1. Steady state laminar flow occurs in a fluid between two parallel plates, shown in figure...

 

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1. Steady state laminar flow occurs in a fluid between two parallel plates, shown in figure Q1. Since the distance, d, between the moving top plate and stationary bottom surface is constant, this problem can be considered in 1D. The governing equation for this physical problem is - d[u(du(x)]- where is the absolute viscosity, v(x) is the velocity and po is the pressure variation along the channel which is constant across the domain. d - Po = 0 and V[x=d] = 0.6 m/s = V[x=0] = 0 m/s Figure Q1: Geometry and boundary conditions laminar flow between 2 plates. a) Using 2 node linear finite elements, show that the element stiffness matrix, K(e), and element load vector, f(e), can be given as Ke = 1 f(e) - Pol(e) = 2 respectively, where [(e) is element length. x • Finite element nodes -0 [12 marks] 1. Steady state laminar flow occurs in a fluid between two parallel plates, shown in figure Q1. Since the distance, d, between the moving top plate and stationary bottom surface is constant, this problem can be considered in 1D. The governing equation for this physical problem is - d[u(du(x)]- where is the absolute viscosity, v(x) is the velocity and po is the pressure variation along the channel which is constant across the domain. d - Po = 0 and V[x=d] = 0.6 m/s = V[x=0] = 0 m/s Figure Q1: Geometry and boundary conditions laminar flow between 2 plates. a) Using 2 node linear finite elements, show that the element stiffness matrix, K(e), and element load vector, f(e), can be given as Ke = 1 f(e) - Pol(e) = 2 respectively, where [(e) is element length. x • Finite element nodes -0 [12 marks]

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