The load over the plate varies linearly along the sides of the plate such that p = 2 3 [x(4 - y)] kPa. Determine the resultant force and its position (x, y) on the plate. p 3 m 4 m y x 8 kPa Prob. 9117

ME 3350 Notes – Week 8 4 – Differential Form of the Conservation of Mass Principle (∆V) Consider arbitrary differentially small CV : δ ∫ ρdV+∮ρV ∙dA=0→ ∮ ρV∙dA= −δ ∫ ρdV=− δρ ∆V=− δρ = 1 ∮ ρV ∙dA δt CV CS CS δt CV δt|atsome p(x,y,z∈CV δt (x,y,z ,) ∆V CS −δρ 1 shrink as ∆V→0 : = lim ∮ ρV ∙dA δt ∆ V →0 CS lim 1 f ∙dA=∇∙ f →−δρ =∇∙ ρV )→ δρ+∇∙ ρV )=0 Divergence Theorem: ∆V → 0V CS δt δt continuity equation (most general form) δρ δ δ δ In Cartesian coordinates: