Curve fitting using python

AIM To solve the differential equation representing the oscillatory motion of a damped pendulum GOVERNING EQUATION `(d^2theta)/dt^2 +b/m*(d theta)/dt+g/l*sintheta=0` `theta`= angular displacement of the pendulum b = damping coefficient m = mass of pendulum ball (kg) g = acceleration due to gravity (m/`s^2`) l = length…

AIM To fit a linear and cubic polynomial to the given c_p data To plot the linear and cubic fit curves along with linear data point. THEORY Curve fitting It is the process of constructing a curve or a mathematical function that fits to a series of data points subjected to constraints, as accurately as possible. Best curve…

AIM To perform a flow simulation on flow bench and obtain the following: 1) Grid dependency for selected  valve lift 2) Effect of valve lift on ass flow rate THEORY An air flow bench is a device used for testing the internal aerodynamic qualities of an engine component and is related to the more familiar wind tunnel.It…

AIM Design and analysis of a centrifugal pump. THEORY Centrifugal pumps are used to transport fluids by the conversion of rotational kinetic energy to the hydrodynamic energy of the fluid flow. The rotational energy typically comes from an engine or electric motor. They are a sub-class of dynamic axisymmetric work-absorbing…

AIM 1) To use the Newton-Raphson method to find value of pressure at 0.6 feet 2) Find the optimal relaxtion factor with the help of suitable plot. 3) To determine pressure for given range of ice thickness THEORY The Newton-Raphson method (also known as Newton's method) is a way to quickly find a good approximation…

AIM To conduct frequency analysis of a rotating shaft and determine 5 mode shapes and the resonant frequencies. THEORY When a body oscillates under absence of any continuous or repeated load, the frequency of oscillation of the body is known as natural frequency. When a load is applied to the body, it can vibrte at various…

AIM To perform static analysis on 2 models of plate with holes and compare the results for stress, strain and displacement. THEORY Plate structure with holes is widely applied in engineering practices. The reason making holes on the plate could vary, some for installing bolts and other connectors, and others for reducing…

AIM To simulate the flow over a cylinder. THEORY Reynolds number, Re = `(rho*V*l)/mu` = `(V*l)/nu` , where `rho` = density of the fluid (kg/`m^3`) V = velocity of the fluid (m/s) l = characteristic length of the fluid (m) `mu` = dynamic viscosity (`Pa*s`) `nu` = kinematic viscosity (`m^2`/s) THEORY Reynolds number…

AIM To model flow over NACA airfoil for angle of attack of 0,2,4,6,8,10 degrees. THEORY Airfoil is defined as cross section of a body that is placed in an airstream in order to generate useful aerodynamic force. NACA stands for national Advisory Committee for Aeronotics. The NACA airfoils are airfoil shapes for aircraft…

AIM To analyse Otto cycle and plot its P-V diagram GOVERNING EQUATIONS Ideal gas equation: `(P*V)/T` = constant. This equation is true for ideal gases and since Otto cycle is an air standard cycle, this equation holds true. Here, P = pressure           T = temperature      …

AIM To perform buckling analysis on a cyclone separator stand with and without stiffener and find the change in factor of safety. To run a design safety and find the optimum position for the stiffener. SETUP The cyclone separator is a device for separating solid particles from contaminated gas streams, and has…

AIM To perform motion analysis of planetary gear in SolidWorks PLANETARY GEAR A planetary gear is also known as epicyclic gear train. It contains and input and an output shaft in a co-axial arrangement. It consists of a sun gear, a ring gear, planetary gears and a carrier carrying the planet gear or gears,all of the same…

AIM To compare the performance of 3 different types of beams under a bending load. THEORY When a bending load is applied to a beam, it experiences a bending moment which causes change in its shape and development of internal stresses. The material is in compression on the inside of the curve and in tension at the outside…

AIM To calculate drag force against a cyclist Governing Equation F = `1/2*rho*S*V^2*C_d` Here, F = Drag force experienced by the cyclist in Newton(N). `rho`= Density of air (kg/`m^3`) S = Frontal area or the area suffering air resistance (`m^2`) V = velocity of the cyclist (m/s) `C_d`= drag coefficient (unitless quantity)…

AIMTo calculate drag force against a cyclist. GOVERNING EQUATIONF = `1/2*rho*A*V^2*C_d`Here,F = Drag force experienced by the cyclist in Newton(N).`rho`= Density of air (kg/`m^3`)A = Frontal area or the area suffering air resistance (`m^2`)V = velocity of the cyclist (m/s)`C_d`= drag coefficient (unitless quantity)Drag…

https://skill-lync.com/projects/mbd-simulation-on-i-c-engin-valve-train

AIM To perform motion analysis of IC engine valve train. THEORY A valve train is a mechanical system that controls operation of intake and exhaust valve in an I.C. engine. Cam lift profile The ‘cam lift’ is actually an abbreviation of the ‘follower lift at the cam side’. The term is usually only…

AIM To run a pipe flow simulation with Reynolds number of 100, 1000, 10000 GOVERNING EQUATION Reynolds number, Re = `(rho*V*l)/mu` = `(V*l)/nu` , where `rho` = density of the fluid (kg/`m^3`) V = velocity of the fluid (m/s) l = characteristic length of the fluid (m) `mu` = dynamic viscosity (`Pa*s`) `nu` = kinematic…

AIM1) To create Rankine cycle simulator.2) To plot T-S and h-S curves for given inputs. RANKINE CYCLEIt is a model designed to predict the performance of a steam turbine system. It consists of 4 major components:• Boiler• Turbine• Condenser• PumpA fuel is used to produce heat within a boiler, converting…

AIM To perform MBD simulation of a piston assembly in SolidWorks PARTS OF PISTON ASEMBLY Piston: It is the moving component that is contained by a cylinder and transfers the force from the expanding gas in the cylinder to the crankshaft via connecting rod. Grooves are made for the piston rings in order to make it air tight.…

Aim To solve the differential equation representing the oscillatory motion of a damped pendulum Governing equation `(d^2theta)/dt^2 +b/m*(d theta)/dt+g/l*sintheta=0` `theta`= angular displacement of the pendulum b = damping coefficient m = mass of pendulum ball (kg) g = acceleration due to gravity (m/`s^2`) l = length…

Aim: To simulate the forward kinematics of a 2-R robotic arm Governing equations For a line of length from a point (`X_1, Y_1`) and making an angle theta with the horizontal, the coordinates of the end point, (`X_2, Y_2`) are given by: `X_2` = `X_1+l*costheta` `Y_2` = `Y_1+l*sintheta`   Setup  …

AIM 1) To extract the coefficients, species and the temperature ranges from the given data file 2) To calculate specific feat, enthalpy and entropy for the given species using the defined formulas, applicable in their local temperature ranges. 3) To plot the properties obtained against temperature for different species…

AIM i) To create the internal geneva mechanism assembly in solidworks using the given 2D CAD models. ii) To perform the motion analysis of the assembly by rotating the driving wheel and obtain various plots. THEORY Multibody dynamics Multibody dynamics is a system consisting of solid bodies or links that are connected…

Aim:To optimise the stalagmite function and obtain the global maxima for the given function Theory:Genetic algorithm is a sort of heuristic or a probabilistic search inspired by Charles Darwin’s theory of natural selection. The process of natural selection starts with the selection of fittest individuals from a population.…

Aim: To fit a linear and cubic polynomial to the given c_p data To plot the linear and cubic fit curves along with linear data points To make the curve fit perfectly and to get the best fit To improve the cubic fit Curve fitting It is the process of constructing a curve or a mathematical function that fits to a series…

Aim To analyse Otto cycle and plot its P-V diagram Governing equations Ideal gas equation: `(P*V)/T` = constant. This equation is true for ideal gases and since Otto cycle is an air standard cycle, this equation holds true. Here, P = pressure           T = temperature      …