Volume displacement is a fundamental concept in fluid mechanics, describing the amount of fluid an object pushes out of the way when it is submerged or partially submerged. The submerged object must physically move the fluid aside to take its place. Volume displacement is measured in cubic units like cubic meters or liters. Understanding this principle provides the basis for calculating the volume of irregularly shaped objects and explaining why certain objects float while others sink.
Defining Volume Displacement and the Governing Law
Volume displacement is governed by the space an object occupies within a fluid, whether liquid or gas. When an object enters a fluid, the fluid molecules must move, and the resulting empty space is the volume that was displaced. If the object is fully immersed, the volume of the displaced fluid is precisely equal to the total volume of the object itself.
The governing principle for this phenomenon is Archimedes’ Principle, a foundational concept in physics. This law states that the upward force exerted on a body immersed in a fluid is equal to the weight of the fluid that the body displaces. This principle is inherently tied to the displaced volume, allowing it to directly link the volume of an object to the measurable volume of the fluid it pushes aside.
This relationship allows scientists and engineers to determine the volume of complex shapes that would otherwise be impossible to calculate with standard geometric formulas. The fluid’s density and the local acceleration due to gravity are the factors that determine the weight of the displaced fluid. However, the volume of the displaced fluid is solely determined by the volume of the submerged portion of the object.
Practical Measurement Methods
The most common practical method for measuring the volume of an irregularly shaped solid utilizes the water displacement technique. This method relies on measuring the change in the fluid’s level before and after the object is introduced. A graduated cylinder or similar container is first partially filled with a liquid, and the initial volume reading is recorded.
The solid object is then carefully lowered into the container until it is completely submerged. The submerged object pushes the water level up, and a new, higher volume reading is taken. The volume of the object is then calculated by subtracting the initial volume from the final volume reading.
Another method, known as the overflow method, uses a container filled to the very brim, often called a Eureka can. When the object is placed inside, the displaced water pours out of a spout and is collected in a separate measuring container. The volume of the collected overflow water is directly measured, providing the volume of the solid object.
The Relationship Between Displacement and Buoyancy
Volume displacement is the prerequisite for buoyancy, but the two concepts represent different physical quantities. Displaced volume is a measure of space, while buoyancy is an upward force exerted by the fluid on the object. This buoyant force is caused by the increase in fluid pressure with depth, creating greater pressure on the bottom of the object than on the top.
According to Archimedes’ Principle, the magnitude of this upward buoyant force is exactly equal to the weight of the fluid displaced. This connection forms the basis for understanding why objects float or sink. When an object is placed in water, if the weight of the water it displaces is less than the object’s own weight, the net force is downward, and the object sinks.
Conversely, if the object is shaped to displace a weight of fluid greater than its own weight, the buoyant force overcomes gravity, and the object floats. This is often described using density: an object with a lower average density than the fluid will float, displacing only the volume necessary to equal its own weight. A denser object must displace its entire volume, but the weight of that displaced fluid is still less than the object’s weight, causing it to sink.
Real-World Examples
The principle of volume displacement is fundamental to the design and operation of large-scale marine and air transport systems. A massive steel ship is able to float because its hollow hull displaces a tremendous volume of water. The resulting buoyant force is greater than the ship’s total weight, allowing it to remain afloat. This explains why a solid steel bar sinks, but the same mass of steel spread into a large, bowl-like shape floats.
Submarines manipulate this principle directly by controlling their volume displacement to achieve neutral buoyancy. They utilize ballast tanks to take on or expel seawater, effectively changing their overall mass and average density. Taking in water increases the submarine’s mass without significantly changing its volume, causing it to displace a fluid weight less than its own, which allows it to dive.
The same governing law applies to objects in the air, which is also a fluid. A hot air balloon operates by displacing a large volume of cooler, denser air with its heated, less-dense air. The weight of the volume of cooler air displaced is greater than the total weight of the balloon system, generating the necessary lift.