Press With One Hand and Lift a Car, but Push a Very Long Way
Learn to state Pascal's law and calculate the force multiplication of a hydraulic press, see the evidence for atmospheric pressure, describe a mercury barometer and quote standard pressure three ways, and explain how pressure falls with altitude.
How can a small push on one piston lift a whole car?
A hydraulic lift in a garage raises a car when a mechanic presses a small lever. Nothing is being created out of nothing — the trick is entirely in the areas.
The liquid inside carries the applied pressure everywhere unchanged. So if you push on a small piston and the liquid meets a large piston somewhere else, the same pressure acts over a much bigger area, and pressure times area is force.
Press with N on a piston of area :
That same Pa acting on a piston of area gives
Fifty times the force out of the same push. The area ratio is fifty, and so is the force ratio.
But nothing is free. The small piston has to travel fifty times farther than the large one rises — and the last section of this page shows that the work done is identical at both ends. Force is multiplied; energy is not.
This page covers the second part of the ICSE Class 9 Physics chapter on pressure in fluids — Pascal's law and the hydraulic machines built on it, atmospheric pressure, the mercury barometer, and how pressure varies with altitude.
The liquid inside carries the applied pressure everywhere unchanged. So if you push on a small piston and the liquid meets a large piston somewhere else, the same pressure acts over a much bigger area, and pressure times area is force.
Press with N on a piston of area :
That same Pa acting on a piston of area gives
Fifty times the force out of the same push. The area ratio is fifty, and so is the force ratio.
But nothing is free. The small piston has to travel fifty times farther than the large one rises — and the last section of this page shows that the work done is identical at both ends. Force is multiplied; energy is not.
This page covers the second part of the ICSE Class 9 Physics chapter on pressure in fluids — Pascal's law and the hydraulic machines built on it, atmospheric pressure, the mercury barometer, and how pressure varies with altitude.
Formula
What does Pascal's law say, and how much force does a press multiply?
Pressure applied to an enclosed liquid is transmitted equally and undiminished in all directions and to every part of the liquid and the walls containing it.
Since the pressure is the same at both pistons,
The force multiplication factor is simply the ratio of the areas.
Worked example 1 — areas given directly. A force of N on a piston of , with the large piston at :
A multiplication factor of **.
Worked example 2 — radii given instead.** The pistons have radii cm and cm. Since area goes as the square of the radius,
so a force of N produces
Ten times the radius gives a hundred times the force. Radii must be squared before the ratio is taken, and forgetting to square is the standard error in these numericals.
Worked example 3 — finding the needed effort. A hydraulic lift must raise a load of N using pistons of area and . The factor is , so
Worked example 4 — the distances. In worked example 1, the same volume of liquid leaves the small cylinder and enters the large one, so
If the large piston rises cm, the small one must descend
One metre of pushing for two centimetres of lift.
Worked example 5 — checking the energy. Work done at each end:
- small piston: J
- large piston: J
Identical. The machine multiplies force by and divides distance by , leaving the energy untouched. A machine that multiplied energy would be impossible, and this check is worth making whenever a force ratio looks too good.
Hydraulic brakes. A light push on the brake pedal raises the pressure in the brake fluid, and by Pascal's law that pressure reaches the cylinders at all four wheels equally and undiminished. So each wheel receives the same braking force, the car does not swerve, and a modest pedal force stops a heavy vehicle. The equal transmission is the safety feature, not merely the multiplication.
Liquids are used, not gases. A liquid is practically incompressible, so a push at one end moves the far end immediately and by a predictable amount. A gas would compress first and the pedal would sink with nothing happening at the wheels. That is why brake systems use fluid and must be bled of any air bubble — a trapped bubble is exactly the compressible gas the design cannot tolerate.
Since the pressure is the same at both pistons,
The force multiplication factor is simply the ratio of the areas.
Worked example 1 — areas given directly. A force of N on a piston of , with the large piston at :
A multiplication factor of **.
Worked example 2 — radii given instead.** The pistons have radii cm and cm. Since area goes as the square of the radius,
so a force of N produces
Ten times the radius gives a hundred times the force. Radii must be squared before the ratio is taken, and forgetting to square is the standard error in these numericals.
Worked example 3 — finding the needed effort. A hydraulic lift must raise a load of N using pistons of area and . The factor is , so
Worked example 4 — the distances. In worked example 1, the same volume of liquid leaves the small cylinder and enters the large one, so
If the large piston rises cm, the small one must descend
One metre of pushing for two centimetres of lift.
Worked example 5 — checking the energy. Work done at each end:
- small piston: J
- large piston: J
Identical. The machine multiplies force by and divides distance by , leaving the energy untouched. A machine that multiplied energy would be impossible, and this check is worth making whenever a force ratio looks too good.
Hydraulic brakes. A light push on the brake pedal raises the pressure in the brake fluid, and by Pascal's law that pressure reaches the cylinders at all four wheels equally and undiminished. So each wheel receives the same braking force, the car does not swerve, and a modest pedal force stops a heavy vehicle. The equal transmission is the safety feature, not merely the multiplication.
Liquids are used, not gases. A liquid is practically incompressible, so a push at one end moves the far end immediately and by a predictable amount. A gas would compress first and the pedal would sink with nothing happening at the wheels. That is why brake systems use fluid and must be bled of any air bubble — a trapped bubble is exactly the compressible gas the design cannot tolerate.
What proves that the atmosphere presses on everything?
Air has weight, and the column of it above any surface presses down with about Pa at sea level — roughly the weight of a kilogram on every square centimetre.
You do not feel it because it presses equally from all directions, inside and out, exactly as law 3 of the previous part of this chapter requires.
Worked example — the force on a hand. A palm of area about carries
over a hundred kilograms-force. It does not crush the hand because the same pressure acts from underneath and from within.
Demonstrations that make it visible.
- A rubber sucker. Press it against a smooth tile and the air between is squeezed out. Atmospheric pressure now acts on the outside with nothing balancing it on the inside, and holds the sucker fast
- A drinking straw. Sucking lowers the pressure inside the straw, and the atmosphere pressing on the drink's surface pushes the liquid up. You never pull the drink up; the air pushes it
- An inverted glass covered with card. Fill a glass with water, cover it with a stiff card and turn it over. The water stays in, because atmospheric pressure pushing up on the card exceeds the water's pressure pushing down
- A collapsing tin. Boil a little water in a thin metal can, cap it and let it cool. The steam condenses, leaving a low pressure inside, and the atmosphere crushes the can inward
- Two joined hemispheres. Pump the air out from between two close-fitting metal hemispheres and they become extremely difficult to pull apart, held together only by the air outside
Everyday consequences.
- A syringe draws liquid in when the plunger is pulled back and the pressure inside falls
- A dropper works the same way
- Ink rises into a fountain pen's filler
- A water pump on a well lifts water because the atmosphere pushes it up the pipe
- A tightly sealed tin of oil will not pour until a second hole is made, letting air in to replace the oil
The last one is the most useful test of understanding. A single hole gives no flow because the oil leaving would leave a lower pressure behind it, and the atmosphere pushing on the hole holds the oil back. Two holes let air in at one and oil out at the other, and the tin empties freely.
Atmospheric pressure is the reason a suction pump has a limit. Since the atmosphere can support only a certain column of water — about m, as the next section shows — no ordinary suction pump can raise water from a well deeper than that, however powerful it is. The pump does not pull; the atmosphere pushes, and the atmosphere has a fixed amount of push available.
You do not feel it because it presses equally from all directions, inside and out, exactly as law 3 of the previous part of this chapter requires.
Worked example — the force on a hand. A palm of area about carries
over a hundred kilograms-force. It does not crush the hand because the same pressure acts from underneath and from within.
Demonstrations that make it visible.
- A rubber sucker. Press it against a smooth tile and the air between is squeezed out. Atmospheric pressure now acts on the outside with nothing balancing it on the inside, and holds the sucker fast
- A drinking straw. Sucking lowers the pressure inside the straw, and the atmosphere pressing on the drink's surface pushes the liquid up. You never pull the drink up; the air pushes it
- An inverted glass covered with card. Fill a glass with water, cover it with a stiff card and turn it over. The water stays in, because atmospheric pressure pushing up on the card exceeds the water's pressure pushing down
- A collapsing tin. Boil a little water in a thin metal can, cap it and let it cool. The steam condenses, leaving a low pressure inside, and the atmosphere crushes the can inward
- Two joined hemispheres. Pump the air out from between two close-fitting metal hemispheres and they become extremely difficult to pull apart, held together only by the air outside
Everyday consequences.
- A syringe draws liquid in when the plunger is pulled back and the pressure inside falls
- A dropper works the same way
- Ink rises into a fountain pen's filler
- A water pump on a well lifts water because the atmosphere pushes it up the pipe
- A tightly sealed tin of oil will not pour until a second hole is made, letting air in to replace the oil
The last one is the most useful test of understanding. A single hole gives no flow because the oil leaving would leave a lower pressure behind it, and the atmosphere pushing on the hole holds the oil back. Two holes let air in at one and oil out at the other, and the tin empties freely.
Atmospheric pressure is the reason a suction pump has a limit. Since the atmosphere can support only a certain column of water — about m, as the next section shows — no ordinary suction pump can raise water from a well deeper than that, however powerful it is. The pump does not pull; the atmosphere pushes, and the atmosphere has a fixed amount of push available.
How does a mercury barometer work, and what is standard pressure?
A barometer balances the atmosphere against a column of mercury, and the height of that column measures the pressure.
Construction. Take a glass tube about m long, closed at one end, and fill it completely with mercury. Close the open end with a finger, invert it, and stand it in a trough of mercury. Remove the finger.
What happens. The mercury falls a little and then stops, leaving a column about cm tall above the trough's surface. The space above it contains no air at all — it is a vacuum.
Why it stops where it does. The pressure at the trough's surface inside the tube must equal the atmospheric pressure outside, by law 2 from the previous part of this chapter. The pressure inside is due entirely to the mercury column, which is . So
and the column settles at whatever height makes that true. **The barometer is a direct application of , run backwards to measure the pressure rather than to calculate it.
Standard atmospheric pressure, three ways.**
and since bar Pa,
All three are the same pressure: cm Hg, Pa, and bar. A question may ask for any of them.
Worked example 1 — a lower reading. On a hill the barometer reads cm of mercury:
Worked example 2 — why not water. To balance the atmosphere with water instead of mercury, equate the two pressures:
A tube over ten metres tall — three storeys high. **Mercury does the job in cm because it is times denser**, and m exactly.
Worked example 3 — the thrust on a barometer's cross-section. A tube of internal area carries
Mercury is chosen for four reasons. It is very dense, keeping the tube short. It does not wet glass, so the column's top is clean and easy to read. It does not evaporate appreciably, so the space above stays a vacuum. And it is opaque and shiny, so the level is visible.
The tube's width and shape make no difference to the reading. A wide barometer and a narrow one both read cm, because contains no area — the hydrostatic result of the previous part of this chapter, appearing in an instrument. Tilting the tube does not change it either: the mercury runs further along the tube but the vertical height stays cm, since is measured vertically.
Air leaking into the space above spoils the instrument. That trapped air would exert its own pressure downward, so the column would stand lower than it should and the barometer would under-read. A barometer with air above the mercury is called a faulty barometer, and checking that the space is a vacuum is part of setting one up.
Construction. Take a glass tube about m long, closed at one end, and fill it completely with mercury. Close the open end with a finger, invert it, and stand it in a trough of mercury. Remove the finger.
What happens. The mercury falls a little and then stops, leaving a column about cm tall above the trough's surface. The space above it contains no air at all — it is a vacuum.
Why it stops where it does. The pressure at the trough's surface inside the tube must equal the atmospheric pressure outside, by law 2 from the previous part of this chapter. The pressure inside is due entirely to the mercury column, which is . So
and the column settles at whatever height makes that true. **The barometer is a direct application of , run backwards to measure the pressure rather than to calculate it.
Standard atmospheric pressure, three ways.**
and since bar Pa,
All three are the same pressure: cm Hg, Pa, and bar. A question may ask for any of them.
Worked example 1 — a lower reading. On a hill the barometer reads cm of mercury:
Worked example 2 — why not water. To balance the atmosphere with water instead of mercury, equate the two pressures:
A tube over ten metres tall — three storeys high. **Mercury does the job in cm because it is times denser**, and m exactly.
Worked example 3 — the thrust on a barometer's cross-section. A tube of internal area carries
Mercury is chosen for four reasons. It is very dense, keeping the tube short. It does not wet glass, so the column's top is clean and easy to read. It does not evaporate appreciably, so the space above stays a vacuum. And it is opaque and shiny, so the level is visible.
The tube's width and shape make no difference to the reading. A wide barometer and a narrow one both read cm, because contains no area — the hydrostatic result of the previous part of this chapter, appearing in an instrument. Tilting the tube does not change it either: the mercury runs further along the tube but the vertical height stays cm, since is measured vertically.
Air leaking into the space above spoils the instrument. That trapped air would exert its own pressure downward, so the column would stand lower than it should and the barometer would under-read. A barometer with air above the mercury is called a faulty barometer, and checking that the space is a vacuum is part of setting one up.
Why does pressure fall as you go up, and what is that used for?
Because there is less air above you — atmospheric pressure at any height is caused by the weight of the air stacked above that point, and climbing leaves some of it below.
Worked comparison. At sea level a barometer reads about cm of mercury. On a high hill it might read cm, and higher still cm. Converting the last one:
about four fifths of the sea-level value.
The fall is not a straight line, though. Air is a gas and therefore compressible, so the lower layers are squeezed by the weight of everything above and are much denser than the upper ones. That means the pressure drops quickly near the ground, where the air is dense, and more gradually higher up where it is thin.
This is where air differs from a liquid. For water, is exact with a constant , so the pressure rises in strict proportion to depth — double the depth, double the pressure, as the previous part of this chapter showed. **For air, itself changes with height, so no such simple proportion holds and the relationship curves.
The altimeter. An aneroid barometer — a sealed metal box that flexes as the pressure outside changes — can be calibrated to read height instead of pressure, since the two are linked. Fitted to an aircraft it is called an altimeter, and it tells the pilot the altitude by measuring the air pressure outside.
Why a pilot resets it. Since the sea-level pressure itself changes from day to day with the weather, an altimeter has to be set to the local value before each flight, or it will read the wrong height. The instrument measures pressure and infers height, so anything that changes the pressure without changing the height fools it.
The barometer in weather forecasting. Because pressure changes accompany weather systems, the trend of a barometer is informative:
- A sudden fall warns of a storm
- A gradual fall suggests rain is coming
- A rise indicates fair, dry weather
- A steady high reading means settled conditions
- A steady low reading with little change suggests continued unsettled weather
It is the change that matters, not the value.** A single reading of cm means little on its own; the same reading after a fall from cm means something quite different from the same reading after a rise from cm. A forecaster reads the barometer twice, and that is why ships and observatories record it at fixed intervals.
Everyday consequences of the fall with altitude.
- Nose bleeds and ear discomfort at high altitude, as the pressure inside the body exceeds the pressure outside
- A pen may leak in an aircraft for the same reason
- Cooking takes longer on a mountain, because water boils at a lower temperature when the pressure on it is less — which is why a pressure cooker, raising the pressure deliberately, does the opposite
- Climbers carry oxygen, since the thinner air supplies less of it per breath
- Aircraft cabins are pressurised, because the outside pressure at cruising height is far too low to breathe
Worked comparison. At sea level a barometer reads about cm of mercury. On a high hill it might read cm, and higher still cm. Converting the last one:
about four fifths of the sea-level value.
The fall is not a straight line, though. Air is a gas and therefore compressible, so the lower layers are squeezed by the weight of everything above and are much denser than the upper ones. That means the pressure drops quickly near the ground, where the air is dense, and more gradually higher up where it is thin.
This is where air differs from a liquid. For water, is exact with a constant , so the pressure rises in strict proportion to depth — double the depth, double the pressure, as the previous part of this chapter showed. **For air, itself changes with height, so no such simple proportion holds and the relationship curves.
The altimeter. An aneroid barometer — a sealed metal box that flexes as the pressure outside changes — can be calibrated to read height instead of pressure, since the two are linked. Fitted to an aircraft it is called an altimeter, and it tells the pilot the altitude by measuring the air pressure outside.
Why a pilot resets it. Since the sea-level pressure itself changes from day to day with the weather, an altimeter has to be set to the local value before each flight, or it will read the wrong height. The instrument measures pressure and infers height, so anything that changes the pressure without changing the height fools it.
The barometer in weather forecasting. Because pressure changes accompany weather systems, the trend of a barometer is informative:
- A sudden fall warns of a storm
- A gradual fall suggests rain is coming
- A rise indicates fair, dry weather
- A steady high reading means settled conditions
- A steady low reading with little change suggests continued unsettled weather
It is the change that matters, not the value.** A single reading of cm means little on its own; the same reading after a fall from cm means something quite different from the same reading after a rise from cm. A forecaster reads the barometer twice, and that is why ships and observatories record it at fixed intervals.
Everyday consequences of the fall with altitude.
- Nose bleeds and ear discomfort at high altitude, as the pressure inside the body exceeds the pressure outside
- A pen may leak in an aircraft for the same reason
- Cooking takes longer on a mountain, because water boils at a lower temperature when the pressure on it is less — which is why a pressure cooker, raising the pressure deliberately, does the opposite
- Climbers carry oxygen, since the thinner air supplies less of it per breath
- Aircraft cabins are pressurised, because the outside pressure at cruising height is far too low to breathe
Exam tip
Exam tip: square the radii, and quote standard pressure three ways
In a hydraulic problem the multiplication factor is the AREA ratio. If radii are given, square them first: radii cm and cm give a factor of , not .
**Use and state Pascal's law as the reason.
Check the energy** when a force ratio looks large: J. Force is multiplied, energy is not.
**Use the volume condition for distance questions.
Say why liquids and not gases — a liquid is practically incompressible, so the push transmits at once.
For brakes, the point is EQUAL transmission to all four wheels, not only the multiplication.
Quote standard atmospheric pressure three ways**: cm of mercury, Pa, bar. Convert with using .
**A water barometer would need m — show the calculation, since it is the standard "why mercury" answer.
The barometer's tube width and tilt do not change the reading** — is the vertical height.
Air above the mercury makes a barometer read LOW.
For an altimeter say it measures pressure and infers height, and for forecasting say the trend matters, not the single value.
And remember air is compressible, so pressure does not fall in proportion to height the way liquid pressure rises with depth.
**Use and state Pascal's law as the reason.
Check the energy** when a force ratio looks large: J. Force is multiplied, energy is not.
**Use the volume condition for distance questions.
Say why liquids and not gases — a liquid is practically incompressible, so the push transmits at once.
For brakes, the point is EQUAL transmission to all four wheels, not only the multiplication.
Quote standard atmospheric pressure three ways**: cm of mercury, Pa, bar. Convert with using .
**A water barometer would need m — show the calculation, since it is the standard "why mercury" answer.
The barometer's tube width and tilt do not change the reading** — is the vertical height.
Air above the mercury makes a barometer read LOW.
For an altimeter say it measures pressure and infers height, and for forecasting say the trend matters, not the single value.
And remember air is compressible, so pressure does not fall in proportion to height the way liquid pressure rises with depth.
Did you know
Why the atmosphere sets a ceiling on every suction pump
A hand pump on a well does not pull water up. It lowers the pressure inside the pipe, and the atmosphere pushes the water up to fill the space.
That matters, because the atmosphere has only so much push available. The most it can manage is a column of water whose own pressure equals atmospheric pressure:
So no suction pump, however well made, can raise water from a well deeper than about ten metres. Make the pump stronger, make the seals perfect, evacuate the pipe completely — the limit does not move, because it was never a property of the pump.
That is a genuinely unusual kind of limit. Most engineering limits can be pushed by better design; this one is set by the weight of the air outside, and the only way past it is to stop relying on suction.
Which is exactly what deep wells do. A submersible pump sits at the bottom and pushes the water up, and a pushing pump has no such ceiling — it can drive water as high as its motor allows. Multi-stage pumps do the same thing in steps.
The same ceiling explains the shape of a barometer. A water barometer would be a tube m tall with the water column always near its limit, while mercury at times the density does the same job in cm.
And it explains why a very long drinking straw does not work. Somewhere past ten metres of straw the drink would refuse to rise no matter how hard you sucked — and it would refuse for the same reason the pump does, because you are not pulling the liquid at all. The atmosphere is pushing it, and it has a fixed amount of push to give.
That matters, because the atmosphere has only so much push available. The most it can manage is a column of water whose own pressure equals atmospheric pressure:
So no suction pump, however well made, can raise water from a well deeper than about ten metres. Make the pump stronger, make the seals perfect, evacuate the pipe completely — the limit does not move, because it was never a property of the pump.
That is a genuinely unusual kind of limit. Most engineering limits can be pushed by better design; this one is set by the weight of the air outside, and the only way past it is to stop relying on suction.
Which is exactly what deep wells do. A submersible pump sits at the bottom and pushes the water up, and a pushing pump has no such ceiling — it can drive water as high as its motor allows. Multi-stage pumps do the same thing in steps.
The same ceiling explains the shape of a barometer. A water barometer would be a tube m tall with the water column always near its limit, while mercury at times the density does the same job in cm.
And it explains why a very long drinking straw does not work. Somewhere past ten metres of straw the drink would refuse to rise no matter how hard you sucked — and it would refuse for the same reason the pump does, because you are not pulling the liquid at all. The atmosphere is pushing it, and it has a fixed amount of push to give.
Exam relevance
How are Pascal's law and atmospheric pressure tested in JEE Main and NEET?
Because Pascal's law is the basis of every hydraulic numerical, and the barometer is the standard setting for pressure-measurement problems.
This is the foundation for Class 11 Physics Mechanical Properties of Fluids, examined in JEE Main and NEET. Pascal's law appears there in the same form, and the hydraulic-lift calculation is used essentially unchanged. The energy check performed on this page becomes the formal statement that a hydraulic machine has a mechanical advantage greater than one and an efficiency of at most one — and questions that ask for the work done at both pistons are testing exactly that distinction.
Gauge pressure and absolute pressure are named in Class 11, and they are the two readings separated on this page. Absolute pressure is the total, ; gauge pressure is the excess over atmospheric, which is what a tyre gauge or a manometer reads. Getting them the wrong way round is a recurring source of lost marks, and the habit of asking pressure due to the liquid, or total? is what prevents it.
Manometers and U-tubes are the standard question type, and they combine Pascal's law with the equal-level law from the previous part of this chapter. A mercury manometer measuring a gas pressure is the barometer argument applied to a different unknown.
Where the barometer's reasoning reappears. Class 11 Thermodynamics and Class 11 Chemistry States of Matter both use the atmosphere as a pressure unit, and the conversions quoted here — cm Hg, Pa, bar, and atm — are used constantly. NEET Biology uses the same ideas for breathing: air enters the lungs because the diaphragm lowers the pressure inside and the atmosphere pushes air in, which is the drinking-straw argument in a body.
The compressibility point matters later. Class 11 Chemistry's gas laws exist because a gas's density changes with pressure, and that is precisely why atmospheric pressure does not fall in proportion to height. **A liquid's and a gas's behaviour part company for a reason worth being able to state.
The boiling-point consequence** is examined in Class 11 Thermal Properties of Matter and in Chemistry: lower pressure means a lower boiling point, which is the mountain-cooking and pressure-cooker pair from the last section.
What the questions look like. For board work, expect state Pascal's law, calculate the force multiplication from areas or radii, explain hydraulic brakes, describe experiments proving atmospheric pressure, describe a mercury barometer and state standard pressure in three units, **show why a water barometer would need m, and explain the altimeter and weather forecasting. For JEE Main and NEET, expect manometer and U-tube numericals, gauge-against-absolute pressure, hydraulic problems, and the pressure-and-boiling-point link.
How board and competitive emphasis differ. A board paper rewards the described experiment and the three unit conversions written out. A competitive paper assumes the law and tests whether the area ratio and the sign of a gauge reading are handled correctly.
The single trap that costs the most marks. Using the ratio of the radii instead of the ratio of the areas** in a hydraulic problem. Radii of cm and cm give a factor of , and using makes the answer ten times too small — a plausible-looking number. **The defence is to write as its own line** before substituting any force, so the squaring cannot be skipped.
This is the foundation for Class 11 Physics Mechanical Properties of Fluids, examined in JEE Main and NEET. Pascal's law appears there in the same form, and the hydraulic-lift calculation is used essentially unchanged. The energy check performed on this page becomes the formal statement that a hydraulic machine has a mechanical advantage greater than one and an efficiency of at most one — and questions that ask for the work done at both pistons are testing exactly that distinction.
Gauge pressure and absolute pressure are named in Class 11, and they are the two readings separated on this page. Absolute pressure is the total, ; gauge pressure is the excess over atmospheric, which is what a tyre gauge or a manometer reads. Getting them the wrong way round is a recurring source of lost marks, and the habit of asking pressure due to the liquid, or total? is what prevents it.
Manometers and U-tubes are the standard question type, and they combine Pascal's law with the equal-level law from the previous part of this chapter. A mercury manometer measuring a gas pressure is the barometer argument applied to a different unknown.
Where the barometer's reasoning reappears. Class 11 Thermodynamics and Class 11 Chemistry States of Matter both use the atmosphere as a pressure unit, and the conversions quoted here — cm Hg, Pa, bar, and atm — are used constantly. NEET Biology uses the same ideas for breathing: air enters the lungs because the diaphragm lowers the pressure inside and the atmosphere pushes air in, which is the drinking-straw argument in a body.
The compressibility point matters later. Class 11 Chemistry's gas laws exist because a gas's density changes with pressure, and that is precisely why atmospheric pressure does not fall in proportion to height. **A liquid's and a gas's behaviour part company for a reason worth being able to state.
The boiling-point consequence** is examined in Class 11 Thermal Properties of Matter and in Chemistry: lower pressure means a lower boiling point, which is the mountain-cooking and pressure-cooker pair from the last section.
What the questions look like. For board work, expect state Pascal's law, calculate the force multiplication from areas or radii, explain hydraulic brakes, describe experiments proving atmospheric pressure, describe a mercury barometer and state standard pressure in three units, **show why a water barometer would need m, and explain the altimeter and weather forecasting. For JEE Main and NEET, expect manometer and U-tube numericals, gauge-against-absolute pressure, hydraulic problems, and the pressure-and-boiling-point link.
How board and competitive emphasis differ. A board paper rewards the described experiment and the three unit conversions written out. A competitive paper assumes the law and tests whether the area ratio and the sign of a gauge reading are handled correctly.
The single trap that costs the most marks. Using the ratio of the radii instead of the ratio of the areas** in a hydraulic problem. Radii of cm and cm give a factor of , and using makes the answer ten times too small — a plausible-looking number. **The defence is to write as its own line** before substituting any force, so the squaring cannot be skipped.
Key takeaways
Pascal's law, atmospheric pressure and the barometer: quick revision
- Pascal's law: pressure applied to an enclosed liquid is transmitted equally and undiminished in all directions and to the walls.
- ****, so — the multiplication factor is the area ratio.
- N on gives Pa, and on that gives ** N** — a factor of .
- Radii must be squared: cm and cm give a factor of , so N lifts N.
- Lifting N with areas and needs only N.
- Distances: , so a cm lift needs m of push at a factor of .
- Energy is unchanged: J. Force is multiplied, energy is not.
- Hydraulic brakes transmit the pedal pressure equally to all four wheels, so the car does not swerve.
- Liquids are used because they are practically incompressible — a trapped air bubble ruins a brake system.
- Atmospheric pressure is caused by the weight of the air above; about Pa at sea level, giving N on a palm.
- It is not felt because it acts equally from every direction, inside and out.
- Demonstrations: a rubber sucker, a drinking straw, an inverted glass on a card, a collapsing tin, joined hemispheres.
- Consequences: a syringe, a dropper, a fountain-pen filler, a well pump, and a sealed oil tin that needs two holes to pour.
- A mercury barometer: a metre-long tube filled with mercury and inverted into a trough; the column falls to about cm with a vacuum above.
- **It stops where equals atmospheric pressure** — used backwards.
- Standard pressure three ways: cm Hg Pa bar.
- A reading of cm gives Pa; cm gives Pa.
- **A water barometer would need m**, since — and .
- Mercury is chosen for its high density, for not wetting glass, for not evaporating, and for being easy to see.
- Tube width and tilt do not change the reading; is the vertical height. Air above the mercury makes it read low.
- Pressure falls with altitude because less air is above — but not in proportion, since air is compressible and denser near the ground.
- An altimeter is an aneroid barometer calibrated to read height, and must be reset for the day's sea-level pressure.
- Forecasting reads the trend: a sudden fall warns of a storm, a gradual fall of rain, a rise of fair weather, a steady high of settled conditions.
- Consequences of low pressure: ear discomfort, leaking pens, slower cooking, oxygen for climbers, pressurised cabins.
- **A suction pump cannot lift water beyond about m**, because the atmosphere does the pushing and has a fixed limit.
Press a rubber sucker onto a tile and work out roughly what force the atmosphere is applying to hold it there — then see whether you can pull it off with less.
- ****, so — the multiplication factor is the area ratio.
- N on gives Pa, and on that gives ** N** — a factor of .
- Radii must be squared: cm and cm give a factor of , so N lifts N.
- Lifting N with areas and needs only N.
- Distances: , so a cm lift needs m of push at a factor of .
- Energy is unchanged: J. Force is multiplied, energy is not.
- Hydraulic brakes transmit the pedal pressure equally to all four wheels, so the car does not swerve.
- Liquids are used because they are practically incompressible — a trapped air bubble ruins a brake system.
- Atmospheric pressure is caused by the weight of the air above; about Pa at sea level, giving N on a palm.
- It is not felt because it acts equally from every direction, inside and out.
- Demonstrations: a rubber sucker, a drinking straw, an inverted glass on a card, a collapsing tin, joined hemispheres.
- Consequences: a syringe, a dropper, a fountain-pen filler, a well pump, and a sealed oil tin that needs two holes to pour.
- A mercury barometer: a metre-long tube filled with mercury and inverted into a trough; the column falls to about cm with a vacuum above.
- **It stops where equals atmospheric pressure** — used backwards.
- Standard pressure three ways: cm Hg Pa bar.
- A reading of cm gives Pa; cm gives Pa.
- **A water barometer would need m**, since — and .
- Mercury is chosen for its high density, for not wetting glass, for not evaporating, and for being easy to see.
- Tube width and tilt do not change the reading; is the vertical height. Air above the mercury makes it read low.
- Pressure falls with altitude because less air is above — but not in proportion, since air is compressible and denser near the ground.
- An altimeter is an aneroid barometer calibrated to read height, and must be reset for the day's sea-level pressure.
- Forecasting reads the trend: a sudden fall warns of a storm, a gradual fall of rain, a rise of fair weather, a steady high of settled conditions.
- Consequences of low pressure: ear discomfort, leaking pens, slower cooking, oxygen for climbers, pressurised cabins.
- **A suction pump cannot lift water beyond about m**, because the atmosphere does the pushing and has a fixed limit.
Press a rubber sucker onto a tile and work out roughly what force the atmosphere is applying to hold it there — then see whether you can pull it off with less.