Concept: It is an application of the law of conservation of energy to fluids in motion.

Speed-Pressure Relationship: If the speed of a fluid increases, its pressure decreases, and if its speed decreases, its pressure increases.

Equation: It is expressed in an equation that relates the kinetic energy, gravitational potential energy, and flow energy (pressure) of the fluid.

Applications: It is used to explain phenomena such as the lift of aircraft and the operation of flow meters.

Definition: In probability, a process is a sequence of random trials (called "Bernoulli trials") where each trial has only two possible outcomes, such as "success" or "failure."

Example: A coin toss that can always result in "heads" or "tails" is a Bernoulli process.

Surface tension is the property of a liquid that make it's surface behave like a strethed elastic sheet. I happens because molecules at the surface experience stronger cohesive forces pulling them inward creating a sort of "skin" on the liquid.

🌟Visual example: water droplets form spheres because this shape minimizes Surface area and energy.

🌿Capillarity

Capillarity is the ability of a liquid to flow in narrow spaces without the help of external forces (like Gravity). It result from the combination of cohesion (molecules sticking to each other) and adhesion (molecules sticking to the walls to the tube or material).

🌱Natural example: water rises through the tiny vessels in plants from roots to leaves.

Life and Work

Birth and Death: He was born in Syracuse, Sicily, around 287 BC and died in the same city during the Roman capture in 212 or 211 BC.

Mathematics: He made important discoveries in geometry, such as the relationship between the volume of a sphere and its cylinder, and he anticipated integral calculus.

Inventions: He is credited with inventing Archimedes' screw for lifting water and the hydrostatic principle (Archimedes' Principle).

Practical Applications: His inventions and principles had practical applications, such as their use in warfare during the defense of Syracuse, where his defense machines were used, or the creation of a device to measure density."

La densidad es la relación entre la masa de un objeto y el volumen que ocupa, indicando qué tan "apretadas" están sus moléculas en un espacio determinado. Se calcula dividiendo la masa (m) entre el volumen (V), es decir, D = m/V, y sus unidades comunes son g/cm³ o kg/m³.Density is the ratio of an object's mass to the volume it occupies, indicating how tightly packed its molecules are in a given space. It is calculated by dividing the mass (m) by the volume (vo) of the object.

The density of water depends on its temperatur

(*´꒳`*) Ships carry most of the world's oil, but accidents such as oil spills often occur, which can harm marine life, birds, and nearby human populations.

Density is defined as the compactness of a substance's mass and is expressed as mass per volume (g/cm³). Different substances with the same volume can have different masses due to their density.

Objects float or sink depending on their density relative to the fluid. If the object's density is greater than that of the fluid, it sinks; if it's less, it floats. For example, a steel anchor sinks because its density is greater than that of water, while wood floats because it's less dense. (๑╹ω╹๑)

🎀Surface Tension🎀

🧸Definition: Surface tension is the property of a liquid that makes its surface act like a stretched elastic sheet.

Cause: Molecules inside a liquid are attracted in all directions, but molecules at the surface have no molecules above them, so they are pulled inward → this creates tension on the surface.🧸

Units: Newton per meter (N/m).

💗 Examples in real life:

🫶🏻Small insects (like water striders) walking on water.🫶🏻

🫶🏻Formation of spherical water

droplets🫶🏻

🫶🏻A needle or paper clip floating on water when placed gently.🫶🏻

🎀 Capillarity🎀

🧸Definition: Capillarity is the ability of a liquid to rise (or fall) in a narrow tube due to the combination of cohesive forces (liquid–liquid attraction) and adhesive forces (liquid–solid attraction).

Relation to surface tension: Capillarity happens because of surface tension and adhesion.🧸

Equation for capillary rise (Jurín’s Law):

h = \frac{2T \cos \theta}{\rho g r}

= height the liquid rises

= surface tension

= contact angle

= density of liquid

= acceleration due to gravity

= radius of the capillary tube

💗 Examples in real life:

🫶🏻Water rising in a thin straw or a capillary tube.🫶🏻

🫶🏻Movement of water from roots to leaves in plants.🫶🏻

🫶🏻Oil rising in the wick of a lamp.🫶🏻

🫶🏻Paper towel soaking up water.🫶🏻

Real-world applications and examples

Airplane lift: Airplane wings are designed to make air travel faster over the curved top surface than the flatter bottom surface. This difference in speed creates a region of lower pressure above the wing and higher pressure below, resulting in an upward lifting force.

Venturi effect: A narrowing in a pipe causes the fluid to speed up, which creates a drop in pressure. This effect is used in devices like venturi meters, carburetors, and aspirators.

Curveball: A baseball pitcher can make a ball curve by giving it a spin. The spin causes the air on one side of the ball to move faster than the air on the other side. This creates a pressure difference that forces the ball to curve.

Sailboats: A sail's curved shape forces air to travel faster over one side than the other, creating a pressure difference that propels the boat forward.

Chimney draft: Wind blowing across the top of a chimney lowers the air pressure there. The higher pressure at the base of the chimney then pushes smoke and air upward, helping to draw it out.

. Capillarity is a direct result of surface tension and the interplay between a liquid's cohesive and adhesive properties.🧸

🎀Surface tension🎀

Surface tension is the tendency of a liquid to shrink into the minimum possible surface area. 🍓

Capillarity🧸

Definition:

🍓The ability of a liquid to flow upwards in narrow spaces, such as a narrow tube, against the force of gravity. 🍓

Cause:

The interaction between three forces: 

• Cohesive forces: Attraction between liquid molecules. 

• 
  

• 🎀Adhesive forces: Attraction between the liquid molecules and the solid surface of the tube. 🎀

such as a sofa in the living room or our feet on the ground when we stand, exert pressure donwnwards. Example of pressure in Liquid:

Like water, exert pressure in all directions. Example of Pressure in Gas:

When we blow air into ballon, the ballon expands because the air molecules inside are pushing against the flexible walls of the ballon.

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Density shows how compact or “heavy for its size”something is

Density is a physical property of matter that tells us how much mass is packed into a certain volume

Example: a gold ring

Imagine you found a gold ring and you want to check if its real or just painted metal

One way to figure it out is by density

Measure the mass and find the volume in

He also invented several very useful machines. One of the most important was the Archimedes’ screw, which was used to raise water and could be applied in agriculture or to drain flooded areas. Another of his studies was about the lever, showing how with little effort it was possible to move very heavy objects. This is where his famous phrase comes from: “Give me a place to stand, and I will move the world.”

In addition to his scientific contributions, Archimedes also dedicated himself to military engineering. When the Romans attacked Syracuse, his hometown, he designed catapults, pulley systems, and even mirrors that, according to some stories, could concentrate sunlight to set enemy ships on fire. Although the story about the mirrors is debated, it shows the creativity that defined him.

In the field of mathematics, he carried out very advanced calculations for his time: he studied areas, volumes, geometric figures, and provided one of the most accurate approximations of the number π.

In conclusion, Archimedes was a man who combined knowledge with practice. His inventions and theories not only solved problems of his time but also laid the foundations for the science and technology we still use today.

Buoyancy is basically the force of water.The force of water is what makes some objects float. If the weight of object is greater than the force of the water, it will rot float. However, if the force of the water is greater than the weight of the object, it will flout. It also depends on the shape and content of the object. For example, if the object is made of a heavy material and its interior is also heavy, it will not float. However, if the object is hollow and made of light material,the force of the object will float.

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Key Characteristics of Density

Formula:

Density is defined by the formula Density = Mass / Volume.

Units:

Common units for density include grams per cubic centimeter (g/cm³) for solids and liquids, or kilograms per cubic meter (kg/m³) in the International System of Units (SI).

Intrinsic Property:

Density is an intrinsic property of a substance, meaning it does not change with the amount of material. For instance, a large bar of aluminum has the same density as a small bar of aluminum.

Temperature Dependence:

The density of a substance can vary with temperature.

Examples of Density

Water:

Has a density of approximately 1 g/cm³.

Steel:

A solid metal, has a high density, meaning it feels heavy for its size.

Air:

A gas, has a low density, as its molecules are spread far apart.

How Density is Used

Identification:

Density can help identify substances.

Buoyancy:

In applications like hot air balloons, heating air reduces its density, causing it to rise because it becomes less dense than the surrounding cooler air.

Construction:

In construction, apparent density considers the combination of materials like bricks, mortar, and air within a wall structure.

Buoyancy is the upward force that a fluid (like water or air) pushes on an object placed in it.

⚖️ Why does it happen?

Because the object pushes fluid out of the way, and the fluid pushes back up.
This is called Archimedes’ Principle:

The upward force equals the weight of the fluid displaced.

🧪 Will it float or sink?

• ✅ Floats: if buoyant force > object’s weight

• ❌ Sinks: if buoyant force < object’s weight

• ⚖️ Stays still: if both are equal

  
  

🛳️ Examples:

• Wood floats (light + displaces enough water).

• Rocks sink (heavy + displaces little water).

• Ships float because they displace a lot of water.

• Balloons float in air because helium is lighter than air.

For example:

A rock thrown into water, it’ll sink because the rock’s weight is greater than the buoyant force the fluid exerted.

Also if an object’s weight is less than the buoyant force it’ll not sink, it’ll instead float. That makes the object buoyant because it floats instead of sinking.

For example:

A balloon that is put into water, it’ll not sink instead it’ll float because it’s lighter than the buoyant force making it buoyant.

Finally, a object that has a weight that is equal to the buoyant force it’ll not sink or float, it would just remain suspended in the fluid.

For example:

A person laying down in the pool, they would not float or sink , that’s because their weight matches the weight of the buoyant force so it doesn’t sink or float.

Thank you very much for reading this was made by Rosie Vasquez.

Archimedes of Syracuse was a Greek physicist, engineer, inventor, astronomer, and mathematician. Although few details of his life are known, he is considered one of the most important scientists of antiquity.

Archimedes of Syracuse (287–212 BC) solved the first problems related to (what is now called) integral calculus. In particular, he determined the center of gravity of a parallelogram, a triangle, and a trapezoid; and of a segment of a parabola. He calculated the area of ​​a segment of a parabola cut by a chord.

In physics, Archimedes discovered the law of buoyancy—now known as Archimedes’ Principle—which explains why objects float or sink depending on the weight of the fluid they displace. According to legend, he realized this while stepping into a bath and noticing the water level rise, leading him to run through the streets shouting “Eureka!” (“I have found it!”). His discovery remains a foundational concept in modern fluid mechanics and engineering. Beyond theoretical science, Archimedes was also a brilliant inventor. He created a variety of mechanical devices, such as the Archimedean screw, a tool still used today to raise water for irrigation and drainage. During the siege of Syracuse by Roman forces, he designed ingenious war machines—such as catapults, cranes, and mirrors said to focus sunlight to burn enemy ships—that delayed the city’s capture for years.

Despite his many accomplishments, Archimedes lived humbly and remained dedicated to his studies until the end of his life. He was killed by a Roman soldier in 212 BCE when Syracuse was finally captured, reportedly while absorbed in a mathematical diagram, begging the soldier not to disturb his work. Although much of his original writing was lost over time, the surviving works—such as On the Sphere and Cylinder, On Floating Bodies, and The Sand Reckoner—reveal the depth of his genius. His methods of reasoning anticipated the use of algebra and calculus centuries before they were formally developed. Archimedes’ legacy transcends his era; his ideas shaped the Renaissance, inspired thinkers like Galileo and Newton, and continue to influence modern science, engineering, and mathematics. His life stands as a timeless symbol of human curiosity, intellect, and the pursuit of knowledge for its own sake.