Uses of Fluid Mechanics with Relevant References. Fluid mechanics is the application of the laws of fore and motion to fluids. Within fluid mechanics there are two studies of fluid mechanics: Fluid statics, the study if fluids at rest within a system, or Fluid Dynamics which is the study of fluids that are in motion within a system. A fluid is a substance that has no fixed shape and yields easily to external pressure. The substance continually deforms or flows under an applied shear stress. Fluids are a subset of the states of matter and include three of the four states of matter [1]. An example of tangential shear stress can be something as simple as a piece of wood floating on a small body of water. If the force, F, is applied at the end of one side, then the board transmits a tangential shear stress, denoted as, t, to the surface of the water. Shear stress is defined as the tangential to the area over which it acts, and is expressed in the same units as Direct Stress [2]. “If a shear stress is applied to the surface of a solid, the solid will deform a little, and then remain at rest (in its distorted shape). One can say that the solid (at rest) is able to resist the shear stress.” [2] Both the board and the water will move as long as the force exerted and the tangential sheer stress are not equal to zero. Think about this, a fluid can only experience a normal stress when there is no force being acted upon the system obtained by the fluid. Therefore, since the fluid is at rest it can’t resist a shear stress. When you are learning about a new topic or are trying to dive deeper with in a specific area, you must know the in’s and the outs of the area of study. So, with fluid mechanics and the understanding of such things you must know the properties behind them to really know how they work. Fluid properties are within the spectra of understanding such things as this. One of the fluid properties is the fluids mass density, p, which is the volumetric mass density of a particular substance [3]. Mass density I directly related to both temperature and the fluid of which is being test. Because there are many different types of fluids there must also be a specific number given to those mass densities, which has the units of kg/m^3. As mentioned before there are two types of Fluid Mechanics: Fluid statics, the study if fluids at rest, or Fluid Dynamics which is the study of fluids in motion. Fluid statics or hydrostatics is the branch of fluid mechanics that studies fluids at rest. It embraces the study of the conditions under which fluids are at rest in equilibrium [4]. The most basic example of hydrostatics is a basic pump. Pumps are used to raise or move fluids, there are two types of pumps, hydrostatic, or positive displacement pumps. Pumps can generally be described as having a piston that fits very closely on the inside of a cylinder that is pushing a fluid back and forth along the cylinder’s channel. Think of how a syringe works, it is used by pulling back or pressing forward that center of that which is located tightly within the channel of the cylinder. In order to find the hydrostatic pressure within a system we have to know a few things first. First, we need to find the density of the liquid that is within our system. Next, we need to know the height or depth of the reservoir holding the fluid. We already know the acceleration due to gravity which is 9.8 m/s^2. Now, in order to find the pressure within the hydrostatic system we take all three of the known items and multiply them together. For example, if we want to find the amount of pressure a scuba diver experiences 20 meters in the ocean; P = p*g*h so, the average density of saltwater found in the ocean is said to be 1,030 kg/m^3 [5]. If we take those numbers and multiply (1,030 kg/m^3) (9.8 m/s^2)(25 m) we are given our pressure in Pascals which in this case is 252,350 Pascals. Our second type of fluid mechanics is fluid dynamics which is the study of fluids that are in motion within a system. Like all things in life the ‘fluids’ that are studied within the realm of fluid dynamics does not necessarily mean that it has to be a liquid it just simply means a ‘fluid like’ motion or action. Like all other motion in Newtonian physics, fluid is conceptualized by Newton’s laws. In some ways or others it is entirely possible to use Newton’s second law to describe the velocity within a fluid as a function of position over time. However, to use Newton’s laws could raise a bit of confusion so instead of talking problems that way, I approached problems using the conservation of energy when trying to describe how dynamic fluids behaved. A well explained example that I came across was to consider a steady fluid flow represented by streamlines. A flow tube which can be best described has a cone like shape with openings at both ends and allows to air to flow through it with ease. The flow tube itself has a cross sectioned area where the fluid velocity and other properties are different depending on the actual cross section itself. At any rate, the fluid could be affected during any section of the flow tube depending on the design and structure type of the flow tube its self. Within the fluid flow of the system, just to keep in mind, the amount of fluid flowing into the flow tube to the left must equal the flow leaving to the right. This does not mean that the velocity entering and leaving must equal one another this just means that the flow rate (gallons per minute) must equal one another, because as we all know that the conservation of energy states that energy can’t be created nor destroyed. As long as the fluid is steady, and the fluid is non-viscous and incompressible, the flow can be looked at from an energy perspective. [6] This is what Bernoulli’s equation does, relating pressure, velocity and height of a fluid at one point to the same parameters at a second point. [6] With Bernoulli’s equation we have to consider fluid running through a pipe parallel with the ground. At a particular point on the pipe is significantly smaller than the rest of the pipe. By using the continuity equation which is pvA= constant along a flow tube, the velocity would be higher in the more narrow sections of the tube [7]. Since the pipe is horizontal the beginning and the end of the pipe are both at the same height we can apply the Bernoulli equation to find the energy flow through the flow tube. That equation is found to be, p + ((1/2)*p*v^2) + p*g*y= constant along the flow tube. When thinking of an example of Bernoulli’s equation, a tank holding water and a hole at the bottom of the tank draining the water is an example that comes to mind. The large tank has a height of h and a liquid density of p. We need to find the speed at which the liquid is emerging from the hole. We’re interested in the water’s velocity at the hole, so at that point is where we will apply most of our formulas. By using Bernoulli’s equation and assuming that the top is equal to zero because of the slow decrease in height we can manipulate the Bernoulli’s equation down to square root(2gh) = Velocity of the hole. Within the realm of fluid mechanics there are two major types associated with the subject, which is the study of fluid statics the study of fluids at rest within a system, and the study of Fluid Dynamics which is the study of fluids that are in motion within a system. The laws of both mass and energy conservation that we previously derived for the fluids allow us to analyze a wide variety of both natural and technological phenomena. When attempting to figure out the answers mathematically, we would usually use both the continuity equation and Bernoulli’s equation as long as you consider the values of the appropriate constants at the flow points at the end of the pipes. Fluid mechanics can be applied to many more applications than what is found within this paper. Some of those include, but are not limited to, Flight and lift of helicopters and planes specifically focusing on the wings and the wind flowing around them. Viscosity and turbulence is another application to the learning of fluid mechanics. Although we have only scratched the surface of fluid mechanics I believe that the basis for conceptual knowledge of this subject can be well understood.

Work Cited

[1] What is a Fluid? - Boundless Open Textbook. (n.d.). Boundless. Retrieved July 31, 2014, from https://www.boundless.com/physics/fluids/fluid-as-a-phase-of-matter/what-is-a-fluid/
[2] What is Fluid Mechanics?. (n.d.). What is Fluid Mechanics?. Retrieved July 31, 2014, from http://www.mne.psu.edu/cimbala/Learning/Fluid/Introductory/what_is_fluid_mechanics.htm
[3] Mass density. (n.d.). The Free Dictionary. Retrieved July 31, 2014, from http://www.thefreedictionary.com/Mass+density
[4] Fluid statics. (2014, July 22). Wikipedia. Retrieved July 31, 2014, from http://en.wikipedia.org/wiki/Fluid_statics
[5] Seawater. (n.d.). Seawater. Retrieved July 31, 2014, from http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/seawater.html
[6] Fluid dynamics and Bernoulli's equation. (n.d.). Fluid dynamics and Bernoulli's equation. Retrieved July 31, 2014, from http://physics.bu.edu/~duffy/py105/Bernoulli.html
[7] Continuity Equation. (n.d.). Princeton University. Retrieved July 31, 2014, from https://www.princeton.edu/~asmits/Bicycle_web/continuity.html