Fluid mechanics formula, what is the fluid mechanics formula?

With the Bernoulli equation.

The conversion formula between static pressure energy and kinetic energy is as follows: 1 2*U 2=δp P=P2-P1; p1 = atmospheric pressure).

The density of water is 1000kg m3.

u is the velocity, m s

p＝1/2*ρ*u^2

P2 PA) on the dimension:

kg m 3*(m s) 2]=[kg (m*s 2)]Remember Newton's second law f m*a? n kg*m s 2, substituting into the above formula.

n/m^2=pa

Dismantling ideas: Let the depth of entering the water be h meters, the weight of the object is g1 kg, the buoyancy in the water is g2, the air resistance is f1, the water resistance is f2, and the gravitational potential energy overcomes the resistance and the underwater buoyancy to do work (the buoyancy in the air can not be counted), and the equation can be built:

10 + h ）g1 =10 f1 + h f2 +h g2

The key lies in the air resistance f1, the determination of the water resistance f2, the resistance of the object is related to the size, shape and the nature of the fluid that rubs against it, and also related to the speed of the relative motion, in the square area of the resistance, the resistance is proportional to the square of the velocity, in this case the velocity increases from 0 to the maximum (to the surface of the water), and from the maximum to 0 (the deepest part of the water), so f1 and f2 are variable forces, Therefore, the first two items at the right end of the equation can only be expressed by the resistance work (of course, negative work) w1 and w2, dw=f dx, (f1 and f2 are both functions of the position coordinates x) must be integrated to find w1 and w2

Three major equations of fluid mechanics: 1. Continuous equations. For the continuous equation, according to the Reynolds transport formula and the concept of conservation of mass, the density is the intensity quantity in the Reynolds transport formula, and the mass is the extension quantity in the formula.

That is, according to the results of the conservation of mass, it can be concluded that the mass growth rate of the system under the Euler method is 0, that is, the left side of the Reynolds transport equation is 0, and the above equation is the integral form of the continuous equation.

2. Renault transport formula. Here we first need to derive the Renault transport formula. In fluid mechanics, we define a certain extension in the flow field (extension refers to the quantity related to the quantity of matter, such as volume, mass, heat conduction, etc.; Strength refers to quantities that are not related to the amount of matter, such as temperature, density, etc.

This is also why the general expression of the extension is expressed in the form of a volume integral). In summary, the Reynolds transport formula is obtained: the growth rate of the extension of a certain fluid in a material system is equal to the growth rate of the same physical quantity in the space occupied by the system at that time, plus the total flux of the physical quantity flowing out of the regional boundary in a unit time.

3. Momentum equation. For the momentum equation, according to the Reynolds transport formula and the momentum theorem, the total momentum of the system becomes the extension quantity in the formula, and the momentum density becomes the intensity quantity in the formula, i.e., yes, and the momentum theorem describes the effect of the external force on the system that causes the change of the momentum of the system. For a fluid system composed of fluid points, the external force is composed of two parts, the volume force and the area force.

where the volume force refers to the force acting on each fluid point, similar to a broad extension, and can therefore be expressed by the volume integral of the "density". The area force on the fluid is mainly reflected in the frictional stress between the fluids, which can be described by the Euler-Cauthy stress principle.

3. Momentum equation. For the momentum equation, according to the Reynolds transport formula and the momentum theorem, the total momentum of the system becomes the extension quantity in the formula, and the momentum density becomes the intensity quantity in the formula, i.e., yes, and the momentum theorem describes the effect of the external force on the system that causes the change of the momentum of the system. For a fluid system composed of fluid points, the external force is composed of two parts, the volume force and the area force.

where the volume force refers to the force acting on each fluid point, similar to a broad extension, and can therefore be expressed by the volume integral of the "density". The area force on the fluid is mainly reflected in the frictional stress between the fluids, which can be described by the Euler-Cauthy stress principle.

There are many formulas in fluid mechanics, and different formulas are used according to different problems, and all of them can be found. Among them, the equations used to solve the problem are mainly as follows:

1.Continuity equation.

2.The momentum equation, in three dimensions, has three.

3.Energy equation.

The details are as follows:The conversion formula between static pressure energy and kinetic energy is as follows: 1 2*U 2=δp P=P2-P1; p1 = atmospheric pressure).

The density of water is 1000kg m3.

u is the velocity, m s

p＝1/2*ρ*u^2。

p2＝ (pa)。

About the dimension: [kg m 3*(m s) 2]=[kg (m*s 2)].

n kg*m s 2, substituting the above equation to get n m 2=pa.

f = m ·am = m(fxi+fyj+fzk) am = f m = fxi+fyj+fzk is a unit mass force, which is numerically equal to acceleration.

Fluid mechanics is a branch of mechanics, which mainly studies the static state and motion state of the fluid itself and the interaction and flow law between the boundary wall of the fluid and the solid under the action of various forces.

There are three basic equations and formulas of fluid mechanics: continuity equation, energy equation, and dynamic land quantity equation.

It is a branch of mechanics that mainly studies the static state and motion state of the fluid itself under the action of various forces, as well as the interaction and flow law between the boundary wall of the fluid and the solid when there is relative motion.

Parallel to the development of hydrokinetics-slip mechanics is hydraulics (see Fluid Dynamics). In order to meet the needs of production and engineering, some empirical formulas have been summarized from a large number of experiments to express the relationship between flow parameters.

Planck came up with a number of new concepts that were widely used in the design of airplanes and steam turbines. This theory not only clarifies the scope of application of an ideal fluid, but also calculates the frictional resistance encountered in the motion of an object. The above two situations have been unified.

A Brief History of Development:

Fluid mechanics is gradually developed in the struggle between human beings and the natural world and in the practice of production. China has the legend of Dayu to control the water and dredge the rivers. Li Bing and his son in the Qin Dynasty (3rd century BC) led the working people to build Dujiangyan, which is still in play today.

Around the same time, the Romans built a massive system of water supply pipes.

Contributing to the formation of the discipline of fluid mechanics was first and foremost Archimedes of ancient Greece. He established the theory of liquid equilibrium, including the buoyancy theorem of objects and the stability of floating bodies, and laid the foundation of hydrostatics. Since then, there have been no major developments in fluid mechanics for more than a thousand years.

It was only in the 15th century that Leonardo da Vinci in Italy wrote about water waves, pipe flow, hydraulic machinery, and the principle of bird flight.

In the 17th century, Pascal articulated the concept of pressure in a stationary fluid. However, fluid mechanics, especially fluid dynamics, as a rigorous science, was gradually formed after classical mechanics established the concepts of velocity, acceleration, force, flow posture, etc., as well as the three conservation laws of mass, momentum and energy.

Fluid formulas are continuity equations, momentum equations, and energy equations.

Continuity equations: In physics, continuity equations are partial differential equations that describe the transmission behavior of conserved quantities. Since mass, energy, momentum, charge, and so on are all conserved quantities under their respective conditions, many kinds of transport behaviors can be described by continuity equations.

The continuity equation is a localized conservation law equation. Compared to the global conservation law, this conservation law is stronger.

All the examples of continuity equations in this entry express the same idea—a change in the total amount of a certain conserved quantity in any region is equal to the number of destroyed ephemerals entering or leaving from the boundary; Conservation quantities cannot be increased or decreased, but can only be migrated from one position to another.

Momentum Fiber Wheel Search Equation: The momentum equation is the specific application of the momentum theorem in fluid mechanics. The momentum theorem states that the magnitude of the resultant external force acting on an object is equal to the rate of change of the momentum of the object in the direction of the force.

Energy equation: Equation of energy is one of the basic equations for calculating the heat transfer process, which is usually expressed as follows: the internal energy increment of the fluid element is equal to the sum of the heat entering the microelement through heat conduction, the heat generated in the microelement and the work done by the surrounding fluid on the microelement.

This equation is a mathematical relation derived from the energy calculation of a nonisothermal flow system.

<> physical significance: In the same constant incompressible flow gravity potential flow, the total specific energy of each point of the ideal fluid is equal, that is, in the whole potential flow field, Bernoulli's constant is equal.

The main fluid macromechanics events are:

In 1738, the Swiss mathematician Bernoulli proposed Bernoulli's equation in his famous work "Fluid Dynamics".

In 1755, Euler put forward the concept of ideal fluid in the famous work "General Principles of Fluid Motion", and established the basic equation and continuous equation of ideal fluid, thus proposing the analytical method of fluid motion and the concept of velocity potential.

In 1781, Lagrange first introduced the concept of the flow function.

In 1904, Plante proposed the boundary layer theory.

1. Fluid mechanics formula: (10+H)G1=10 F1+HF2+HG2.

2. Fluid mechanics is a branch of mechanics, which mainly studies the static state and motion state of the fluid itself and the interaction and flow law between the boundary wall of the fluid and the solid under the action of various forces.

3. For the inherent flow phenomena in nature or the full-scale flow phenomena of existing projects, the systematic observation of various instruments is carried out by various instruments, so as to summarize the laws of fluid movement and the evolution of the flow phenomena. In the past, the observation and forecasting of the weather was basically carried out in this way. However, the occurrence of on-site flow phenomena cannot be controlled, and the occurrence conditions are almost impossible to completely repeat, which affects the study of flow phenomena and laws. The current chain field observation also costs a lot of material, financial and human resources.

Therefore, laboratories were set up so that these phenomena could occur under controlled conditions for easy observation and study.