Machinery's Handbook, 31st Edition
Fluid Flow
1491 (3)
Q Av Av = = 1 1 2 2
where Q = volume rate of flow; A = cross-sectional area of the liquid stream; v = the aver- age velocity of the liquid at that cross-sectional location; and subscripts 1 and 2 indicate two different locations in the liquid flow. Sprue Design: The shape of the sprue can be calculated using Equation (2) and Equation (3). Assuming that pressure at the top of the sprue is equal to pressure at the bottom and that there are no frictional losses, the relationship between height and cross-sectional area at any point in the sprue is given by the parabolic relationship: (4) Flow Characteristics: A molten metal’s flow characteristics are an important consider - ation in the gating system because of the possible consequences of turbulence. There are two types of real fluid flow: laminar and turbulent. In laminar flow, fluid moves in layers called laminas . Laminar flow need not be in a straight line; the flow may follow curved surfaces. The fluid layers slide smoothly over one another, without fluid being exchanged between the layers. In turbulent flow , secondary random motions are superimposed on the principal flow, and there is an exchange of fluid from one adjacent sector to another. More important, there is an exchange of momentum: slow-moving fluid particles speed up, while fast-moving particles give up their momentum to slower-moving particles and are slowed down. The factor that determines which type of flow is present is the ratio of the inertial forces to the viscous forces within the fluid. This ratio is expressed by the dimensionless Reyn - olds number as: (5) where R e = Reynolds number; v = mean fluid velocity; L = characteristic length (equal to diameter if cross section is a circle); µ = dynamic fluid viscosity; ρ = density of the fluid. The higher the R e, the greater the tendency for turbulent flow to occur in the gating system: (1) laminar flow: 0 = R e < 2000; (2) transition flow: 20 < R e < 20,000; (3) turbulent flow: R e > 20,000. Turbulent flow leads to inclusions, and therefore a reduction in fluidity. Fluidity of Molten Metal The phrase fluidity of molten metal describes the capability of molten metal to fill mold cavities, based on two factors: characteristics of the molten metal and casting parameters. The following characteristics of molten metal influence fluidity: Viscosity: If viscosity (a measure of the metal’s deformation in a molten state) and sensi- tivity to temperature (viscosity index) increase, fluidity decreases. Surface Tension: High surface tension of the liquid metal reduces fluidity. Oxide films that develop on the surface of molten metal increase surface tension and thus can signifi - cantly reduce fluidity. Fluxing processes (treating metal with flux to promote melting) in the heating of metals are used to reduce or eliminate oxidation and to improve fluidity of metal surface layers. Inclusions: Metallic and non-metallic inclusions have long been recognized as one of the most important quality issues in metal casting. As insoluble particles, inclusions can have a significant adverse effect on fluidity; the presence of inclusions often is the cause of decreased fluidity. Solidification Pattern of the Alloy: Fluidity is inversely proportional to the freezing tem- perature range. In general, pure metals and alloys of eutectic composition have the highest values of fluidity. Solid-solution and other alloys have lower fluidity. Superheat: The difference between the melting temperature and the pouring temper- ature also influences fluidity. For given alloy compositions, if the melt temperature is higher, fluidity increases. The pouring temperature is often specified, rather than the su - perheat temperature, because it is easier to do so. A A h h 1 2 1 2 = R e = ρ μ vL
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