Neglecting the atmospheric pressure
Density of mercury = 0.490 lb/in3
gravity = 32.17 ft/s2
h = 15 inch
Pressure in water main = pgh
= 0.490x32.17x12x15
=2837.4 psi
Exercise 2: Finite element method We are interested in computing numerically the solution to a 2D...
Orthogonal projections. In class we showed that if V is a finite-dimensional inner product space and U-V s a subspace, then U㊥ U↓-V, (U 1-U, and Pb is well-defined Inspecting the proofs, convince yourself that all that was needed was for U to be finite- dimensional. (In fact, your book does it this way). Then answer the following questions (a) Let V be an inner product space. Prove that for any u V. if u 0, we have proj, Pspan(v)...
Write a MATLAB code to solve below 2nd order linear ordinary differential equation by finite difference method: y"-y'-0 in domain (-1, 1) with boundary condition y(x-1)--1 and y(x-1)-1. with boundary condition y an Use 2nd order approximation, i.e. O(dx2), and dx-0.05 to obtain numerical solution. Then plot the numerical solution as scattered markers together wi exp(2)-explx+1) as a continuous curve. Please add legend in your plot th the analytical solution y-1+ Write a MATLAB code to solve below 2nd order...
In this exercise, your will be creating the function euler2 which applies Euler's method to numerically solve a first order ODE, but with no overshoot. Input variables: ODEFUN – A function representing the the equation for y'. It must be a function of t and y. TSPAN – a vector containing the start time and end time (TSPAN = [tStart,tEnd]). Y0 – The value for y at tStart. h – The step size. Output variables: TOUT – The output time...
Q2 (a) (0) Explain what is meant by interpolation in the Finite Element Method and why it is used (3 marks) What is a shape function? (3 marks) PLEASE TURN OVER 16363,16367 Page 2 of 3 0.2 (a) (Continued) (iii) For an isoparametric element, explain the relationship between shape functions, the geometry of the element and the shape the loaded element will deform to. (3 marks) (iv) Describe the relationship between structural equilibrium and the minimum potential energy state. (3...
Project Being able to analytically calculate the solution to a given partial differential equation is often a much more difficult (if not impossible) task than presented here. Possible challenges include irregular domains and strange numerical techniques are often used to approximate the solution to a PDE. The most basic of such methods is the finite difference method. To illustrate the method, consider the Dirchlet Poisson equation in one dimension given by 10:Finite Difference Approximation ary conditions. In those cases, The...
solve problem #1 depending on the given information Consider the following 1D second order elliptic equation with Dirichlet boundary conditions du(x) (c(x)du ) = f(x) (a $15 b), u(a) = ga, u(b) = gb dr: where u(x) is the unknown function, ga and gb are the Dirichlet boundary values, c(x) is a given coefficient function and f(x) is a given source function. See the theorem 10.1 in the textbook for the existence and uniqueness of the solution. 1.1 Weak Formulation...
PLEASE WRITE/PRINT CLEARLY AND SOLVE USING THE FINITE ELEMENT METHOD UNCLUDING MATRICIES 2. The flow rate at node 1 is 0.16 liter/s (0.16 *10-2 m/s). The pressure at node 4 is 0 Pa (g). For the given conditions, the flow is laminar throughout the system. Using hand calculation determine i. The pressure in each node. ii. Flow in each element iii. Verify your results (25 + 10 + 5 = 40) (1) L=10 m D=20 mm u = 8 x...
PLEASE WRITE/PRINT CLEARLY PLEASE SOLVE USING THE FINITE ELEMENT METHOD WHICH INCLUDES THE MATRIXES 2. The flow rate at node 1 is 0.16 liter/s (0.16 *10 m/s). The pressure at node 4 is 0 Pa (g). For the given conditions, the flow is laminar throughout the system. Using hand calculation determine i. The pressure in each node. ii. Flow in each element iii. Verify your results (25 + 10 + 5 = 40) (1) L= 10 m D-20 mm [2]...
X=0 x = 1/2 x= L u U2 Uz (a) Trial solution for a 1-D quadratic elastic bar element can be written as follows: ū(x) = [N]{u} where, [N] = [N1 N2 N3] and {u} u2 13 1 and Ni L2 L2 [N] and {u} are known as interpolation function matrix and nodal displacement, respectively. (272 – 3L + L´), N= = (22- La), Ns = 12 (2=– LE) Derive the expression for element stiffness matrix, (Kelem) and element force...