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Applications on pascal's principle , Manometer types and uses

From Online Sciences - November 4, 2017

The aqueous manometer is preferred to the mercuric one to measure small pressure differences because the density of water is small compared to that of mercury , So , the difference in water levels in the two branches of the manometer becomes clear and easy to be measured which decreases the error in measurement .

Manometer

The manometer consists of U-shaped tube containing proper amount of liquid of known density , One of its ends is connected to the gas reservoir whose pressure to be measured and the other end exposed to air , The pressure at all points in the same horizontal plane in a homogeneous liquid is the same .

Manometer is used in measuring the pressure of enclosed gas , It is used in measuring the difference between the pressure of enclosed gas and the atmospheric pressure .

Manometer types

It is preferable to use the mercuric manometer for measuring high pressure difference because the mercury has high density , so , mercury neither rash out the tube nor into the gas reservoir .

How it is used ?

If the liquid level in the free end branch is the same liquid level in the other branch that connected to the gas reservoir , Then , Pa = Pgas

P = Pgas Pa = zero

P = zero , If the liquid used is mercury

If the liquid level in the free end branch is higher than the liquid level in the other branch that connected to the gas reservoir , Then ,Pgas > Pa .

Pgas = Pa +g h

P = Pgas Pa

P = +g h ( N / m )

If the liquid used is mercury then : Pgas = Pa + h

P = Pgas Pa , P = + h ( cm Hg ) .

If the liquid level in the free end branch is lower than the liquid level in the branch that connected to the gas reservoir ,Then ,Pgas < Pa .

Pgas = Pag h

P = Pgas Pa

P =g h ( N / m )

If the liquid used is mercury then : Pgas = Pah

P = Pgas Pa ,P =h ( cm Hg ) .

Pascals principle

When a liquid is put in a glass container equipped with a piston at the top , then the pressure at point A at depth h is :

P = P1 +g h

Where : P1 is the pressure at the liquid surface and it is due to the atmospheric pressure and the weight of the piston ,g h is the pressure of the liquid column on point A , when putting extra load on the piston , the pressure increases by P .

P = P1 +g h + P

The piston does not move down because the liquid is incompressible , If the pressure on the piston is increased to a certain limit , the glass container breaks down , This means that the pressure acting on the piston is transferred to all parts of the liquid and to the walls of the container , The French scientist Pascal set his principle based on this result .

Pascals principle : When pressure is applied on a liquid in a container , the pressure is transmitted in full to all parts of the liquid as well as the walls of the container , Pascals principle is not applied to gases because unlike liquids , they can be compressed due to the big intermolecular spaces between their molecules .

Applications on pascals principle

The hydraulic press

Hydraulic press consists of a tube with 2 pistons at its ends , one small of area ( a ) and the other big of area ( A ) where the space between them is filled with an appropriate liquid such as oil , It is used in lifting high loads using a small force and it is based on Pascals principle .

When a force ( f ) acts on the small piston , pressure ( P ) is produced , P = f / a , The pressure ( P ) transfers completely through the liquid to the lower surface of the big piston where a force ( F ) is produced , P = F / A , In this case the pistons are in equilibrium at one horizontal level where :

Pressure on the small piston = Pressure on the big piston

F/ f = y1 / y2

Cases of hydraulic press

The mechanic advantage of the hydraulic press

The hydraulic brake system in a car is two types

Diving suit

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