7. (D* + 16D² + 36D + 19)y = 0

The uniaxial bar finite element equation can be used for other types of engineering problems, if proper analogy is applied. For example, consider the piping network shown in the figure. Each section of the network can be modeled using a finite element. If the flow is laminar and steady, we can write the equations for a single pipe element as: - q₁ = K(P; — P;) qi q;= K(P; - P;) qj where q; and q; are fluid flow at nodes i and j, respectively; P; and P; are fluid pressure at nodes i and j, respectively; and K is K = πD4 128μL where D is the diameter of the piper, μ is the viscosity, and L is the length of the pipe. The fluid flow is considered positive away from the node. The viscosity of the fluid is 9×104 Pa's. a. Write the element matrix equation for the flow in the pipe element. b. The net flow rates into nodes 1 and 2 are 10 and 15 m³/s, respectively. The pressures at the nodes 6, 7, and 8 are all zero. The net flow rate into the nodes 3, 4, and 5 are all zero. What is the outflow…

Euler Cauch equation is used to solve * Non linear differential equation Linear differential equation O Linear and non linear differential equation O Homogenous differential equation Non of the above

Problem 6: Inputs: ● ● ● a = 600 mm b = 400 mm c = 200 mm F = 100 N The line of action of the force vector passes through points B and C. B X Z (a) Use the cross product to compute the moment about point A. For this part, you must use B in your vector formulation. F That is, compute MA = B x F. Express your answer as a vector and convert "mm" to "m". IB a A IC с (b) Now use a different position vector, r, in the cross product. This time use rc to to compute the moment about point A. For this part, you must use rc in your vector formulation. Compute MA = rcx F. Express your answer as a vector and convert "mm" to "m". c) Do your answers agree? Yes or no. F y

By integrating the differential equations of equilibrium, calculate V, and M, for 0 < x < L. Clearly state the boundary conditions. Verify the solution by using the free body diagram method. Plot V, and M, vs L < 1. for 0 < L Vy Vy(z) Vy(0) V,(0) is V,(x) at 1 = 0 M, = M-(2) Po TTX' Py = Po sin () EI, L

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