Pressure in Fluids and Atmospheric Pressure

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Questions and Answers

Explain how the concept of thrust applies when you stand on loose sand versus lying on it. Why do your feet sink in one case but not the other, even though your weight (thrust) is the same?

When standing, the thrust (weight) is concentrated on a smaller area (feet), resulting in high pressure, causing sinking. Lying down distributes the thrust over a larger area, reducing pressure and preventing sinking.

A container is filled with a liquid. Explain why the pressure at a specific depth is the same regardless of the shape or size of the container.

Pressure at a specific depth in a liquid depends only on the depth, density of the liquid, and acceleration due to gravity, but is independent of the shape or size of the container.

Two containers are filled with different liquids. If the pressure at the bottom of both containers is the same, what can you conclude about the densities and heights of the liquids?

If the pressures are equal, then the product of the density and height ($h\rho$) must be the same for both liquids, meaning a higher density liquid will have a smaller height and vice versa.

A balloon filled with air is submerged in water. Describe how the pressure exerted by the water on the balloon changes as it descends deeper, and relate this to the balloon's volume.

<p>As the balloon descends, the water pressure increases, compressing the air inside. This decreases the balloon's volume according to Boyle's Law, which states that volume is inversely proportional to pressure at a constant temperature.</p> Signup and view all the answers

Explain why the walls of a dam are constructed to be thicker at the bottom than at the top, relating this to the properties of liquid pressure.

<p>Liquid pressure increases with depth. Therefore, the walls of a dam are made thicker at the bottom to withstand the greater pressure exerted by the water at deeper levels.</p> Signup and view all the answers

Describe the relationship between the pressure inside a bubble and its size as it rises from the bottom of a lake. Use physical principles to explain this phenomenon.

<p>As a bubble rises, the external pressure decreases, causing the bubble to expand. This is because the total pressure on the bubble equals atmospheric pressure plus the water pressure ($h\rho g$). As $h$ decreases (bubble rises,), external pressure decreases.</p> Signup and view all the answers

Why do divers need to wear special protective suits when working in deep sea environments, and how do these suits function?

<p>Divers need protective suits because the pressure increases significantly with depth. The suits maintain internal pressure equal to or near atmospheric pressure to counteract the external water pressure, preventing the diver from being crushed.</p> Signup and view all the answers

Explain Pascal's Law and its significance in the functioning of a hydraulic lift or brake system. Focus on the relationship between force, pressure, and area.

<p>Pascal's Law states that pressure applied to a confined fluid is transmitted equally throughout the fluid. In hydraulic systems, a small force applied over a small area creates pressure that is transmitted to a larger area, resulting in a proportionally larger force.</p> Signup and view all the answers

Explain why it is easier to cut an object with a sharp knife compared to a blunt one, even if the same amount of force is applied.

<p>A sharp knife concentrates the applied force over a very small area, creating high pressure. This high pressure exceeds the material's resistance, causing it to separate. A blunt knife distributes force over a larger area, creating low pressure.</p> Signup and view all the answers

If a submarine changes its depth, how does this affect the pressure experienced on its surface? Explain the relationship, and discuss how submarines are designed to withstand these changes.

<p>As a submarine changes depth, the pressure on its surface changes linearly with depth according to $P = h\rho g$. Submarines are built with reinforced hulls to withstand the immense pressures at great depths without collapsing.</p> Signup and view all the answers

Consider a scenario where you have two barometers, one using mercury and the other using water. Explain why mercury is preferred over water in barometers, detailing the reasons based on their respective properties.

<p>Mercury is preferred due to its high density, which results in a manageable barometer height. It also has low vapour pressure, is opaque for easy reading, and does not wet the glass tube, thus giving a more accurate measurement.</p> Signup and view all the answers

Explain how the presence of air in the Torricellian vacuum of a simple barometer would affect the accuracy of atmospheric pressure readings.

<p>The presence of air in the Torricellian vacuum would exert its own pressure, lowering the mercury column's height and thus underestimating the actual atmospheric pressure.</p> Signup and view all the answers

An aneroid barometer doesn't use liquid. Explain its working principle and how it measures atmospheric pressure. Focus on the role of the metallic box and its calibration.

<p>An aneroid barometer uses a partially evacuated metallic box that expands or contracts with changes in atmospheric pressure. These movements are mechanically linked to a pointer on a calibrated scale that indicates pressure directly.</p> Signup and view all the answers

Describe how atmospheric pressure changes with altitude and explain the two main factors that contribute to this change.

<p>Atmospheric pressure decreases with altitude due to (i) a reduction in the height of the air column above, causing a linear decrease, and (ii) a non-linear decrease in air density.</p> Signup and view all the answers

Explain why a fountain pen might start leaking when taken to a high altitude.

<p>At high altitudes, the external atmospheric pressure is lower than it is on the ground. Thus a greater pressure inside the refill of the pen as it was filled at ground level. Ink is then forced out of the pen.</p> Signup and view all the answers

Explain how a barometer can be used to forecast weather changes, specifically detailing what a sudden drop in barometric height indicates and why.

<p>A sudden drop in barometric height indicates a rapid decrease in atmospheric pressure, suggesting the imminent arrival of a storm or cyclone. This is because low pressure systems are often associated with unstable weather conditions.</p> Signup and view all the answers

Explain how an altimeter works, relating its functionality to the principles of atmospheric pressure and calibration.

<p>An altimeter is an aneroid barometer calibrated to measure altitude. It uses the principle that atmospheric pressure decreases with increasing height. The scale is calibrated to display altitude based on the measured atmospheric pressure.</p> Signup and view all the answers

In a hydraulic system, if the area of the input piston is doubled while the output piston area remains constant, what changes would you observe in the force multiplication and the distance the output piston moves for a given input displacement?

<p>Doubling the input piston area halves the pressure for the same input force, therefore halving the output force. With a constant output piston area and force halved, the output distance correspondingly doubles, conserving energy.</p> Signup and view all the answers

Two objects of equal weight are placed on a hydraulic lift. One object has a larger base area in contact with the piston than the other. Will the hydraulic lift exert more force on one object compared to the other? Explain why or why not.

<p>The hydraulic lift will exert the same force on both objects. Since the objects weigh the same, they exert an equal force on the output piston of the hydraulic lift regardless of their respective base areas.</p> Signup and view all the answers

Calculate the force needed on the narrow piston ($A_1$) of a hydraulic machine to overcome a force of $100 \text{ N}$ on the wider piston ($A_2$), given the areas of cross-section are in the ratio $A_1:A_2 = 1:10.

<p>The force needed on the narrow piston is $10 \text{ N}$.</p> Signup and view all the answers

For a hydraulic press with a press plunger area of $4 \text{ m}^2$, determine the force on the pump plunger area, given an area of $0.01 \text{ m}^2$ and requirement to overcome a resistive load of $400 kgf$ on it.

<p>The force required on the pump plunger is $1 \text{ kgf}$.</p> Signup and view all the answers

Explain why, in a hydraulic braking system, the pressure exerted is the same on all wheels of the vehicle connected to the same pipeline, and how this relates to Pascal's Law.

<p>According to Pascal's Law, pressure applied to a confined fluid is transmitted equally throughout the fluid. In a hydraulic braking system, the pressure from the master cylinder is transmitted equally to all wheel cylinders via the brake fluid. Thus resulting in equivalent forces.</p> Signup and view all the answers

What does it mean if the atmospheric pressure at a place is 75 cm of Hg, and how would you express this pressure in $N/m^2$, given the density of Hg is 13.6 g/cm$^3$ and g = 9.8 m/s$^2$?

<p>A atmospheric pressure equal to 75 cm of Hg means that the local atmospheric pressure is sufficient to support a column of mercury 75 cm high. This value expressed in N/m$^2$ is {$9.996 \times 10^4$} N/$m^2$.</p> Signup and view all the answers

The pressure at the top of a dam is $P_1$ and at a depth h inside the water (density p) is $P_2$. How are these pressure values related? What equation represents that relationship?

<p>The pressure values are related by the formula representing the additional pressure due to the water column at depth h. In other words, ( P_2 - P_1 = \rho g h ).</p> Signup and view all the answers

How does the pressure exerted by a sharp wedge or cutting tool demonstrate the principles of thrust and pressure? Explain.

<p>A sharp wedge concentrates the applied force over a very small area, creating high pressure. When this high pressure exceeds the compressive strength of the other material, it induces a fracture through it.</p> Signup and view all the answers

Flashcards

What is Thrust?

Force acting normally on a surface.

What is Pressure?

Thrust per unit area of a surface.

What is a Pascal?

Pressure exerted on a surface of 1 m² by a force of 1 N.

What are Fluids?

Liquids and gases, substances that can flow.

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What is P = hpg?

Pressure exerted by a liquid column due to depth, density, and gravity.

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What is Pascal's Law?

Pressure applied to a confined liquid is transmitted equally in all directions.

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What is a Hydraulic Machine?

A machine that multiplies force using Pascal's Law.

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Examples of Pascal's Law?

Hydraulic press, hydraulic jack, hydraulic brakes

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What is a Barometer?

Used to measure atmospheric pressure.

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Atmospheric Pressure

The pressure exerted by the air column above the Earth's surface.

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What is an Altimeter?

Instrument that measures altitude by sensing atmospheric pressure.

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Liquid Pressure Rules?

Pressure is the same at all points on a horizontal plane in a stationary liquid.

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Liquids Transmit?

Pressure is exerted equally and undiminished in all directions.

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What is Nose Bleeding?

Occurs due to excess blood pressure at high altitudes.

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Air Column Weight?

The weight of air column exerts a thrust on the earth surface

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Study Notes

Pressure in Fluids and Atmospheric Pressure

  • Pressure changes with depth are calculated using the formula P = hpg.
  • The transmission of pressure in liquids is also examined, along with atmospheric pressure.
  • The scope includes understanding thrust and pressure, their units, pressure exerted by liquid columns (P = hpg).
  • Real-world examples such as the broadness of a dam's base and diver's suits illustrate the principles.
  • The syllabus covers Pascal's law, atmospheric pressure, its manifestations, variation with altitude, and applications in weather forecasting and altimeters.

Thrust and Pressure

  • Thrust is a force acting normally on a surface.
  • The thrust exerted by a body on a surface equals its weight.
  • Thrust is a vector quantity.
  • The S.I. unit of thrust is the newton (N), and the C.G.S. unit is the dyne (1 N = 10^5 dynes).
  • In the M.K.S. system, the gravitational unit is kgf, while in the C.G.S. system, it's gf (1 kgf = 9.8 N, 1 gf = 980 dynes).
  • Pressure is the thrust per unit area of surface.
  • Mathematically, Pressure = Thrust/Area or P = F/A.
  • Pressure is a scalar quantity.
  • The S.I. unit of pressure is newton per metre² (N m⁻²), also known as pascal (Pa), where 1 Pa = 1 N m⁻².
  • One pascal is the pressure exerted on a 1 m² area by a 1 N force.
  • In C.G.S. units, pressure is measured in dyne cm⁻² (1 dyne cm⁻² = 0.1 N m⁻² or 1 N m⁻² = 10 dyne cm⁻²).

Units and Factors Affecting Pressure

  • The pressure unit is gf cm⁻² if thrust is in gf and area in cm².
  • Other pressure units include bar and millibar (1 bar = 10^5 N m⁻², 1 millibar = 10² N m⁻²).
  • Atmospheric pressure is expressed via the height of a mercury column in a barometer.
  • At normal temperature and pressure, the barometric height at sea level is 0.76 m of Hg, defined as one atmosphere (atm).
  • 1 atmosphere (atm) equals 0.76 m of Hg or 1.013 × 10^5 Pa.
  • The torr is used as a pressure unit, named after Torricelli (1 torr = 1 mm of Hg, 1 atm = 760 torr).
  • Pressure on a surface depends on the applied thrust and the area.

Increasing and Decreasing Pressure

  • Pressure on a surface increases with thrust, and decreases as area increases.
  • Increasing pressure involves reducing the surface area, as seen with pointed nails and sharp cutting tools.
  • Decreasing pressure involves increasing the surface area, like wide wooden sleepers under railway tracks and wider building foundations.

Pressure in Fluids

  • Fluids are substances that can flow, including liquids and gases.
  • Fluids exert pressure in all directions due to their tendency to flow.
  • A fluid in a vessel exerts pressure at all points.

Liquid Pressure and Pressure in a Liquid Column

  • Liquid pressure increases with depth below the free surface.
  • The pressure exerted by a liquid column is defined as P = hpg.
  • P = depth × density of liquid × acceleration due to gravity
  • The total pressure in a liquid is the sum of atmospheric pressure and the pressure due to the liquid column (Total pressure = Po + hpg).
  • Liquid pressure depends directly on depth, liquid density, and acceleration due to gravity.
  • Liquid pressure is independent of the shape/size of the vessel and the surface area on which it acts.

Laws of Liquid Pressure and Consequences of Liquid Pressure

  • Liquid pressure increases with depth.
  • Pressure is the same at all points on a horizontal plane in a stationary liquid.
  • Pressure is the same in all directions about a point in a liquid.
  • At the same depth, pressure varies with liquid density.
  • A liquid seeks its own level.
  • Due to higher density: pressure in seawater is greater than in river water at the same depth.
  • Dams are thicker at the bottom because pressure increases with depth.
  • Water supply tanks are placed high to increase water pressure in taps.
  • Divers wear protective suits to withstand high pressure in deep sea.
  • Gas bubble size increases as it rises in water due to decreasing pressure.

Pascal's Law and Hydraulic Machines

  • Pascal's law states that pressure exerted in a confined liquid is transmitted equally and undiminished in all directions.
  • Hydraulic machines apply Pascal's law to transmit pressure in liquids.
  • A small force on a small piston produces a large force on a bigger piston.
  • F1/A1=F2/A2 in a hydraulic machine,
  • a small force F1 applied on the smaller piston A can be used to produce a large force F2 on the bigger piston B

Hydraulic Press

  • A hydraulic press is a hydraulic machine that works on Pascal's law.
  • Uses: pressing cotton bales and goods like quilts and books, extracting juice from sugarcane and sugar beet, squeezing oil, and engraving monograms.
  • Hydraulic jacks works on Pascal's principle by a force is applied, increasing pressure, and lifting a platform.
  • Used for lifting heavy vehicles in service stations.

Hydraulic Brakes

  • Hydraulic brakes are also based on Pascal's principle
  • To apply brakes, pressure is exerted on the brake pedal, which transmits pressure through liquid to the wheel cylinder.
  • Equal pressure is exerted on all vehicle wheels connected to the pipeline.
  • Mechanical Advantage (M.A.) is greater than 1
  • Velocity Ratio is greater than 1.
  • Hence a hydraulic machine acts like a force multiplier.

Atmospheric Pressure

  • The Earth is surrounded by atmosphere (air up to ~300 km).
  • Atmospheric pressure is the thrust exerted per unit area due to the air column.
  • On Earth's surface the atmospheric pressure is ~1 kgf per cm², or 10^5 N m⁻².
  • The atmosphere exerts massive thrust on our bodies, but it is balanced by blood pressure.
  • At high altitudes, lower atmospheric pressure causes nosebleeds due to higher blood pressure.

Demonstration of Atmospheric Pressure

  • Atmospheric pressure is demonstrated by the collapsing tin can experiment.
  • After boiling water in the can, sealing it, and pouring cold water, the can collapses due to external atmospheric pressure.

Consequences of Atmospheric Pressure

  • Sucking a drink with a straw involves decreasing air pressure inside the straw, allowing atmospheric pressure to push the drink up.
  • Syringes fill with liquid when the plunger is pulled, decreasing pressure inside.
  • Fountain pens work due to atmospheric pressure filling the pen with ink.
  • Rubber suckers create a vacuum when pressed against a wall.
  • Siphon systems use pressure differences.

Barometers for Measuring Atmospheric Pressure

  • A barometer is an instrument to measure atmospheric pressure.
  • Types: simple, Fortin, and aneroid barometers.
  • Torricelli designed a simple barometer using mercury.
  • Barometric height is ~0.76 m (or 76 cm) of mercury at normal temperature/pressure/sea level.
  • Barometric height changes occur solely with atmospheric pressure variations.
  • Barometric height remains constant despite shape, depth of a tube, changed, or tilting.

Using Mercury in a Barometer

  • Mercury is preferrable as a barometric liquid because of its high density.
  • The vapor pressure of mercury is negligable.
  • Water is tranparent, so its surface is difficult ti be seen.

Variation of Atmospheric Pressure and Weather Forecasting

  • Atmospheric pressure decreases with altitude due to decreasing air column height and air density.
  • Weather can be predicted by atmospheric pressure and its changes, as barometers are used.
  • Sudden drops in barometric height indicate storms or cyclones.
  • Gradual decrease points to increasing moisture and rain.
  • Gradual increases mean decreasing moisture and dry weather.
  • Sudden rises indicate extremely dry conditions.
  • The weather will remain unchanged without any abrupt changes.

Altimeters

  • Since atmospheric pressure decreases with height above sea level.
  • Altimeters are used in aircraft to measure altitude.

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