CN101882391A - Authentication instrument of Bernoulli equation - Google Patents

Abstract

The invention discloses an authentication instrument of a Bernoulli equation, comprising a case and a ball. The case is provided with an air inlet on the front and a rectangular air outlet on the lateral surface, the ball is fixedly connected with a connecting rod, the upper end of the connecting rod is articulated with the lateral surface of the air outlet, the diameter of the ball is smaller than the height of the air outlet, and the positive projection of the ball on the lateral surface is positioned between an extension line of the upper edge of the air outlet and an extension line of the lower edge and is not crossed with the air outlet. The authentication instrument of the Bernoulli equation has simple structure, low manufacture cost, simple operation in experiments and intuitive and sensible experimental phenomena. The instrument is not only suitable for physical teaching in colleges and universities to be popularized as an authentication experiment, but also suitable for experimentally authenticating the Bernoulli equation by engineering researchers.

Description

Authentication instrument of Bernoulli equation

Technical field

The invention belongs to instruments used for education, relate in particular to a kind of experimental provision that can verify Bernoulli equation.

Background technology

Bernoulli equation is a very important equation in the fluid mechanics.It is the fundamental equation about fluid mobility of deriving under the prerequisite of ignoring the fluid glutinousness.For real fluid, as long as its glutinousness is enough little, Bernoulli equation just can be used.Because water, alcohol, the fluid glutinousness of this class of air " thin " often can be ignored, thereby uses many spontaneous phenomenons that Bernoulli equation can well explain that the flowability by this class fluid causes.But in present university physics teaching, some colleges and universities does not arrange the confirmatory experiment of Bernoulli equation, and some colleges and universities verifies with liquid by venturi tube.The latter's experimental program exists the experimental cost height, and occupation area of equipment is big, and experimental phenomena does not intuitively wait deficiency and defective.

Summary of the invention

The purpose of this invention is to provide a kind of simple to operately, the experimental phenomena visual sense is verified authentication instrument of Bernoulli equation effective and with low cost.

For achieving the above object, the present invention adopts following technical scheme: a kind of authentication instrument of Bernoulli equation, comprise a casing, on the front of casing air intake vent is arranged, an air outlet is arranged on the side of casing, air outlet is rectangular, also comprise a ball, ball and connecting rod are connected, the side at the upper end of connecting rod and air outlet place is hinged, the diameter of ball is less than the height of air outlet, and ball, and does not intersect with air outlet between the extended line of air outlet top and following extended line in the orthogonal projection on the side.

The height at ball center is identical with the height at air outlet center.

Described casing is a rectangular parallelepiped.

The distance of the side at air outlet place is arrived at the air intake vent center greater than the casing front center to the distance of side, air outlet place.

Being centered close on the same horizontal line of the center of air intake vent and casing front.

On the side at air outlet place index dial is arranged, the pin joint of connecting rod and side, air outlet place is the center of circle of index dial.

Support is equipped with at the top of side, air outlet place, is hinged with a pole on the support, and small end links to each other with pole, on this side index dial is arranged, and the center of pole is the center of circle of index dial.

Support is equipped with at the top of side, air outlet place, and a pole is arranged on the support, and small end and pole are hinged, on this side index dial is arranged, and the center of pole is the center of circle of index dial.

Adopt the authentication instrument of Bernoulli equation of technique scheme, simple in structure, cheap for manufacturing cost, and simple to operate when experiment, the experimental phenomena visual sense.This device both had been fit to the university physics teaching, promoted as a confirmatory experiment, was fit to the engineering research personnel again to the Bernoulli equation checking that experimentizes.

Description of drawings

Fig. 1 is a structural representation of the present invention.

Fig. 2 is the vertical view of Fig. 1.

Fig. 3 is the left view of Fig. 1.

Fig. 4 is ball force analysis figure.

Embodiment

As Fig. 1, Fig. 2, authentication instrument of Bernoulli equation shown in Figure 3, comprise a casing 2, casing is a rectangular parallelepiped, air intake vent 1 is arranged on the front of casing 2, an air outlet 3 is arranged on the side of casing, air outlet 3 is rectangular, being centered close on the same horizontal line of the center of air intake vent 1 and casing front, the air intake vent center to the distance of the side at air outlet place greater than the distance of casing front center to the side at air outlet place.Also comprise a ball 4, ball 4 is connected with connecting rod 5, support 6 is equipped with at the top of side, air outlet place, side on the support 6 is hinged with a pole 8, connecting rod 5 upper ends link to each other with pole 8, for conveniently reading the angle of ball deflection, index dial 7 is arranged on this side, the center of pole 8 is the center of circle of index dial.As shown in Figure 3, the height at ball 5 centers approaches the height at air outlet 3 centers, and preferably the two is highly identical, and the diameter of ball 5 is less than the height of air outlet, ball, and does not intersect with air outlet between the extended line of air outlet top and following extended line in the orthogonal projection on the side.

Casing also can be a square, perhaps can be other arbitrary shape, but should make air intake vent as far as possible away from air outlet, to guarantee the uniform and stable of air outlet place air-flow.

Connecting rod is connected except that adopting aforesaid way with casing, also can otherwise on support, bearing or axle sleeve be housed on the support such as strut fixation, and small end links to each other with bearing or axle sleeve; Or: mounting bracket not, only pole one end is fixed on the casing, bearing or axle sleeve are housed on the support, small end links to each other with bearing or axle sleeve.

Also can adopt simpler structure: without support and pole, but small end has one section horizon bar, and this horizon bar directly is hinged on casing top, and pin joint is the center of circle of index dial.

The diameter of ball is unsuitable too small, because the gaseous tension that ball is subjected to is directly proportional with lifting surface area, when its diameter is too small, is subjected to the interference of friction force and environmental baseline easily, thereby influences experimental result.When the ball diameter is excessive, such as near or when surpassing the height of air outlet, then its pressure that is subjected to can be unbalanced, also can influence experimental result.The ratio of the diameter of ball and air outlet height was good between 1: 2 to 1: 5.

Principle of work of the present invention is as follows:

Because gas is very thin fluid, so its glutinousness can be ignored.Under the condition of constant flow rate, can think that gas is incompressible fluid.According to Bernoulli equation

$\mathrm{Po}+\frac{1}{2}\mathrm{\ρ}{v}^2+\mathrm{\ρgh}=K$ (K is a constant)

Choosing one one end section is infinitely-great stream pipe, and two places that choose sustained height are studied, and a place is infinitely great end, and there is certain sectional area at another place.Then have

${\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="H2009100648297E0000011.png"\; state="\{\{state\}\}">P</figure-callout>}}_1+\frac{1}{2}\mathrm{\&rho;}{v_1}^2+\mathrm{\&rho;}{\mathrm{<figure-callout\; id="2"\; label="gh"\; filenames="H2009100648297E0000011.png"\; state="\{\{state\}\}">gh</figure-callout>}}_2={\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="H2009100648297E0000011.png"\; state="\{\{state\}\}">P</figure-callout>}}_2+\frac{1}{2}\mathrm{\&rho;}{v_2}^2+\mathrm{\&rho;}{\mathrm{<figure-callout\; id="2"\; label="gh"\; filenames="H2009100648297E0000011.png"\; state="\{\{state\}\}">gh</figure-callout>}}_2$

According to non-individual body equation s ₁v ₁=s ₂v ₂, s ₂So approximates infinity is v ₂Be approximately zero, the pressure of infinite general goal is atmospheric pressure, is in sustained height owing to two again, can cast out ρ gh item.So

${\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="H2009100648297E0000011.png"\; state="\{\{state\}\}">P</figure-callout>}}_1+\frac{1}{2}\mathrm{\&rho;}{v_1}^2=\mathrm{Po}$

Can measure v accurately by anemoscope ₁, and for P ₁, can measure by authentication instrument of Bernoulli equation of the present invention, thereby Bernoulli equation is verified.

Can derive air outlet place pressure by ball being carried out force analysis.As shown in Figure 4, force analysis is as follows:

mg?sinθ＝Fcosθ

F＝(p ₀-p ₁)S

p ₁＝p ₀-(mg?tanθ)/S

Wherein S is the projected area of ball on surface level.

When experiment, hair-dryer is aimed at air intake vent, energized, gas is blown into through air intake vent, after the buffering, blow out with certain speed square shape from air outlet in case, by Bernoulli equation as can be known, pressure reduces herein, the ball both sides produce pressure difference, and deflection certain angle θ, with θ substitution formula

p ₁=P ₀-(mg tan θ)/S calculates P ₁

Accurately determine the wind speed v of place, air port with anemoscope ₁Experiment should repeat 5-8 time under the same conditions, asks P ₁, v ₁Mean value is with P ₁, v ₁Substitution

${\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="H2009100648297E0000011.png"\; state="\{\{state\}\}">P</figure-callout>}}_1+\frac{1}{2}\mathrm{\&rho;}{v_1}^2=\mathrm{Po},$

Can verify Bernoulli equation.

Claims (8)

1. authentication instrument of Bernoulli equation, it is characterized in that: comprise a casing, on the front of casing air intake vent is arranged, an air outlet is arranged on the side of casing, air outlet is rectangular, also comprise a ball, ball and connecting rod are connected, and the side at the upper end of connecting rod and air outlet place is hinged, and the diameter of ball is less than the height of air outlet, ball, and does not intersect with air outlet between the extended line of air outlet top and following extended line in the orthogonal projection on the side.

2. authentication instrument of Bernoulli equation as claimed in claim 1 is characterized in that: the height at ball center is identical with the height at air outlet center.

3. authentication instrument of Bernoulli equation as claimed in claim 1 or 2 is characterized in that: described casing is a rectangular parallelepiped.

4. authentication instrument of Bernoulli equation as claimed in claim 3 is characterized in that: the distance of the side at air outlet place is arrived at the air intake vent center greater than the casing front center to the distance of side, air outlet place.

5. authentication instrument of Bernoulli equation as claimed in claim 4 is characterized in that: being centered close on the same horizontal line of the center of air intake vent and casing front.

6. authentication instrument of Bernoulli equation as claimed in claim 1 is characterized in that: on the side at air outlet place index dial is arranged, the pin joint of connecting rod and side, air outlet place is the center of circle of index dial.

7. authentication instrument of Bernoulli equation as claimed in claim 1 is characterized in that: support is equipped with at the top of side, air outlet place, is hinged with a pole on the support, and small end links to each other with pole, on this side index dial is arranged, and the center of pole is the center of circle of index dial.

8. authentication instrument of Bernoulli equation as claimed in claim 1 is characterized in that: support is equipped with at the top of side, air outlet place, and a pole is arranged on the support, and small end and pole are hinged, on this side index dial is arranged, and the center of pole is the center of circle of index dial.

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