Bernoulli’s theorem states that the total energy of an incompressible, in-viscid fluid, either liquid or gas, flowing at a steady state from one point to another remains constant throughout the displacement. Bernoulli’s equation recognizes that an increase in kinetic energy (velocity) triggers a decrease in pressure within the fluid. Bernoulli’s equation relates the pressure at a point in the fluid to its position and velocity.
P_2+ρ 〖u_2〗^2/2+(ρgh_2 )=P_1+ρ 〖u_1〗^2/2+(ρgh_1 ) (1)
Both P_1 and P_2 represent pressure at points one and two, ρ and u are fluid characteristics density and velocity, g represents the gravity constant 9.81m/s^2 and h_1 and h_2 signify the heights at points one and two.
Viscosity is a measure of a fluid’s resistance to flow. An example of this being the comparison between honey and water; flowing honey through a pipe is a slower process then repeating the same process with water this indicates honey has a higher viscosity level compared with water. Viscous properties tend to steady and organise the flow of a fluid however excessive fluid inertia tends to unsettle flow leading to more disordered turbulent behaviour. Kinematic viscosity is a dimensionless number measuring the ratio of absolute viscosity to density.
In practice, fluids experience friction against surface area. The friction generated corresponds to an energy transformation from kinetic → heat and results in a –ΔP over the length of the fluid flow. We denote this energy loss between point 1 and point 2 as ΔPfriction and account for it experimentally, depending on whether the flow is described as laminar or turbulent by the Reynolds number. Reynolds number is determined by the ratio of inertia forces to viscous forces.
Re=ρuD/μ ...
... middle of paper ...
...on using the data P1 = P2 = Patm and U1 = U2 ≈ 0 m∕s:
〖∆P〗_pump/ρ=〖∆P〗_f/ρ+ gz_2-gz_1
In order to determine a system curve the flow rate must be determined at a range of points. Plotting both the system curve and pump curve together enables the operating point to be found which corresponds to the ideal flow rate. The pump curve can be determined experimentally by modifying the system curve one of two ways; either opening a valve or changing the height difference.
In order to study the aspects of fluid mechanics that need to be taken into account when constructing our cooling tower, a breakdown of different behaviours of fluids under different conditions must be performed and tested against the flow rate. The experimental design would have to explore the influence of the length of the flow pipe as well as the density and temperature on the flow rate of the fluid.
They just forgot to mention the other effects of fluids in nature. “The influence of the fluid on a body moving through it depends not only on the body’s velocity but also on the velocity of the fluid,” this is called relative velocity ( ). The relative velocity of a body in a fluid has an effect on the magnitude of the acting forces. For example, as a long distance runner is running into a head wind, the force of the fluid is very strong. If the runner is running with the help of a tail wind, the current’s force is reduced and may even be unnoticeable.
values by using buffers set at PH 1, 3, 5, 7, 9. I predict that there
The data which was collected in Procedure A was able to produce a relatively straight line. Even though this did have few straying points, there was a positive correlation. This lab was able to support Newton’s Law of Heating and Cooling.
Have you wondered why airplanes were ever able to fly or how racecars are able to stay on the ground at high speeds? They all use a scientific concept called Bernoulli’s principle, or more commonly known as Bernoulli’s equation. His principle simply states that the faster a fluid flows, the less pressure it applies, the slower the fluid flows, the more pressure it applies.
In classical fluid dynamics, the Navier-Stokes equations for incompressible viscous fluids and its special (limiting) case the Euler equations for inviscid fluids are sets of non-linear partial differential equations that describes the spatiotemporal evolution of a fluid (gas). Both equations are derived from conservative principles and they model the behavior of some macroscopic variables namely: mass density, velocity and temperature.
Bernoulli’s principle is the concept that as the speed of a moving fluid (liquid or gas) increases, the pressure within that fluid decreases. This principle was originally formulated in 1738 by the Swiss mathematician and physicist Daniel Bernoulli, it states that the total energy in a steadily flowing ...
Introduction to Aerodynamics Aerodynamics is the study of the motion of fluids in the gas state and bodies in motion relative to the fluid/air. In other words, the study of aerodynamics is the study of fluid dynamics specifically relating to air or the gas state of matter. When an object travels through fluid/air there are two types of flow characteristics that happen, laminar and turbulent. Laminar flow is a smooth, steady flow over a smooth surface and it has little disturbance. Intuition would lead to the belief that this type of air flow would be desirable.
The purpose of this lab report is to state the results gathered by the values of the coefficients of kinetic friction and the coefficient of static friction for two particular surfaces. The theory behind it is that if a body is at rest or moving with constant velocity, it is in equilibrium and the vector sum of all the forces acting on it is zero. The force of friction is always opposing the motion and is always opposite in direction. This lab gave us a chance to bring the inclined plane problems we have been doing in class to real life.
To investigate the relationship between the air pressure in a ball and the bounce height of that ball where the drop height (gravitational potential energy), temperature and location are kept constant.
At the same time, melt flow rate is a measure of the ability of the material's melt to flow under pressure. Melt flow rate is inversely proportional to viscosity of the melt at the conditions of the test, though it should be borne in mind that the viscosity for any such material depends on the applied force. Ratios between two melt flow rate values for one material at different gravimetric weights are often used as a measure for the broadness of the molecular weight distribution.
where p is the density of the fluid (in runner’s case: air); v is the velocity of the runner; A is the cross-sectional area perpendicular to the runner’s velocity; and D is the dimensionless quantity called the drag coefficient.
A process flow diagram of the pump system is shown in Figure 1. The main components of the system are a centrifugal pump with a 4½-inch impeller, a 2-horsepower motor, a piping system with an effective length of about 285 feet, a rotameter for low liquid flow rates (0-2 gpm), a magnetic flow meter for high liquid flow rates (0-90 gpm), and a tank.
A force F applied along the axis of piston A, which has an area S produces in the fluid a rise of pressure P=F/S and generates on the axis of position A’ a force F’ so that F’=PS’
Investigating What Factors Affect the Efficiency of Siphoning I have chosen to investigate siphoning because as a kid I was always intrigued and puzzled by this "phenomena" when I used to clean my fish tank. The difficulty factor also played a major role. I wanted to do something which could be carried out comfortably in a relatively short time. An investigation, which is not so demanding on the practical side to allow more time for processing of the data captured. =
To facilitate the calculation of the pressure coefficient P, the ogive semi-vertex angle is given by,[2]