on the surface of water in each tube.

(ii) Pressure at a given depth acts equally in all directions:

Pascals principle of transmission of pressure in fluids

It states that pressure in an enclosed fluid is equally transmitted through out the fluid in all directions. Pascals principle works because liquids are incompressible. That is to say, their volumes cant be reduced by squeezing. An experiment to verify Pascals principle.

Pascal`s principle of transmission of pressure in fluids

Holes of equal size are drilled in a round bottomed flask and covered with cork.
The flask is then filled with water and the piston pushed inside the flask.
Water shoots out equally in all directions, and travels equal distances. This verifies Pascal`s principle.

Hydraulic machines

Pascal’s principle states that: When a force exerted on a liquid, pressure is produced which is transmitted equally throughout the liquid.
The above principle is applied in hydraulic press, hydraulic brakes and hydraulic jacks. Liquids are almost uncompressible so they can pass on any pressure applied to them.
In hydraulic press a small force is applied to a small piston in order to raise, large force (load) placed on large piston.

(a) Hydraulic press

It consists of two interconnected cylinders of different diameters enclosed by means of pistons which fit tightly in the cylinders.
A high-density liquid like oil is used to fill the system.
Effort applied on the smaller piston can be used to overcome a larger load on the bigger piston.
When a force (effort) is acting on the smaller piston, exerts pressure on the liquid. According to Pascal’s principle, the pressure will be transmitted equally to every point of the liquid since the system is enclosed by the cylindrical pistons.
The same pressure then acts on the bigger piston, where it overcomes a bigger force (heavy load) because of the large area of the piston.

qe

Thus assuming a hydraulic press, which is 100% efficient, then,

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Where r and R are the radius of the smaller and bigger pistons respectively.

Example 1:
A hydraulic press is made of two cylinders of cross-section areas 20cm2 and 120cm2 respectively fitted tightly with pistons A and B. A force of 10N applied on A is used to raise a load on piston B. Calculate the maximum possible force that can be raised on piston B.

Solution:

qq

2: A hydraulic press requires an effort of 100N acting on a piston of area 20cm2 to press a bale of cotton placed on a piston of area 240cm2. If the percentage efficiency of the press is 80%, calculate the force applied on the bale.

Solution:

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Advantage
A small force applied on small piston can overcome a large place load placed on a large piston.