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Unformatted text preview: 1. Hydrostatics p = g or dp dz =- g p 2- p 1 =- z 2 Z z 1 gdz Force on submerged plane surface, F = p cg A , where p cg is the pressure at the center of gravity. cg = 1 A Z dA where is the slant distance from the surface. The center of pressure is given by y cp =- I xx sin /h cg A, x cp =- I xy sin /h cg A I xy = R xydA, I xx = R y 2 dA The force on a curved surface equals the force acting on the projection of the surface onto a vertical plane. 2. Control Volume Analysis Reynolds Transport Theorem dN dt system = d dt ZZZ dV + ZZ V n dS Conservation of Mass: d dt ZZZ dV =- ZZ V n dS Conservation of Momentum: d dt ZZZ V dV + ZZ VV n dS = F F pressure =- ZZ p n dS Conservation of Energy: Q- W shaft = d dt ZZZ edV + ZZ e + p V n dS e = u + 1 2 V 2 + gz 3. Differential Equations of Motion Continuity: t + ( V ) = 0 Momentum: V t + ( V ) V = g- p + ij u i t + u j u i x j = g i- p x i + ij x j 1 2 For incompressible flow, ij = u i x j + u j x i Then, ij x j = 2 u i x j x j = 2 V 4. Streamfunction Two-dimensional, incompressible flow V = 0 u = y , v =-...
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This note was uploaded on 07/23/2008 for the course AERSP 308 taught by Professor Morris during the Spring '05 term at Pennsylvania State University, University Park.
- Spring '05