Fluid mechanics terminologies

Aim: To derive 4th order approximations of second order derivative for central difference, right skewed and left skewed schemes and write a matlab program to compare error between them   Method The code for comparison of error between different schemes is shown below clc clear all close all dx=linspace(1/40,1/20,25);…

Objective To simulate fluid flow through pipeusing open foam for differnt wedge angles  and compare results between them   Method For simulation, instead of the complete cylinder a right circular cylindrical sector/wedgeis considered as the computational domain. This is done to avoid unnecessarycomputations by…

Objective To simulate fluid flow thorugh pipe using open foam solver for incompressible flows (icofoam) and to write a program in matlab to genetrate mesh file required for solving fluid flow in pipe    Method: From Hagen poiseuille pressure drop equation we can determine the decrease in thepressure per unit…

The finite volume method (FVM) is a method for representing and evaluating partialdiffrential equation in the form of algebraic equations. This method is apply for over theentire volume & properties are assumed to be concentrated at geometric centre of thevolume concerned. Actually finite volume method there is use…

Objective: To simulate flow over backward flow step using icofoam solver in open foam Setup: 1. Open the terminal in the Linux Operating System2. just type \'cd $FOAM_TUTORIALS\', and it takes you to the in-built tutorial files of the OpenFOAMsoftware. Type \'ls\' (list) to view the contents in the tutorials.3. Type \'cd…

Objective: To solve the conservative and non conservative governing equations of 1D supersonic nozzle and understand its flow properties at throat,and to perform a grid independence test   Code: Code for Non conservative form close all clear all clc n=31; gamma=1.4; x =linspace(0,3,n); dx=x(2)-x(1); a=1+2.2*(x-1.5).^(2);…

Objective: To obtain solution of 2D heat conduction equation using discretization and 3 different iterative methods   Method Steady state method   clear all close all clc % Defining lenghts of domain Lx=1; Ly=1; % Defining the number of mesh points and w w=1.56; nx=ny=10; % Dividing the lengths along x and y…

Main function: clc clear all close all L=1; timespan = linspace(0,20,30); yo = [0 3]; [theta,t] = lsode (\"pendulum_equation\", yo, timespan); a=theta(:,1); for i= 1:length(a) x(i)= L*sin(a(i)); y(i)= -L*cos(a(i)); x(1)=0;y(1)=0; plot([x(1) x(i)],[y(1) y(i)]) hold on plot (x(i),y(i),\'k.\',\'MarkerSize\',16); grid on axis([-1.5…

For C = 1 and time = 0.4 econds,the original function is of step like function while the final velocity profile is of parabolic shape whose image is attached below .   Moreover it is seen that initially the corners of step function are very sharp in nature but with progress in time this sharpness decreases gradually…

1.1Problem statement: To simulate the tension test of specimen made of steel 1006 material using explicit dynamics, to compare the results for different materials and displacements.       1.2Modelling description: The model downloaded in STEP format is imported into ANSYS design modeller   1.3Analysis…

https://projects.skill-lync.com/projects/ANALYIS-OF-STRESS-AND-DEFORMATION-IN-A-BEAM-31251

https://projects.skill-lync.com/projects/analysis-of-stress-concentration-in-flat-plate

Fourth_order_approx program code function out = fourth_order_approx(x,dx); analytical_derivative=((x^3*cos(x))-(sin(x)*3*x^2))/x^6; fourth_order_equation=((sin(x-2*dx)/(x-2*dx)^3)-(8*sin(x-dx)/(x-dx)^3)+(8*sin(x+dx)/(x+dx)^3)-(sin(x+2*dx)/(x+2*dx)^3))/(12*dx) out=abs(fourth_order_equation-analytical_derivative); end​  …

Fourth_order_approx program code function out = fourth_order_approx(x,dx); analytical_derivative=((x^3*cos(x))-(sin(x)*3*x^2))/x^6; fourth_order_equation=((sin(x-2*dx)/(x-2*dx)^3)-(8*sin(x-dx)/(x-dx)^3)+(8*sin(x+dx)/(x+dx)^3)-(sin(x+2*dx)/(x+2*dx)^3))/(12*dx) out=abs(fourth_order_equation-analytical_derivative); end​  …

Fourth_order_approx program code function out = fourth_order_approx(x,dx); analytical_derivative=((x^3*cos(x))-(sin(x)*3*x^2))/x^6; fourth_order_equation=((sin(x-2*dx)/(x-2*dx)^3)-(8*sin(x-dx)/(x-dx)^3)+(8*sin(x+dx)/(x+dx)^3)-(sin(x+2*dx)/(x+2*dx)^3))/(12*dx) out=abs(fourth_order_equation-analytical_derivative); end​  …

Program coding: clear all close all x=pi/3; dx=1/40; analytical_function=sin(x)/x^3; analytical_derivative=((x^3*cos(x))-(sin(x)*3*x^2))/x^6; first_order_approx=(((sin(x+dx))/((x+dx)^3))-((sin(x)/x^3)))/(dx); second_order_approx=(((sin(x+dx))/((x+dx)^3))-((sin(x-dx))/(x-dx)^3))/(2*dx); fourth_order_approx=((sin(x-2*dx)/(x-2*dx)^3)-(8*sin(x-dx)/(x-dx)^3)+(8*sin(x+dx)/(x+dx)^3)-(sin(x+2*dx)/(x+2*dx)^3))/(12*dx);…

For Alkanes: Solving the coefficients manually for the equations, we get stoichiometric coefficient to be 2 and 3.5 respectively when no of moles of carbon are 1 and 2 correspondingly, Developing an equation uing these two points and plotting it matlab gives following graph. >> x=linspace(1,25,100); >> y=linspace(1,25,100);…

Boundary conditions are those condition that are given at extremes of domain of given PDE Initial conditions are those that are given at lower limits or values of domain of given PDE  Types of boundary conditions in PDEs: Dirichilet boundary condition: In this boundary condition,the value of the function is specified…

1.Kinematic viscosity of a fluid can be defined as proportion of dynamic viscosity of fluid to density of that fluid. It\'s unit is m^2/s  2.Dynamic viscosity of fluid is defined as internal resistance to the flow of fluid between it\'s molecules in presence of some external force. Dynamic viscosity is given by …

1.Kinematic viscosity of a fluid can be defined as proportion of dynamic viscosity of fluid to density of that fluid. It\'s unit is m^2/s  2.Dynamic viscosity of fluid is defined as internal resistance to the flow of fluid between it\'s molecules in presence of some external force. Dynamic viscosity is given by …

1. Divergence of vector field defines the degree of expansion or outward flow of that vector field. It is said to be positive if vector field moves outward and negative if vector field moves inward.       2.Gradient of vector is defined as rate of change of that particular vector.    3.Curl…

1. Divergence of vector field defines the degree of expansion or outward flow of that vector field. It is said to be positive if vector field moves outward and negative if vector field moves inward.       2.Gradient of vector is defined as rate of change of that particular vector.    3.Curl…

1. A=[1,2,3,4,5] returns the output of a matrix A consisting of one row and 5 columns with elements 1,2,3,4,5. 2. A=[1;2;3;4;5] returns ouput of matrix B consisting of one column and 5 rows with elements 1,2,3,4,5 3.C= A*B\' returns an error because both A and B matrices are of the same size consisting of 1 row and 5 columns…

1. A=[1,2,3,4,5] returns the output of a matrix A consisting of one row and 5 columns with elements 1,2,3,4,5. 2. A=[1;2;3;4;5] returns ouput of matrix B consisting of one column and 5 rows with elements 1,2,3,4,5 3.C= A*B\' returns an error because both A and B matrices are of the same size consisting of 1 row and 5 columns…

1A) For the bar shown in figure above F1, F2,F3 can be written as follows F1 = F1 F2 = 0 F3 = -W where -W is the weight of entire beam acting in downward direction and F1 is the force acting at node 1 which is the reaction force because the beam is supported at node 1.   B)   C)        

1.Problem decription: The objective of the project is to analyze the stress and deformation of a beam and validate these results using values from analytical method. Another objective of the project is  1.1.Model description The model below is modelled with the help of ANSYS design modeller. The model description…

1.Problem ststement: The objective of the problem is to analyze the stress concentration in a flat plate with a hole in centre and determine the maximum deformation and stress developed in flat plate due to given load.   1.1.Model description: The model is modelled using ANSYS design modeller. The model is modelled…