Hello, and welcome to today's physics lesson. In this session, we will explore Chapter Four: Pressure in Fluids and Atmospheric Pressure. We will begin by understanding what thrust and pressure really mean, then discover how liquids exert pressure and why that pressure changes with depth. We will learn about Pascal's law and its remarkable applications in hydraulic machines. Finally, we will turn our attention upward to examine atmospheric pressure, how we measure it, and how it shapes our weather and our lives. Let us begin.
Let us start with the basics: thrust and pressure. When you push against a wall, you apply a force. But when that force acts perpendicular, or normal, to a surface, we give it a special name: thrust.
Thrust is the force acting normally on a surface.
For any object resting on a surface, the thrust it exerts equals its weight. Thrust is a vector quantity, meaning it has both magnitude and direction. Its S.I. unit is the newton.
Now, thrust alone does not tell us everything about the effect of a force. Imagine standing on loose sand. When you stand on your feet, you sink. But when you lie down, you do not. The thrust, your weight, is the same in both cases. What changes is the area over which that thrust is distributed. This brings us to pressure.
Pressure is the thrust per unit area of surface.
Mathematically, pressure equals thrust divided by area.
Or, P = F/A, where P is pressure, F is thrust, and A is area.
Unlike thrust, pressure is a scalar quantity, it has no direction.
The S.I. unit of pressure is the pascal, abbreviated as Pa. One pascal equals one newton per square metre.
One pascal is the pressure exerted on a surface of area one square metre by a force of one newton acting normally on it.
Other common units include the bar, where one bar equals ten to the fifth pascals, and the atmosphere, where one atmosphere equals 1.013 times ten to the fifth pascals, equivalent to 76 centimetres of mercury.
From the formula, we see two ways to change pressure. For a given thrust, reduce the area to increase pressure. This is why nails have pointed ends, and why sharp knives cut better than blunt ones. Conversely, increase the area to decrease pressure. This is why railway tracks rest on broad sleepers, and why building foundations are wide.
Now let us turn to fluids, substances that can flow. Liquids and gases are both fluids. Unlike solids, which only exert pressure downward on their base, fluids exert pressure in all directions.
A fluid contained in a vessel exerts pressure at all points and in all directions.
If you make holes in the side of a water container, water spurts out sideways, proving that pressure acts horizontally too. And the deeper the hole, the farther the water travels, showing that pressure increases with depth.
This leads us to a fundamental formula. The pressure exerted by a liquid column depends on three things: the depth, the liquid's density, and gravity.
The pressure P at depth h in a liquid of density rho is given by: P = hρg.
Here, h is the vertical depth below the free surface, rho is the density of the liquid, and g is the acceleration due to gravity.
Let us understand why this formula works. Imagine a horizontal surface at depth h in a liquid. The pressure on it comes from the weight of the liquid column above it. The volume of this column is area times height, so its mass is area times height times density, and its weight is area times height times density times g. This weight, divided by the area, gives pressure equals h rho g. Notice that the pressure does not depend on the shape of the container or the total amount of liquid, only on the vertical depth.
In reality, we must also consider atmospheric pressure acting on the liquid's surface. So the total pressure at depth h equals atmospheric pressure P naught plus h rho g.
From this formula, we can state five important laws of liquid pressure. First, pressure increases with depth from the free surface. Second, at any given depth in a stationary liquid, pressure is the same at all points on a horizontal plane. Third, at any point, pressure is the same in all directions. Fourth, at the same depth, pressure is greater in denser liquids. Fifth, a liquid seeks its own level.
These laws explain many everyday phenomena. Dam walls are thicker at the bottom because pressure increases with depth. Water supply tanks are placed high to create sufficient pressure in taps. Sea divers wear protective suits because deep underwater, the total pressure far exceeds their blood pressure. A gas bubble rising from a lake bottom expands as it rises because the surrounding pressure decreases with decreasing depth.
Now we come to one of the most elegant principles in fluid mechanics: Pascal's law.
Pascal's law states that the pressure exerted anywhere in a confined liquid is transmitted equally and undiminished in all directions throughout the liquid.
This means if you increase pressure at one point in an enclosed fluid, every other point experiences that same increase.
This principle is the foundation of hydraulic machines. Consider two connected cylinders with pistons of different areas. A small force on the smaller piston creates pressure that is transmitted throughout the fluid. This same pressure, acting on the larger piston's greater area, produces a much larger force. The machine multiplies force.
Mathematically, if the small piston has area A one and force F one, and the large piston has area A two and force F two, then by Pascal's law: F₁/A₁ = F₂/A₂.
Therefore, F₂ = F₁ × (A₂/A₁). Since A two is greater than A one, F two exceeds F one.
Common applications include the hydraulic press, used for compressing cotton bales and extracting oils, the hydraulic jack for lifting vehicles, and hydraulic brakes in automobiles. In each case, a modest effort produces a powerful result.
Let us now lift our gaze to the atmosphere itself. Earth is enveloped by air extending about 300 kilometres upward. This air has weight, and that weight creates pressure on everything below.
The thrust exerted per unit area on Earth's surface due to the column of air is called atmospheric pressure.
At sea level, this equals about 100,000 newtons per square metre, or roughly one kilogram-force per square centimetre. We do not feel this enormous pressure because our blood pressure slightly exceeds it, creating a balance.
Atmospheric pressure can be demonstrated dramatically. Heat water in a sealed can until steam drives out the air, then seal it and cool it. The steam condenses, leaving very low pressure inside. The external atmospheric pressure crushes the can inward, proving air exerts real force.
We experience atmospheric pressure constantly. When you sip through a straw, you reduce pressure inside, letting atmospheric pressure push the liquid up. When a doctor fills a syringe, pulling the plunger creates low pressure, drawing in medicine. Rubber suckers stick to walls because pressing them expels air, allowing atmospheric pressure to hold them firm.
To measure atmospheric pressure, we use a barometer. The simple barometer, invented by Torricelli in 1643, uses a glass tube about one metre long, filled with mercury and inverted into a mercury trough. The mercury column falls until its height, about 76 centimetres, balances the atmospheric pressure. The space above the mercury is called the Torricellian vacuum.
Mercury is ideal for barometers because its high density means a manageable tube length, its vapour pressure is negligible, it does not wet glass, and its shiny surface is easy to see. Water would require a tube over ten metres tall and has other practical problems.
The Fortin barometer improves on the simple design with a leather cup and screw adjustment to set the mercury level precisely at a zero mark, plus a vernier scale for accurate reading. The aneroid barometer contains no liquid; it uses a partially evacuated metal box with a flexible diaphragm that moves with pressure changes, rotating a pointer over a calibrated scale. It is portable and convenient.
Atmospheric pressure decreases with altitude for two reasons. First, the height of air above you decreases, reducing the weight of the air column. Second, air density itself decreases with height, though not in a simple linear way. At the summit of Mount Everest, atmospheric pressure is only about 30 percent of its sea level value.
This variation has important consequences. At high altitudes, lower atmospheric pressure can cause difficulty breathing and nose bleeding, as blood pressure exceeds the external pressure. Fountain pens may leak because the air inside them, at higher pressure than the thin atmosphere, forces ink out.
Barometers also help predict weather. A sudden fall in barometric height suggests an approaching storm. A gradual fall indicates increasing moisture and possible rain. A gradual rise suggests drier weather approaching. A sudden rise indicates extremely dry conditions.
An altimeter is essentially an aneroid barometer calibrated to read altitude directly. Since pressure decreases predictably with height, measuring pressure reveals how high you are. The scale increases toward the left because pressure decreases as you ascend.
Let us recap the key takeaways from this chapter.
First, pressure equals thrust divided by area, and its S.I. unit is the pascal. Pressure increases when area decreases, and vice versa.
Second, fluids exert pressure in all directions, and liquid pressure at depth h is given by P equals h rho g, depending on depth, density, and gravity.
Third, Pascal's law states that pressure in a confined fluid transmits equally in all directions, enabling hydraulic machines to multiply force.
Fourth, atmospheric pressure results from the weight of air above us, equals about 76 centimetres of mercury at sea level, and decreases with increasing altitude.
Fifth, barometers measure atmospheric pressure, with mercury barometers being most accurate and aneroid barometers being most portable.
And sixth, changes in atmospheric pressure help us forecast weather and determine altitude.
That brings us to the end of our exploration of pressure in fluids and atmospheric pressure. You have learned how the same physical principles govern the water in your glass, the brakes in your car, and the air you breathe. Physics connects the everyday to the extraordinary. Keep questioning, keep observing, and keep discovering. Until next time, stay curious.