Introduction To Fluid Mechanics

Bernoulli’s theorem is a special application of the laws of motion and energy. The principle equation describes the pressure measured at any point in a fluid, which can be a gas or a liquid, to the density and the velocity of the specified flow. The theorem can be explained by the means of imagining a particle in a cylindrical pipe. If the pressure on both sides of the particle in the pipe is equal, the particle will be stationary and in equilibrium. By implementing the second law of motion the particle will accelerate or decelerate if there exists a pressure difference over the particle.

¬¬¬¬¬¬Abstract Electrical circuits are described with mathematical expressions. Usually, it is possible to calculate the currents and voltages in a circuit by solving a set of equations, the calculations are required to design a safe circuit.and this is one reason why advanced mathematics is so important in the field of electrical engineering. The circuit equations can be determined using Ohm’s Law, which gives the relationship between voltage and current in a resistor (V=IR), and Kirchhoff’s Current and Voltage Laws, which govern the currents entering and exiting a circuit node and the sum of voltages around a circuit loop, respectively. Objective(s) The purpose of this experiment is to verify Ohm's Law using resistor in dc and ac circuits.

KEY CONCEPTS FOR UNDERSTANDING THE LAWS OF THERMODYNAMICS To understand the laws of thermodynamics, it's essential to understand some other thermodynamics concepts that relate to them. • Thermodynamics Overview - an overview of the basic principles of the field of thermodynamics • Heat Energy - a basic definition of heat energy • Temperature - a basic definition of temperature

Thus ΔT = final temperature – initial temperature However, if the question does provide a graph such as the one shown above, extrapolation would be needed to determine a more accurate ΔT. Hess’s Law of Constant Heat Summation Not all enthalpy changes of reaction can be measured directly by using calorimetry and hence Hess’s Law can be used to determine the enthalpy changes that cannot be determined by direct measurements. Hess’s Law states that the enthalpy change of a reaction is independent of the pathways between the initial and final states, i.e. enthalpy change is a state function. An energy cycle or energy level diagram is used to determine the relationship between all reactions involved before using Hess’s Law to solve for the unknown ΔH.

These are called variational principles and are usually expressed by stating that some integral is a maximum or a minimum. Minimization problems that can be analysed by the calculus of variations serve to characterize the equilibrium configurations of almost all continuous physical systems, ranging through elasticity, solid and fluid mechanics, electro-magnetism, gravitation, quantum mechanics, string theory, and many others. Many geometrical configurations, such as minimal surfaces, can be conveniently formulated as optimization

Engineers came up with idea of using different types of fluids that can change its property according to the external forces. For example MR (Magneto-Rheological) fluids and ER (Electro-Rheological) fluids. MR fluids are materials that expose a change in rheological properties such as elasticity, viscosity or plasticity with the application of a magnetic field. On the other hand, ER fluids alters its rheological property when an electric field is applied to the fluid. MR fluids require small voltages and current, while ER fluids require very large voltage and very small currents.

Introduction Chromatography is a laboratory technique for the separation of a mixture. The mixture is dissolved in a fluid called the mobile phase, which carries it through a structure holding another material called the stationary phase. The various constituents of the mixture travel at different speeds, causing them to be separated. In fact, the separation is based on differential partitioning between the mobile and stationary phases [1]. Chromatography may be preparative or analytical.

The mathematical relationship that exists between pressure and volume when temperature and quantity are held constant is that pressure is inversely proportional to volume. This relationship is known as Boyle’s Law. P1 x V1 = P2 x V2. When the volume of a container is decreased, when still containing the same amount of molecules, more molecules will hit the sides of the container, thus increasing the pressure. We were asked to graph pressure and the inverse of volume because the graph of pressure and inverse volume is inversely related to the graph of pressure and volume.

the dynamical system into a regular stationary process produces such a sequence, then the dynamical system is called a Bernoulli system. 1.6.1 Deterministic Chaos Small differences in initial conditions (such as those due to rounding errors in numerical computation) yield widely diverging outcomes for chaotic systems, rendering long-term prediction impossible in general. This happens even though these systems are deterministic, meaning that their future behavior is fully determined by their initial conditions, with no random elements involved. In other words, the deterministic nature of these systems does not make them predictable. This behavior is known as deterministic chaos, or simply chaos.

Newton 's First Law of Motion states that a force must act upon it in order for the motion of an object to change . This is a concept which generally called as inertia. This law also states that if the net force which is the vector sum of all forces acting on an object is zero, then the velocity of the object is constant. Velocity is a vector quantity which indicates both the object 's speed and the direction of its motion. Hence, the statement that states the object 's velocity is constant is a statement that both its speed and the direction of its motion are constant.