Physics of Fluids: Principles and Applications

A steel ship floats while a solid steel block sinks due to its hollow shape, which allows it to displace a larger volume of water. According to Archimedes' Principle, an object will float if it displaces an amount of water equal to its weight. The ship's design ensures that the weight of the water displaced is greater than or equal to the ship's weight, resulting in a net upward buoyant force. This makes the average density of the ship, when considering its hollow structure, less than that of water, enabling it to float.

According to Pascal's Principle, pressure applied to a confined fluid is transmitted undiminished throughout the fluid. The pressure on the small piston (P1 = F1/A1) is equal to the pressure on the large piston (P2 = F2/A2). Given the small piston area (A1 = 0.05 m²) and applied force (F1 = 200 N), the pressure is 4000 Pa. Using the large piston area (A2 = 0.50 m²), the output force (F2) can be calculated as F2 = P2 × A2 = 4000 Pa × 0.50 m² = 2000 N.

Bernoulli's Principle states that in a flowing fluid, an increase in velocity leads to a decrease in pressure. As fluid moves through a narrowing pipe, it must speed up to conserve mass flow rate. This increased speed results in lower static pressure within the fluid, as the kinetic energy of the moving fluid takes precedence over its potential energy. Hence, the relationship between speed and pressure is inversely proportional, confirming that higher fluid velocity corresponds to reduced internal pressure.

A wooden block with a density of 0.40 kg/L is less dense than water, which has a density of 1.00 kg/L. According to Archimedes' principle, an object will float if the buoyant force acting on it equals its weight. In this case, the block will displace a volume of water equal to its weight before it is fully submerged, resulting in it floating partially submerged. Thus, the buoyant force matches the weight of the block, allowing it to remain afloat.

When a submarine takes in seawater into its ballast tanks, it increases its overall weight. According to Archimedes' Principle, an object submerged in fluid experiences an upward buoyant force equal to the weight of the fluid displaced. By increasing its weight beyond the buoyant force, the submarine becomes denser than the surrounding water, leading it to sink. This principle effectively explains how submarines control their buoyancy and navigate underwater by manipulating their weight relative to the buoyant force acting on them.

During a hurricane, wind speeds increase significantly, creating a difference in air pressure. According to Bernoulli's Principle, as the wind moves rapidly over the roof, it generates lower pressure above it. Meanwhile, the air pressure inside the house remains higher due to the enclosed space. This pressure differential results in an upward force on the roof, which can exceed the roof's ability to remain attached to the house, ultimately causing it to be blown off. This principle effectively explains the mechanics of how the roof is lifted during severe wind events.

Archimedes' Principle explains buoyancy, which is why hot air balloons rise as the heated air inside becomes less dense than the cooler air outside. Pascal's Principle states that pressure applied to a confined fluid is transmitted undiminished throughout the fluid, which is the principle behind hydraulic car brakes that amplify force. Bernoulli's Principle describes how the pressure of a fluid decreases as its velocity increases, which is crucial for airplane wings, as the shape of the wing causes air to move faster over the top, creating lift.

When a hydrometer is placed in a liquid, it floats at a level that corresponds to the liquid's density. If the hydrometer floats higher in liquid A than in liquid B, it indicates that liquid A has a higher density. This is because a denser liquid will support the hydrometer more effectively, requiring it to displace less volume to achieve buoyancy. Hence, the hydrometer's position reflects the relationship between the densities of the two liquids, confirming that liquid A is denser than liquid B.

In a hydraulic braking system, Pascal's Principle states that when pressure is applied to a confined fluid, it is transmitted equally in all directions. This means that even a small force exerted on the brake pedal can create a significant pressure increase throughout the brake fluid, enabling effective force transfer to all brake components. Consequently, this allows the brakes on all wheels to engage simultaneously and with sufficient force, ensuring efficient and reliable braking performance.

For an object to remain fully submerged and stationary in a fluid, the buoyant force acting on it must balance its weight. This balance indicates that the upward buoyant force is equal to the downward gravitational force on the object. Additionally, when the object is neither sinking nor rising, its average density must match that of the fluid, ensuring that it neither floats nor sinks. This equilibrium condition is essential for maintaining a stationary position in the fluid.