Comparison of numerical derivative and analytical derivative

                      GEAR SLOSHING ANALYSIS USING WATER AND OIL In industrial applications, it is very important to use lubricants in between rotating gears. Lubrication is necessary to reduce coefficient of friction between gear teeth. It also limits the rise of…

Rayleigh Taylor Instability Rayleigh-Taylor instability, or RT instability is an instability of an interface between two fluids of different densities which occurs when the lighter fluid is continuously pushing the heavier fluid. RT instability is a buoyancy-driven instabilty, where the fluids are initially at hydrostatic…

An Ahmed body is a generic car body which represents a simplified ground vehicle geometry of a bluff body type. The Ahmed Body was first created by S.R. Ahmed in 1984 in one of his research. A typical CAD model of Ahmed body is shown below: The geometrical dimensions of the body are: LENGTH = 1.044 metres HEIGHT = 0.288…

OBJECTIVE- To develop a code and demonstrate the motion of a simple pendulum using Matlab Given below is the equation of motion of a simple pendulum with damping in the form of Ordinary Differential Equation (ODE) : `(d theta^2)/dt +(b/m)(d theta)/dt +(g/L)sin theta = 0` where g= gravity in m/s^2        …

The purpose of this project is to compare the exact derivative of the given function with the first order, second order and fourth order approximations of the first derivative of the same function and find out the magnitude of error introduced while using these numerical schemes. Here the given function is `sin(x)/x^3`…

Main program: clear allclose allclcx=pi/3;dx=linspace(pi/30,pi/4000,10);for i=1:length(dx)first_order_error(i)=first_order_approximation(x,dx(i));second_order_error(i)=second_order_approximation(x,dx(i));fourth_order_error(i)=fourth_order_approximation(x,dx(i));endfigure(1)loglog(dx,first_order_error)hold onloglog(dx,second_order_error,'r')hold…

The purpose of this project is to compare the exact derivative of the given function with the first order, second order and fourth order approximations of the first derivative of the same function and find out the magnitude of error introduced while using these numerical schemes.Here the given function is `sin(x)/x^3`The…

In this project we will study the mixing efficiency of hot and cold air when they are mixed in a tee shaped pipe. For this we have taken 3 cases. In all the 3 cases the inlet of hot air is considered to be the left hand side and outlet is the right hand side. The top opening is for the cold air. CASE I : Short Tee  …