pressure in a moving fluid. Static pressure

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The basis for the design of any engineering networks is the calculation. In order to properly design a network of supply or exhaust air ducts, it is necessary to know the parameters air flow. In particular, it is required to calculate the flow rate and pressure loss in the channel for correct selection fan power.

In this calculation, an important role is played by such a parameter as dynamic pressure on the walls of the duct.

Behavior of the medium inside the air duct

The fan, which creates an air flow in the supply or exhaust duct, imparts potential energy to this flow. During the movement to confined space pipes, the potential energy of air is partially converted into kinetic energy. This process occurs as a result of the action of the flow on the walls of the channel and is called dynamic pressure.

In addition to it, there is also static pressure, this is the effect of air molecules on each other in a stream, it reflects its potential energy. The kinetic energy of the flow is reflected by the dynamic impact indicator, which is why this parameter is involved in the calculations.

At a constant air flow, the sum of these two parameters is constant and is called the total pressure. It can be expressed in absolute and relative units. The reference point for absolute pressure is full vacuum, while relative pressure is considered starting from atmospheric, that is, the difference between them is 1 atm. As a rule, when calculating all pipelines, the value of the relative (excessive) impact is used.

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The physical meaning of the parameter

If we consider straight sections of air ducts, the sections of which decrease at a constant air flow, then an increase in the flow rate will be observed. In this case, the dynamic pressure in the air ducts will increase, and the static pressure will decrease, the magnitude of the total impact will remain unchanged. Accordingly, in order for the flow to pass through such a narrowing (confuser), it should initially be informed required amount energy, otherwise the consumption may decrease, which is unacceptable. By calculating the magnitude of the dynamic impact, you can find out the number of losses in this confuser and choose the right power for the ventilation unit.

The reverse process will occur in the case of an increase in the channel cross section at a constant flow rate (diffuser). The speed and dynamic impact will begin to decrease, the kinetic energy of the flow will turn into potential. If the pressure developed by the fan is too high, the flow rate in the area and throughout the system may increase.

Depending on the complexity of the scheme, ventilation systems have many turns, tees, constrictions, valves and other elements called local resistances. The dynamic effect in these elements increases depending on the angle of attack of the flow on the inner wall of the pipe. Some parts of the systems cause a significant increase in this parameter, for example, fire dampers in which one or more dampers are installed in the flow path. This creates increased flow resistance in the area, which must be taken into account in the calculation. Therefore, in all of the above cases, you need to know the value of the dynamic pressure in the channel.

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Parameter calculations by formulas

On a straight section, the speed of air movement in the duct is unchanged, and the magnitude of the dynamic impact remains constant. The latter is calculated by the formula:

Rd = v2γ / 2g

In this formula:

• Pd is the dynamic pressure in kgf/m2;
• V is the air velocity in m/s;
• γ — specific gravity air in this area, kg/m3;
• g is the acceleration due to gravity, equal to 9.81 m/s2.

You can get the value of dynamic pressure in other units, in Pascals. There is another version of this formula for this:

Pd = ρ(v2 / 2)

Here ρ is the air density, kg/m3. Since there are no conditions for compression in ventilation systems air environment to such an extent that its density changes, it is taken constant - 1.2 kg / m3.

Further, it is necessary to consider how the magnitude of the dynamic action is involved in the calculation of the channels. The meaning of this calculation is to determine the losses in the entire supply or exhaust ventilation to select the fan pressure, its design and engine power. The calculation of losses takes place in two stages: first, the losses due to friction against the channel walls are determined, then the drop in the power of the air flow in local resistances is calculated. The dynamic pressure parameter is involved in the calculation at both stages.

Friction resistance per 1 m of the round channel is calculated by the formula:

R = (λ / d) Rd, where:

• Pd is the dynamic pressure in kgf/m2 or Pa;
• λ is the friction resistance coefficient;
• d is the duct diameter in meters.

Friction losses are determined separately for each section with different diameters and flow rates. The resulting value of R is multiplied by the total length of the channels of the calculated diameter, the losses on local resistances are added and get general meaning for the whole system:

HB = ∑(Rl + Z)

Here are the options:

1. HB (kgf/m2) — total losses in the ventilation system.
2. R is the friction loss per 1 m of the circular channel.
3. l (m) is the length of the section.
4. Z (kgf / m2) - losses in local resistances (bends, crosses, valves, and so on).

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Determination of parameters of local resistances of the ventilation system

The magnitude of the dynamic impact also takes part in determining the Z parameter. The difference with the straight section is that in different elements of the system the flow changes its direction, branches, converges. In this case, the medium interacts with the inner walls of the channel not tangentially, but under different angles. To take this into account, a trigonometric function can be introduced into the calculation formula, but there are a lot of difficulties. For example, when passing a simple 90⁰ bend, the air turns and presses against the inner wall at least three different angles (depending on the design of the bend). There are a lot of more complex elements in the duct system, how to calculate the losses in them? There is a formula for this:

1. Z = ∑ξ Rd.

In order to simplify the calculation process, a dimensionless coefficient of local resistance has been introduced into the formula. For each element ventilation system it is different and is a reference value. The values ​​of the coefficients were obtained by calculations or empirically. Many manufacturing plants producing ventilation equipment, conduct their own aerodynamic studies and product calculations. Their results, including the coefficient of local resistance of the element (for example, fire damper), are entered in the product passport or placed in technical documentation on your website.

To simplify the process of calculating the losses of ventilation ducts, all values ​​of the dynamic action for different speeds are also calculated and summarized in tables, from which they can be simply selected and inserted into formulas. Table 1 lists some values ​​for the most commonly used air velocities in air ducts.

STATE MEDICAL UNIVERSITY OF SEMEY

Toolkit on this topic:

Study of the rheological properties of biological fluids.

Methods for studying blood circulation.

Rheography.

Compiled by: Lecturer

Kovaleva L.V.

The main questions of the topic:

1. Bernoulli equation. Static and dynamic pressure.
2. Rheological properties of blood. Viscosity.
3. Newton's formula.
4. Reynolds number.
5. Newtonian and non-Newtonian fluid
6. laminar flow.
7. turbulent flow.
8. Determination of blood viscosity using a medical viscometer.
9. Poiseuille's law.
10. Determination of blood flow velocity.
11. total body tissue resistance. Physical foundations rheography. Rheoencephalography
12. Physical basis of ballistocardiography.

Bernoulli equation. Static and dynamic pressure.

Ideal is called incompressible and does not have internal friction, or viscosity; A stationary or steady flow is a flow in which the velocities of the fluid particles at each point in the flow do not change with time. The steady flow is characterized by streamlines - imaginary lines coinciding with the particle trajectories. Part of the fluid flow, bounded on all sides by streamlines, forms a stream tube or jet. Let us single out a stream tube so narrow that the particle velocities V in any of its sections S, perpendicular to the tube axis, can be considered the same over the entire section. Then the volume of liquid flowing through any section of the tube per unit time remains constant, since the movement of particles in the liquid occurs only along the axis of the tube: . This ratio is called the condition of the continuity of the jet. This implies that for a real fluid with a steady flow through a pipe of variable cross section, the amount Q of fluid flowing per unit time through any pipe section remains constant (Q = const) and the average flow velocities in different pipe sections are inversely proportional to the areas of these sections: etc.

Let us single out a current tube in the flow of an ideal fluid, and in it a sufficiently small volume of fluid with mass , which, during the fluid flow, moves from the position BUT to position B.

Due to the smallness of the volume, we can assume that all particles of the liquid in it are in equal conditions: in the position BUT have pressure speed and are at a height h 1 from the zero level; pregnant AT- respectively . The cross sections of the current tube are S 1 and S 2, respectively.

A pressurized fluid has internal potential energy (pressure energy), due to which it can do work. This energy Wp measured by the product of pressure and volume V liquids: . In this case, the movement of the fluid mass occurs under the action of the difference in pressure forces in the sections Si and S2. The work done in this A r equals the difference in potential energies of pressure at the points . This work is spent on work to overcome the effect of gravity and to change kinetic energy masses

Liquids:

Hence, A p \u003d A h + A D

Rearranging the terms of the equation, we get

Regulations A and B are chosen arbitrarily, so it can be argued that at any place along the stream tube, the condition

dividing this equation by , we get

where - liquid density.

That's what it is Bernoulli equation. All members of the equation, as you can easily see, have the dimension of pressure and are called: statistical: hydrostatic: - dynamic. Then the Bernoulli equation can be formulated as follows:

for a stationary flow of an ideal fluid, the total pressure equal to the sum static, hydrostatic and dynamic pressures, remains constant in any cross section flow.

For horizontal current tube hydrostatic pressure remains constant and can be referred to the right side of the equation, which in this case takes the form

static pressure determines the potential energy of the fluid (pressure energy), dynamic pressure - kinetic.

From this equation follows a derivation called Bernoulli's rule:

The static pressure of an inviscid fluid when flowing through a horizontal pipe increases where its velocity decreases, and vice versa.

Question Static pressure Is it atmospheric or what? given by the author Eating Bondarchuk the best answer is I urge everyone not to copy overly clever encyclopedia articles when people ask simple questions. Golem physics is not needed here.
The word "static" literally means - constant, unchanging in time.
When you pump a soccer ball, the pressure inside the pump is not static, but different every second. And when you pump up, inside the ball there is a constant air pressure - static. And atmospheric pressure is static in principle, although if you dig deeper, this is not so, it still changes slightly over days and even hours. In short, there is nothing abstruse here. Static means permanent, and nothing else.
When you say hello to guys, rraz! Shock from hand to hand. Well, it happened to everyone. They say "static electricity". Correctly! A static charge (permanent) has accumulated in your body at this moment. When you touch another person, half of the charge passes to him in the form of a spark.
That's it, I won't load any more. In short, "static" = "permanent", for all occasions.
Comrades, if you do not know the answer to the question, and moreover, you have not studied physics at all, you do not need to copy articles from encyclopedias !!
just like you are wrong, you didn’t come to the first lesson and they didn’t ask you Bernoulli’s formulas, right? they began to chew on you what pressure, viscosity, formulas, etc., etc. are, but when you come and give you exactly as you said, a person is disgusted by this. What curiosity for learning if you don't understand the symbols in the same equation? It's easy to say to someone who has some sort of base, so you're completely wrong!

Answer from roast beef[newbie]
Atmospheric pressure contradicts the MKT of the structure of gases and refutes the existence of a chaotic movement of molecules, the result of which impacts is the pressure on the surfaces bordering on the gas. The pressure of gases is predetermined by the mutual repulsion of like molecules. The repulsion voltage is equal to the pressure. If we consider the column of the atmosphere as a solution of gases of 78% nitrogen and 21% oxygen and 1% others, then atmospheric pressure can be considered as the sum of the partial pressures of its components. The forces of mutual repulsion of molecules equalize the distances between like ones on isobars. Presumably, oxygen molecules do not have repulsive forces with others. So, from the assumption that like molecules repel with the same potential, this explains the equalization of gas concentrations in the atmosphere and in a closed vessel.

Answer from Huck Finn[guru]
Static pressure is that which is created under the influence of gravity. Water under its own weight presses on the walls of the system with a force proportional to the height to which it rises. From 10 meters this indicator is equal to 1 atmosphere. In statistical systems, flow blowers are not used, and the coolant circulates through pipes and radiators by gravity. These are open systems. Maximum pressure in open system heating is about 1.5 atmospheres. AT modern construction such methods are practically not used, even when installing autonomous circuits country houses. This is due to the fact that for such a circulation scheme it is necessary to use pipes with a large diameter. It's not aesthetically pleasing and expensive.
Pressure in closed system heating:
The dynamic pressure in the heating system can be adjusted
Dynamic pressure in a closed heating system is created by an artificial increase in the flow rate of the coolant using electric pump. For example, if we are talking about high-rise buildings, or large highways. Although, now even in private homes, pumps are used when installing heating.
Important! We are talking about overpressure excluding atmospheric.
Each of the heating systems has its own permissible tensile strength. In other words, can withstand different load. To find out what working pressure is in a closed heating system, it is necessary to add a dynamic one, pumped by pumps, to the static one created by a column of water. For correct operation system, the pressure gauge must be stable. A manometer is a mechanical device that measures the pressure with which water moves in a heating system. It consists of a spring, an arrow and a scale. Gauges are installed in key locations. Thanks to them, you can find out what the working pressure is in the heating system, as well as detect malfunctions in the pipeline during diagnostics (hydraulic tests).

Answer from able[guru]
In order to pump liquid to a given height, the pump must overcome static and dynamic pressure. Static pressure is the pressure due to the height of the liquid column in the pipeline, i.e. the height to which the pump must raise the liquid .. Dynamic pressure - the sum of the hydraulic resistances due to the hydraulic resistance of the pipeline wall itself (taking into account the roughness of the wall, pollution, etc.), and local resistances (pipeline bends, valves, gate valves, etc.). ).

Answer from Eurovision[guru]
Atmospheric pressure - the hydrostatic pressure of the atmosphere on all objects in it and the earth's surface. Atmospheric pressure is created by the gravitational attraction of air to the Earth.
And static pressure - I did not meet the current concept. And jokingly, we can assume that this is due to the laws of electric forces and attraction of electricity.
Maybe this? -
Electrostatics is a branch of physics that studies the electrostatic field and electric charges.
Electrostatic (or Coulomb) repulsion occurs between like-charged bodies, and electrostatic attraction between oppositely charged bodies. The phenomenon of repulsion of like charges underlies the creation of an electroscope - a device for detecting electric charges.
Statics (from the Greek στατός, “immovable”):
A state of rest in any certain moment(book). For example: Describe a phenomenon in statics; (adj.) static.
A branch of mechanics that studies the conditions for the equilibrium of mechanical systems under the action of forces and moments applied to them.
So I have not seen the concept of static pressure.

Answer from Andrey Khalizov[guru]
Pressure (in physics) is the ratio of the force normal to the interaction surface between bodies to the area of ​​this surface or in the form of a formula: P = F / S.
Static (from the word Statics (from the Greek στατός, “immovable”, “constant”)) pressure is a constant in time (unchangeable) application of a force normal to the surface of interaction between bodies.
Atmospheric (barometric) pressure - the hydrostatic pressure of the atmosphere on all objects in it and the earth's surface. Atmospheric pressure is created by the gravitational attraction of air to the Earth. On the earth's surface, atmospheric pressure varies from place to place and over time. Atmospheric pressure decreases with height because it is created only by the overlying layer of the atmosphere. The dependence of pressure on height is described by the so-called.
That is, these are two different concepts.

Bernoulli's Law on Wikipedia
See the Wikipedia article about Bernoulli's Law

In a flowing fluid, there are static pressure and dynamic pressure. The cause of static pressure, as in the case of a stationary fluid, is the compression of the fluid. Static pressure is manifested in the pressure on the wall of the pipe through which the liquid flows.

Dynamic pressure is determined by the fluid flow rate. To detect this pressure, it is necessary to slow down the liquid, and then it is, as well as. static pressure will manifest itself in the form of pressure.

The sum of the static and dynamic pressures is called the total pressure.

In a fluid at rest, the dynamic pressure is zero; therefore, the static pressure is equal to the total pressure and can be measured with any pressure gauge.

Measuring pressure in a moving fluid is fraught with a number of difficulties. The fact is that a pressure gauge immersed in a moving liquid changes the speed of the liquid in the place where it is located. In this case, of course, the value of the measured pressure also changes. In order for a pressure gauge immersed in a liquid not to change the velocity of the liquid at all, it must move with the liquid. However, it is extremely inconvenient to measure the pressure inside a liquid in this way. This difficulty is circumvented by giving the tube connected to the pressure gauge a streamlined shape, in which it almost does not change the velocity of the fluid. In practice, narrow gauge tubes are used to measure pressures inside a moving liquid or gas.

Static pressure is measured using a manometer tube, the plane of the hole of which is parallel to the streamlines. If the liquid in the pipe is under pressure, then in the manometric tube the liquid rises to a certain height corresponding to the static pressure at a given point in the pipe.

The total pressure is measured with a tube whose hole plane is perpendicular to the streamlines. Such a device is called a Pitot tube. Once in the hole of the Pitot tube, the liquid stops. Liquid column height ( h full) in the gauge tube will correspond to the total pressure of the liquid in a given place in the pipe.

In what follows, we will only be interested in the static pressure, which we will simply refer to as the pressure inside a moving liquid or gas.?

If you measure the static pressure in a moving fluid in various parts pipes of variable cross section, it turns out that in the narrow part of the pipe it is less than in its wide part.

But the fluid flow rates are inversely proportional to the cross-sectional areas of the pipe; therefore, the pressure in a moving fluid depends on the speed of its flow.

In places where the fluid moves faster (narrow places in the pipe), the pressure is less than where this fluid moves more slowly (wide places in the pipe).

This fact can be explained on the basis of the general laws of mechanics.

Let us assume that the liquid passes from the wide part of the tube to the narrow one. In this case, the particles of the liquid increase their speeds, i.e., they move with accelerations in the direction of motion. Neglecting friction, on the basis of Newton's second law, it can be argued that the resultant of the forces acting on each particle of the fluid is also directed in the direction of fluid movement. But this resultant force is created by pressure forces that act on each given particle from the surrounding fluid particles, and is directed forward, in the direction of fluid movement. This means that more pressure acts on the particle from behind than from the front. Consequently, as experience also shows, the pressure in the wide part of the tube is greater than in the narrow part.

If a liquid flows from a narrow to a wide part of the tube, then, obviously, in this case, the particles of the liquid are decelerated. The resultant of the forces acting on each particle of the liquid from the particles surrounding it is directed to the side, opposite movement. This resultant is determined by the pressure difference in the narrow and wide channels. Consequently, a liquid particle, passing from a narrow to a wide part of the tube, moves from places with less pressure to places with more pressure.

So, during stationary motion in the places of narrowing of the channels, the fluid pressure is reduced, in the places of expansion it is increased.

Fluid flow velocities are usually represented by the density of the streamlines. Therefore, in those parts of a stationary fluid flow where the pressure is less, the streamlines should be denser, and, conversely, where the pressure is greater, the streamlines should be less frequent. The same applies to the image of the gas flow.

Types of pressure

Static pressure

Static pressure is the pressure of a stationary fluid. Static pressure = level above the corresponding measuring point + initial pressure in the expansion vessel.

dynamic pressure

dynamic pressure is the pressure of the moving fluid.

Pump discharge pressure

Operating pressure

The pressure present in the system when the pump is running.

Permissible operating pressure

The maximum value of the working pressure allowed from the conditions of safe operation of the pump and system.

Pressure- a physical quantity that characterizes the intensity of normal (perpendicular to the surface) forces with which one body acts on the surface of another (for example, the foundation of a building on the ground, liquid on the walls of a vessel, gas in an engine cylinder on a piston, etc.). If the forces are uniformly distributed along the surface, then the pressure R on any part of the surface p = f/s, where S- the area of ​​this part, F is the sum of the forces applied perpendicular to it. With an uneven distribution of forces, this equality determines the average pressure on a given area, and in the limit, when the value tends S to zero, is the pressure at a given point. In the case of a uniform distribution of forces, the pressure at all points of the surface is the same, and in the case of an uneven distribution, it changes from point to point.

For a continuous medium, the concept of pressure at each point of the medium is similarly introduced, which plays an important role in the mechanics of liquids and gases. The pressure at any point in a fluid at rest is the same in all directions; this is also true for a moving liquid or gas, if they can be considered ideal (without friction). In a viscous fluid, pressure at a given point is understood as the average value of pressure in three mutually perpendicular directions.

Pressure plays an important role in physical, chemical, mechanical, biological and other phenomena.

Pressure loss

Pressure loss- pressure reduction between the inlet and outlet of the structural element. Such elements include pipelines and fittings. Losses occur due to turbulence and friction. Each pipeline and valve, depending on the material and the degree of surface roughness, is characterized by its own loss factor. For relevant information, please contact their manufacturers.

Pressure units

The pressure is intense physical quantity. Pressure in the SI system is measured in pascals; The following units are also used: