Classical Mechanics of Fluids - Essay Example

FLUID Student’s Name Course Professor’s Name University City (State) Date 1. Classical mechanics of fluids 1.1 (a) The Navier-Stokes equations with the equations of energy conservation The continuity equation Equation of motion Conservation of energy equation Where; velocity vector field = u, thermodynamic (internal energy) = ɛ, pressure = p, temperature = t, density =, viscosity =, heat conduction coefficient = and external force per unit mass = F a) Physical meaning of terms in the conservation energy equation Mass: the term refers to the unit property of an object. It is the measure with which an object resists any change in the motion state of the property after a force has been applied. To solve for the mass of the energy the continuity equation is applicable. Energy (heat): refers to transferable properties of an object that can drastically be transformed into other forms. The amount of heat needed to affect the motion of an object respectively depends on the mass of that particular object. Momentum: refers to the state of movement affecting an object. Therefore, it can be noted that both velocity and mass are factors of momentum to ensure that there is motion within the state of the object’s properties from one place to another. b) Terms that need turbulence modelling In turbulence modeling, the effects are enormous on both momentum and mass of the object since kinetic energy acts in both cases. c) Necessity of turbulence models The importance of turbulence models helps in stabilizing the flow of laminar within the structural composition of the object is properties that is contained within the framework of the computer. When the levels of the (RE) Reynolds Numbers are high, the relationship between the vicious and inertial equations are dependent on the rational composition of the object’s mass. d) Example of a source term The right side of the equation represents the source term. 1.2 (a) Diagram showing the system b) Calculation of the pressure The equation for the move concept is; From this equation to means the appropriate time for an event. For instance, the time calculated when an event and observer are within the same gravitational likely area.tf is the time one measures when they are at an absolute position from any mass. Nevertheless, the important point's c and G are again the Newtonian speed of light and gravitational potential simultaneously. Alternatively, r and M are to be considered the mass of the object that one is within touching distance, r is one's distance from the object in question. c) Calculation of the velocity and volume flow The equation can be spelled out differently by using Schwarzschild's solution to the general relativity which returns the Schwarzschild radius; the radius which is for an object of the mass M, for which if all mass is withheld amidst that limit consequently the gravitational space is very stable so that light has no escape route. If a person uses this formula whose mass is trapped within the Schwarzschild radius like Black Holes, in case something makes it to the edge of the black hole when the time for the person will appear to halt from an observer’s point of view standing far away. Therefore, one can never observe anything fall into a black hole as time ends at the edge of the black hole. On the whole, it then becomes stronger if at all a person falls into the black hole as the value within the square root moderator turns negative. On the whole, the answer emerges as an imaginary figure and yet no person knows how to read an imaginary consequence to the world. 2. Dimensional analysis When one moves into the future or their past times, he walks into various age-old passions like discovering what their future holds together with witnessing historical events like seeing one's loved ones who died long ago. Otherwise, observing the methods and technology employed in time travel is truly fun. Again, like the majority of the technology in the field of science fiction, the factions of real science always puts a measure against other considerations like visual splendor, budget, and the plot. Therefore, with the introduction of atomic clocks scientists are in a position to reveal the truth regarding Einstein's assumptions about how time can speed up or slow down depending on the place of whichever person is drawing the observation. On the whole, from this concept comes the idea that the greater the gravitational pull on a clock, the slower time runs. 3. Heat transfer, fluid dynamics of combustion and Thermochemistry 3.1 (a) Burning wood In the combustion of wood the process takes place under the influence of gases contained in an object and the reaction with oxygen. However, this process is indirect in nature since there is no actual burning, but combustion, as a result, of oxygen-gas reactions. As a result, the propensity levels of wood are enormous due to the properties produced that easily react with oxygen when heat is applied. In pyrolysis, the cellulose reaction resulting from the detonation and combustion of products intermixed with gases, oxygen and temperatures leads to decomposition. However, during decomposition, the by-products reside within the material after the gases have exhumed from the wood. During the burn of the object, the mixture of gases and oxygen act as catalysts to the movement of heat from one point to another. It’s noticeable during the process that the products given off create a flame when they tangle with the fire, they produce a flame. The reaction in the force of combustion creates a burning flame due to the oxygenated wood chips. The final outcome from the combustion is a char substance that is a makeup of the original piece of wood involved in the thermal burning. The effect of char on the wood content depends on the resistance level of each product material like the substance gradients of the timber during burning. Although, each timber is considered combustible, there are materials that make it propellant to the effects of fire due to their different structural designs. During thermal conductivity, the cladding substances in nimble wood protects it from forming char, while in thick wood a retarded char layer keeps the fire out during penetration. It’s noticeable that the surface area of the thick timber is relatively equal to the temperature of the fire it is exposed to during combustion. As such, when the outer surface of the timber exudes to the burning point, the speed of ignitions increases making the wood reduce in size. As the wood reaches its burning point, a layer of char forms which acts as an insulator to curtail the extreme temperature, which affects the combustion process in wood. Therefore, as the beam of wood burns, the char formed reduces the speed heat is transferred from one point to another thereby protecting the last bit of the timber until the oxygenation of the wood takes place. 3.2 Reaction Rate A reaction rate refers to the propensity with which heat transfers through a particular substance. The chemical reaction that takes place when a fire is exposed on a piece of wood depends on the reaction of the surface it’s is being exposed to in the process of combustion. However, the rate of reaction differs from one material to another. In metals it is longer compared to wood, which has energy levels high during the burning process. The surface area of any material affects the rate of reaction since solid substance regulates the amount of heat during combustion. When the surface area of an object reduces in size, the reaction increases and the rate of heat transfer is more propellant than when the area is enormous and the reaction turns reluctant, it reduces the chemical reaction. In cases where the heterogeneous state of the subject is inconclusive, the combustion rates depend on the nature of the surface area’s condensation phase. As a result, the sustainability of the surface has to occur at the exact time when the integration is taking place. The concentration effects of the substances equally affects the rate of reaction since two objects cannot have the same particle constituents have a similar reaction. As a result, if contact reaction is absent, the rate will be zero. Moreover, as the number of units colliding during combustion increases, the more reactive it becomes. Therefore, depending on the particle concentration, the reluctance of the subjects will undergo a more aggressive reactions to effectively ensure that they are at par with each other. Likewise, the temperature levels of a subject have a significant impact on the rate of reaction. The kinetic energy of an object increases upon an increment in the temperatures surrounding the object. As result, a rise in kinetic energy results in a performance reaction and motion as the body mass of the substance is affected by the force applied; hence, there is a reaction. Therefore, to clearly understand the rate of reaction, it’s imperative to understand the environment the subject is bound to so that the temperature readings provides a chemical outcome. The flammable reaction rate of wood chips is different from that of a wood block since the ignition factors within the chips is more visible to the fire that the surface of the block. As a result, the chemical reaction in a block undergoes a number of stages to prepare it for conduction unlike the chips that have the particles at the premise of the heat propensity. 4. Characteristics of flames and fire plumes 4.1 Fire plumes and dynamics Fire plumes are a reaction to the nature of compartment surrounding the structural cluster of the substance in the reaction. Fire plumes are characterized by buoyancy of the flame plume created during combustion process. In most case the rise in the height of the flame clusters into a mold structure that can be influenced by the turbulence of fluid velocity. The vorticity variations of flame plumes creates small scale thermal mantles in regions that have low viscous due to the compartment of the inner region. During the rising tide in the fire, the smoke particles gather and gain a mold shape that moves in a cluster form leading to a vented feature in a cornered area of a structure. The axisymmetric model considers the convective nature of the plumes as they movement through a stationary region of fluidity. To determine the height and size of the flame, the boundary layer must be composed of an infinite vorticity on the portent properties. The velocity produced during a flame plume will largely depend on the cluster nature of the place. For instance, in a vehicle, the flame will rise up the roof creating plume ignited by pressure to escape. Further, the type of structure experiencing a fire flame will determine its capacity as the temperatures rise, the residue given of creates a radiation reaction, which increases the heat levels. As a result, during the calculations of the flame plume consideration focuses on the rapid and adjacent acceleration of the flame and its growth rates. 4.2 Diffusion flames During combustion, solid fuels react differently to the occurrence of fires. As such there are factors considered for the whole process to occur. The presence of an oxidant affects the spread of a flame as it will require to have enough supporting force in form of heat to ensure that it resistance nature’s forces against fire. When the oxidant reduces in capacity, the magnitude of the flame will be affected since it seizes to have the holding capacity to push flames beyond the solid material. The existence of a fuel source like petrol for instance can affect the spread of a flame. In case, the fuel comes in contact with another liquid like water, the difference on particle structure will hinder the progress of the flame since the conduction levels of the two solids is different. However, the fact that both have different heat reactions the vapor from water will create a flame plume, which is capable of supporting the chemical reaction of the fuel. The presence of sufficient energy as heat is vital in the spread of a flame. When the solid has resistance particles, heat acts a pushing factors to ensure that the flame can transit from one place to another. As a result, a mixture of heat and the oxidant in this case oxygen supports burning, which is crucial in the movement of flames. Lastly, a chemical reaction needs to occur to ensure that the flame has sufficient tetrahedron to spread across the designated space. As a result, the factors will determine the process and existence of a flame over a solid surface. The movement of a flame over a solid or liquid like a gas will depend on the temperature levels of held within the flammable liquids. As a result, thermo-physical process will undergo a chemical reaction, which purifies the gas to give it a light structure that can easily be influenced once there is contact between the flames. Read More