Classical Mechanics of Fluids - Assignment Example

Author Professor University Date Classical mechanics of fluids List of Navier-stokes equation a) The equation of continuity b) The equation of momentum X-component 0 Y-component  Z-component  Momentum equation V(x, y, z): velocity, : refers to pressure forces: viscous force, ρ: density, t: time Terms that needs turbulence modeling Velocity, time and pressure Turbulence flow is characterized by eddies always due to the fast rate of flow. These eddies interact with one another as they move through a pipe or any other medium of transport causing them to mix. The mixing of the turbulence flow of fluids increases the rate at which they interact with each other hence increasing the efficient process of transport and hence improve the exchange of energy and momentum. Example The net rate of heat addition and net rate at which work done on the fluid 1.2) Diagram Swamee –Jain equation f =  Re =   Re = 133,333.33 f =  f = 0.036907 Bernoulli’s equation P = |104,170| P = 104,170 2.1) Dimensional analysis [Density ()]:  =  =  [Length] = L (a, b) =  [Velocity]: [length/time] = L/T =  [Viscosity ()]: [force x distance] / [area x velocity] = () / () =   =  =  =  Q2.2 Kolmogorov scale of velocity Kinetic viscosity coefficient v = [force x distance] / [area x velocity] = () / () =  Specific dissipation rate  = M Fluid density () = =  Velocity =  Velocity =  =  Q3.1) process of burning wood In our environment, many of the materials wood products included burn indirectly in that these materials do not physically burn, but rather combustion takes place as a reaction between oxygen and some gases released from these materials. However, in this process combustion of charred wood where oxygen reacts directly with carbon is excluded. Furthermore, with the influence of heat, wood quickly produces substances that react eagerly with oxygen, leading to the susceptibility of wood to ignite and burn. (KTH biotechnology, 2011) Pyrolysis process For wood to ignite and combust it depends mainly on the thermal decomposition(pyrolysis) of the cellulose and the reactions with gasses in the air which is primarily oxygen and pyrolysis products with each other. It occurs when the temperature increases, making the cellulose to start to decompose. During this process of decomposition, decompose products are either released as gasses or remain inside the material, in this case, the wood. The volatile substances react with oxygen and each other producing significant amount of heat that further induces combustion reactions and pyrolysis. (KTH biotechnology, 2011) Charring process This process occurs when the wood product burns at a constant rate of heat release per area. The charring rate is an important quantity for the fire resistance of the wood; This is because the wood under this process preserves its original properties. Further, cellulose transformed to unstable, or rather active cellulose that continues to decompose further to carbon dioxide and water. (KTH biotechnology, 2011) Flaming For this process to take place, it depends on the environmental conditions such as oxygen concentration, moisture, temperature, ph, and fire retardants. The process occurs at 300 °C and mainly related to traditional wood burning. In this process, a lot of levoglucosan (tar) is produced that decomposes quickly into burning gasses due to the influence of heat. (Gupta, 2000) Heat transfer process In this process, heat transfer is the driving force of a fire. When there is high heat in any combustion; the restricting surfaces decrease when the gasses is becoming hotter, and the rate of diffusion is on the rise. A significant quantity of a scorching material is the rate of heat transfer; and depend strongly on external factors such as; Net heat flux to the surface andOxygen concentration of the ambient. On the other hand, the intrinsic properties of the material burning are affected by the following: The heat of combustion, heat of gasification and the specific heat capacity. Well, the char forming means the cellulose undergo a transformation to an unstable which decomposes slowly hence hindering the heat transfer since the larger the heat, the faster the rate of transfer. (Gupta, 2000) Q 3.2) definition of reaction rate The response rate of fire is how fast a reaction takes place, and an example is burning methane. Factors affecting Concentration: reaction rate increases with level, as describe by the rate law; the frequency of collision increases as the reaction concentration increases. Nature of the reactants: The complexity of the reactants and other factors can significantly influence the rate of response. Temperature: with higher temperatures increases energy into the system hence enhances the speed of response by causing more collision of particles. Catalyst: In the presence of a catalyst, the higher the reaction rate by providing an alternative route with lower energy of activation. Surface area: An increase in the area hence increase in the response rate because of the more particles exposed to the reactants. Q4) characteristics of flames and fire plumes Flame depth: This implies the width of the area that is continuously blazing behind the fire front. The flare depth always determines the length of time of flash exposure and heat burning across a given area. Flame angle: It is the measurement of flames on the horizontal plane in front of the fire. This characteristic is mostly affected by wind speed and the topography mostly. A flare with less than 90-degree angle is likely to dry out faster. Flame height: This is the vertical measure from the ground level to the flame tip. The fuel moisture and wind speed always determined the height of the flash at any given time. The lower the wind speed and the higher the humidity, the shorter the flame height. 4.2) Factors that affect the spread of fire on the solid fuel surface Amount: the amount of fuel load or the amount of fuel to burn will influence the spread of flames. In this case, if there is a bigger fuel load the intensity of the flames will increase. The increase is regarding the energy produced by the fires. Moisture content: Dry fuel is easy to ignite and burn with a lot of intensity. However, that fuel that isn't dry enough or rather has a lot of moisture content in them would not burn or would burn slowly. Oxygen availability: Oxygen is the crucial factor in the spread of flames. A low concentration of oxygen will slow down the process of spreading of fires, for example, the backdraught burns with little oxygen. In this scenario, if there is an opening or supply of oxygen will explode. Gaseous fuels only need proper mixture with air, and they can ignite while the liquid in a pool is hard to ignite but require a fine spray. (Gupta, 2000) References Gupta, P., 2000. https://ntrs.nasa.gov. [Online] Available at: HYPERLINK "https://ntrs.nasa.gov" https://ntrs.nasa.gov [Accessed 12 March 2017]. KTH biotechnology, 2011. Burning of wood. [Online] Available at: HYPERLINK "http://virtual.vtt.fi" http://virtual.vtt.fi [Accessed 12 March 2017]. Read More