Differential equation

figure below: Firstly, we have a fluid problem. To solve this problem, we should know the physical properties of fluid by using Fluid Mechanics. Then we can use mathematical equations to describe these physical properties. This is Navier-Stokes Equation and it is the governing equation of CFD. As the Navier-Stokes Equation is analytical, human can understand it and solve them on a piece of paper. But if we…

course, I had learned to oversee two equations (x-axis and y-axis) and separate two equations. Afterward, the first question asks to solve for the max force of static friction that must be encountered before block initially moves. Therefore, I knew I must use the max friction formula which is coefficient of static friction times normal force. On the other hand, I have solved for normal force using y-axis equation, but instead, I used an inclined normal force equation to explain for max, static…

 Musical Notes Can Count Jerri Pineda Abstract— The development of mathematics involves early connections with music and the basic physics of sound. Mathematics is present in the natural occurrence of the ratios and intervals found in music and modern tuning systems. As people age, their hearing becomes dull and require change in the music ratio and interval to hear the same tune as when young. In like manner, the interval increases until a perfect pitch is heard. In this paper we will examine…

Oasis Inc wants to earn enough revenue to create their newest heated luxury massage chair:The Tranquility 5000. However, the company needs to estimate the equilibrium price and quantity in order to find the optimal retail price needed to create this launch. This report will provide concrete analysis on the prices. The beginning of the analysis focused on the demand data. The demand included a range of prices and the quantity demand of n=110 test weeks. This can bee seen on Figure 1, which…

Introduction: In today’s world, the majority of people have a work computer, home computer, and/or a lap top, because computers have become affordable for the average person. If you look at the history of computers, it has taken us over a century to get to this point. Computers were first used primarily for businesses and government, because they were too expensive and large for personal use by the average person. According to Wikipedia (2016), “a computer is a device that can be instructed to…

trends are similar. This led us to believe that some of the measurements could have been slightly off due to difficulty in measuring the dimensions of the jug. After testing two different bottles, it was apparent that the Helmholtz resonant frequency equation is an accurate tool when estimating the resonant frequency of Helmholtz resonators. Figure 2: Plot of the frequency vs volume of a jug for theoretical and experimental results.…

The SMD model based on density, solves the Poisson-Boltzmann equation analogously to PCM, but does so using a set of specifically parametrised radii which construct the cavity.[7 ,8] The COSMO solvation model or (CPCM) :This model uses the scaled conductor boundary condition, which is a fast and robust approximation to the exact dielectric equations and reduces the outlying charge errors as compared to PCM. Isodensity PCM ( IPCM): Cavity formed using gas-phase…

As explained above, the governing equations of the gas mixture that include continuity, momentum and mass fraction of the components, are solved at first. Transient conservation equations are as follow: Mass conservation (1) (∂(ε(1-s)ρ_g))/∂t+∇.(ρ_g u ⃗_g )=S_m In this equation u ⃗_g is superficial velocity vector of gas mixture, which related to intrinsic fluid velocity U as following: (2) (u_g ) ⃗=ε(1-s)U ⃗ In the gas transfer channel, the porosity is equal one and the liquid water volume fraction…

highly complex model which describes 7 groups of bacteria and archaea (included in a total of 32 dynamic state concentration variables) catalyzing 19 biochemical kinetic processes coupled to 105 kinetic and stoichiometric parameters. The set of differential equations (DE) of the ADM1 for the calculation of the variables include 10 DE to model the evolution of soluble matter concentrations in the liquid phase and two DE to model inorganic carbon and inorganic nitrogen levels in the liquid phase.…

Application of Bernoulli’s Equation to Fluid Dynamics Bernoulli’s equation has been used widely in an engineering aspects, the conservation of energy is the most famous one. This paper will talk about the application of Bernoulli’s equation to fluid dynamics. Fluids flow can be in different forms, such as water in the ocean, blood within our body and etc. Thus, it is necessary to study the mechanism of fluids. In the year of 1738, Daniel Bernoulli published a book called Hydrodynamica, which…