Question

Archimedes' principle states that when an object is immersed in a fluid, it is bucryed up by a force equal to the weight of the fluid displaced. Assume (slightly incorrectly) that tissue has the same density as water. Using Archimedes principle, explain why the gill filarnents of aquatic animals typically flop into a crooping mass in air even though they float near neutral bucyancy in water. How do these differences between air and water affect the ability of gills to function in gas ewchange?

Short answer

Gill filaments in aquatic animals float near neutral buoyancy in water due to the similar densities of tissue and water, making the weight of water displaced, more or less equal to the weight of filaments (Archimedes' principle). In air, due to its lesser density compared to tissue, the weight of air displaced by the filaments is lesser than the weight of filaments, which doesn't provide sufficient buoyant force for them to maintain their shape and they droop. This changes the shape of gills, and hinders their function in gas exchange.

Step-by-step solution

Understanding Archimedes' Principle

Archimedes' principle states that an object immersed in a fluid experiences a buoyant force equal to the weight of the fluid displaced by the object. The force acting on an object submerged in a fluid (in this case, water) is equal to the weight of that quantity of fluid.

Behavior of gill filaments in water

In water, gill filaments of aquatic animals stay afloat near neutral buoyancy. This is due to the similar densities of tissue and water which results in the weight of water displaced by the filaments being more or less equal to the weight of filaments, based on Archimedes' principle. This aids in maintaining their shape underwater.

Behavior of gill filaments in air

In air, gill filaments tend to collapse into a drooping mass. The density of air is less than the density of water or tissues. Hence, the weight of air displaced by the filaments is less than the weight of filaments, resulting in inability to provide enough buoyant force to keep their shape and making them droopy.

Impact on the functionality of gills

The functionality of gills is largely affected by these differences. In water, gills are capable of maintaining their form, which promotes the exchange of gases (Oxygen, Carbon dioxide) between the water and the fish's bloodstream. However, in air, the drooping of gills restricts the surface area available for gas exchange, hence reducing their effectiveness.

Key concepts

Buoyant Force

Imagine you're in a pool and you feel lighter when you're submerged in the water. That sensation is due to the buoyant force, a fundamental concept derived from Archimedes' principle. This force is what makes objects appear to weigh less in a fluid, such as water, and is equal to the weight of the fluid displaced by the object. This physical phenomenon is crucial for a variety of applications, from designing ships to understanding how fish stay afloat. In our gill filament analysis, the buoyant force allows fish to float in water, as the density of their tissues is similar to water. However, in air, the buoyant force is not enough to support the gill filaments, leading them to droop since air's density is much lower than water's, resulting in a lesser displacement of air weight.

Understanding the buoyant force is not only essential for building boats or submarines but also for analyzing how living organisms interact with their fluid environments.

Neutral Buoyancy

Neutral buoyancy occurs when an object's overall density is equal to the fluid it's in, causing it to neither sink nor float. For aquatic animals with gill filaments, achieving neutral buoyancy in water is like balancing perfectly on a tightrope. It means their gill filaments are suspended in the water, exerting a downward force equal to the weight of the water displaced. The concept is crucial for animals because it minimizes the energy they use to stay afloat and for the proper functioning of their respiratory structures.

For instance, the gill filaments float almost effortlessly in water, maintaining the required shape for gas exchange. But once out of the water, the air's buoyant force is not sufficient to counterbalance their weight, and they lose this neutral buoyancy, collapsing and becoming ineffective for gas exchange. This demonstrates the importance of neutral buoyancy in the functionality of physiological features.

Gill Filament Functionality

Maintaining Shape Underwater

In water, gill filaments are supported by buoyant forces, allowing them to spread out and maintain a structure optimal for their primary function - gas exchange. The gills' delicate, feathery structures are supported because they achieve neutral buoyancy, much like a leaf floating on a calm surface.

Importance of Physical Support

Physical support is imperative for gill filament functionality. Without it, such as when a fish is taken out of water, these structures clump together, reducing the surface area necessary for effective gas exchange. It's like trying to drink a thick milkshake through a collapsed straw; without the structure's integrity, the process becomes incredibly difficult.

Gas Exchange in Gills

Just as we need air to breathe, fish require a well-orchestrated mechanism for gas exchange to survive, which occurs through their gills. Gill filaments are rich in blood vessels and allow for the exchange of oxygen and carbon dioxide between the fish and the surrounding water. This is akin to how our lungs work in the air, but instead of air sacs, fish use the vast surface area provided by the gill filaments.

Due to their neutral buoyancy and the support of the surrounding water, gill filaments can present an extensive surface area for this exchange. If a fish's gills lose their support, as they do in air, the filaments stick together, and the area for gas exchange is dramatically reduced. It's as though our lungs were unable to expand; breathing would become much less efficient, just as the gills' ability to facilitate gas exchange becomes compromised out of water.