Xd is the interface height in mg is acceleration due to gravityis the ambient temperature in KTg is the temperature of the hot gas in the upper layer in KXN is height of the neutral plane in mThe rate of mass flow through an opening is described in the equation below. H0 is the height of the opening in m (Hurley, 2016). The interface between the lower and the upper layers in fires near or post flashover is near the flor level. Experiment has shown that the density flow through an opening is influenced by a ventilation factor.
The widely used correlation is Where Ao is the area of the openingH0 is the height of the opening Ma is mass burning ratek is a constant which equal to 0.09The out flow of hot gases through the opening and the inflow of cold gases are influenced by fire. External factors that may influence the results such as the effects of air conditioning system and mechanical ventilation are ignored. Thermal discontinuity occurs when the cold air outside the room flows in a contra-flow to the out flowing hot air close to the floor and below the level of the window (Feasey & University of Canterbury, 1999). b) The governing equations of a fluid dynamics model are shown below.
Explain the physical sense of each term. Continuity equation The continuity equation shown below expresses conservation of massIt also expresses a continuous velocity as it is a partial differential equation. To obtain this equation, it is assumed that there is no change of phase. For two phases like water and steam, it is assumed that the rate of increase of mass of the first fluid is equal to the rate at which the mass of the second fluid is decreasing.
The first and the second terms in the equation are the change in density with time and the change in velocity respectively (Currie, 2012). Momentum An equation that expresses conservation momentum of a fluid flow isThe term represents the inertia force per unit volume of fluid. The first term represents a local change with time and the second term expresses the momentum convection. It covers the acceleration around an obstacle even at a steady flow.
The term is nonlinear as it velocity appears quadratic. The other side of the equation represents the forces that causing the acceleration. P is a symbol for thermodynamic pressure; δi is Kronecker delta and represents the shear stress, and the symbol µ dynamic viscosity. The term expresses body forces like gravity that act on the fluid. The term accounts for the force on the surface. The term, , is diffusion which is the momentum exchange of the molecules. A good knowledge of the physical meaning of each term is important when approximating the full governing equation (Currie, 2012).
Mass The equation for mass conservation is and The first two terms shows the change in mass of a given fluid with time. This is caused by the change in the properties of the fluid and change in position at any given time in a fluid flow. The third term represents diffusion and the fourth term shows a change due to heat being produced.