# Fluid Mechanics

A fluid is a substance that deforms continuously when subjected to a tangential or shear stress, however small the shear stress may be. Such a continuous deformation under the stress constitutes a flow. Fluid mechanics is therefore the study of mechanics of such matter. As such, it pertains mostly to the study of liquids and gases, however the general theories may be applied to the study of amorphous solids, colloidal suspensions and gelatinous materials.
Fluid mechanics is a subdivision of continuum mechanics. Consequentially, fluids are considered continuous media for analysis, and their discrete nature is of no consequence for most applications. This assumption is valid mostly on length scales much larger than intramolecular distances. The departure from continuum is characterised by a dimensionless parameter, the Knudsen Number, defined by $K_{n}=\lambda /L$, where L is a characteristic length scale of the flow. The continuum hypothesis holds good if Kn < 0.01. However, recent applications in nanotechnology and biotechnology are demonstrating that the governing equations are still relevant on smaller scales, specifically when they are modified to include the effects of electrostatic, magnetic, colloidal and surface-tension driven forces.
Some fluid mechanics problems can be solved by applying conservation laws (mass, momentum, energy) of mechanics to a finite control volume. However, in general, it is necessary to apply those laws to an infinitesimal control volume, then use the resulting differential equations. Additionally, boundary values, initial conditions and thermodynamic state equations are generally necessary to obtain numeric or analytic solutions.

### Brief History

Fluid interactions help fish in a school swim faster. The collective motion of a fish school results from every animal responding solely to the motion of it's neighbour. This is what happens to bird flocks, but unlike the birds, fish usually move in a liquid which may be a river, lake or fish pond. A group of researchers recently used computer simulations to explain the water flow that fish induce can have a substantial influence on the coordinated patterns that they do create. Schooling of fish, shown by nearly half of the known species of fish can take various forms (Hemelrijk et al., 2015). The group can just swarm together with no string degree of alignment, or the fish can swim in collectively oriented rings, streams, or balls. These particular motions are thought to help in avoiding predators as well as foraging. Use of Theoretical models can assist in understanding this by reproducing this fish schooling behaviour with no need for any large institution. They hold an assumption that every fish follows a simple “local “rules like aligning itself with the average orientation of the fish that are near it. Fish have the ability to sense fluid flow through the use of their lateral line. The lateral line is a series of tiny, hair-like sensory organs that are distributed evenly along the sides of the fish body (Ball, 2018). Also, each can enhance its swimming efficiency by swimming in the clip steam of another. But how and if these hydrodynamic effects impact the collective motion of fish schools has not been studied much by scholars and researchers. Christophe Eloy, a member of the “Ecole Centrale Marseille” in France and his colleagues, studied the effects of fluid dynamics through the use of virtual fish moving in dual dimensions (Hemelrijk et al., 2015). Similar to the preceding model, the researchers held an assumption that the fish attract each other and to orient themselves to a certain extent with others in their field of view. Again, they assume that there is a smooth flow, such that turbulent vortices in the wake are overlooked. Under these conditions or assumptions, the researchers found out that fish portray four different joint motion modes, which depend on the parameters of the rule of behavior. These include random and cohesive swarming; aligned, mainly swimming in a straight line or schooling; collective circle swimming or milling; and rapid, aligned swimming with a regular spontaneous turn or turning (Ball, 2018). The average speed of fish is higher with the fluid included. "Turning" resulted from noise or greater rotational randomness caused by hydrodynamic effects. What may appear to be a consequence of behavior, the fish's free will may actually be an outcome of fluid dynamics. This research can be furthered by relating the modelling results to an observation which are real.
References Ball, P. (2018). Fluid Interactions Help Fish in a School Swim Faster. Physics Online Journal, 11. Hemelrijk, C. K., Reid, D. A. P., Hildenbrandt, H., & Padding, J. T. (2015). The increased efficiency of fish swimming in a school. Fish and Fisheries, 16(3), 511-521.

## Chapters

* Fluid Mechanics/Fluid Statics
* Analysis Methods
* Kinematics: Motion without Friction
* Chapter 2: Vector/Tensor Algebra and Calculus
* Chapter 3: Conservation Equations: Control Volume Analysis
* Chapter 4: Dimensional Analysis
* Chapter 5: Differential Analysis of Fluid Flow
* Chapter 6: Flow Fields with More than One Independent Variable
* Chapter 7: Exact Solutions to Navier Stokes Equations: Special Conditions
* Chapter 8: Incompressible Flow
* Chapter 9: Compressible Flow
* Chapter 10: Turbulent Flow
* Chapter 11: Geophysical Fluid Dynamics
* Appendix: Fluid Properties
* Appendix:Formulas and Glossary