CN106816065A - Bernoulli equation experimental instrument and the method that Bernoulli equation is verified using it - Google Patents
Bernoulli equation experimental instrument and the method that Bernoulli equation is verified using it Download PDFInfo
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- CN106816065A CN106816065A CN201611195880.8A CN201611195880A CN106816065A CN 106816065 A CN106816065 A CN 106816065A CN 201611195880 A CN201611195880 A CN 201611195880A CN 106816065 A CN106816065 A CN 106816065A
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- G—PHYSICS
- G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
- G09B—EDUCATIONAL OR DEMONSTRATION APPLIANCES; APPLIANCES FOR TEACHING, OR COMMUNICATING WITH, THE BLIND, DEAF OR MUTE; MODELS; PLANETARIA; GLOBES; MAPS; DIAGRAMS
- G09B23/00—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes
- G09B23/06—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes for physics
- G09B23/08—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes for physics for statics or dynamics
- G09B23/12—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes for physics for statics or dynamics of liquids or gases
Abstract
Bernoulli equation experimental instrument and the method that Bernoulli equation is verified using it,The experiment instrument includes support 1,Support 1 is arranged on carrier base 2,The side of carrier base 2 is placed with beaker 3,Support 1 is being provided with the outwardly directed first support piece 4 of vertical bar perpendicular to support 1 with the same upper lateral part of beaker 3,First support piece 4 is provided with clutch shaft bearing 5,The VERTICAL TUBE of T-shaped three-way pipe 6 is submerged beaker 3 straight down through clutch shaft bearing 5 and first support piece 4,Motor 7,Revolution recorder 8 and digitisation laser tachometer 9 are arranged on the cross bar on the top of support 1,Motor 7 is connected with T-shaped three-way pipe 6,Revolution recorder 8 is connected with motor 7,Laser aperture 10 is provided with the cross bar that digitisation laser tachometer 9 is set on support 1,The transverse tube of T-shaped three-way pipe 6 is being provided with photosensitive scraps of paper patch 11 with the place of being vertically aligned of laser aperture 10,Measurement apparatus 12 are used for the water level lifting height of the VERTICAL TUBE for measuring T-shaped three-way pipe 6.
Description
Technical field
The present invention relates to physics educational apparatus, more particularly to a kind of experimental provision that can verify Bernoulli equation and use
The method of its checking Bernoulli equation.
Background technology
In a fluid system, such as in air-flow, flow velocity is faster, and the pressure that fluid is produced is just smaller, here it is " Bernoulli Jacob
Law ".Bernoulli effect is applied to including all fluids including gas, be fundamemtal phenomena when fluid does steady flow it
One, reflect the flow velocity of fluid and the relation of pressure, the flow velocity of fluid is bigger, and pressure is smaller；The flow velocity of fluid is smaller, and pressure is got over
Greatly.Correspondingly, Bernoulli equation is one of big fundamental equation of hydraulics three, there is substantial amounts of application in engineering design.
" Bernoulli equation experimental instrument " is then the quantitative verification experiment needed for the hydromechanical learning aid of College Physics
Instrument.At present, it is existing in laboratory in colleges and universities " Bernoulli equation experimental instrument ", be survey flow velocity of the water in varying cross-section and
Pressure size is set up verifying " Bernoulli equation ", and its design is complicated, and error is big.
The content of the invention
For above-mentioned the deficiencies in the prior art, it is an object of the invention to provide a kind of Bernoulli equation experimental instrument, its behaviour
Make simple, checking effective and with low cost.
A kind of the first embodiment of the invention, there is provided Bernoulli equation experimental instrument：
A kind of Bernoulli equation experimental instrument, it includes support, carrier base, beaker, first support piece, clutch shaft bearing, T-shaped three
Siphunculus, motor, revolution recorder, digitisation laser tachometer, laser aperture, photosensitive scraps of paper patch and measurement apparatus, its medium-height trestle
On carrier base.Carrier base side (such as left side) is placed with beaker, and support is being provided with vertical with the same upper lateral part of beaker
In the outwardly directed first support piece of the vertical bar of support.First support piece is provided with clutch shaft bearing, the VERTICAL TUBE of T-shaped three-way pipe
Submerged straight down beaker through clutch shaft bearing and first support piece.Motor, revolution recorder and digitisation laser tachometer are equal
It is arranged on the cross bar of frame upper.Motor is connected with T-shaped three-way pipe, revolution recorder and motor connection, and number is set on support
Laser aperture is provided with the cross bar of positionization laser tachometer.The transverse tube of T-shaped three-way pipe is provided with the laser aperture place of being vertically aligned
Photosensitive scraps of paper patch.Measurement apparatus are used to measure the water level lifting height in the VERTICAL TUBE of T-shaped three-way pipe.
Preferably, support is provided with the second support alignd with first support piece in the same side for being provided with first support piece
Piece, the height of the height less than first support piece of second support piece.
Preferably, second support piece is provided with second bearing.
In the present invention, the center of first support piece, clutch shaft bearing, second support piece and second bearing is same perpendicular
On straight line, it is vertical that the VERTICAL TUBE of T-shaped three-way pipe sequentially passes through clutch shaft bearing, first support piece, second bearing and second support piece
Submerge downwards beaker.Clutch shaft bearing and second bearing are used for the rotation of the VERTICAL TUBE for supporting T-shaped three-way pipe.
Revolution recorder is used to record the rotating speed n of T-shaped three-way pipe.
In the present invention, the experiment instrument also includes time set, the time t for recording T-shaped three-way pipe rotation.
In the present invention, the center of digitisation laser tachometer, laser aperture and the photosensitive scraps of paper patch three is same vertical
On line, digitisation laser tachometer is used to be drawn according to the revolution n and time t of T-shaped three-way pipe the angular speed of T-shaped three-way pipe.
Preferably, T-shaped three-way pipe is made up of transparent material (such as glass, plastics).
Preferably, motor is direct current generator.
In this application, support may be configured as frame shape, including vertical bar and top cross bar.Motor is preferably direct current
Machine, for driving T-shaped three-way pipe to rotate.The linear velocity of the VERTICAL TUBE mouth of pipe of T-shaped three-way pipe is flow velocity of the air with respect to the mouth of pipe.
For convenience of measurement water level lifting height, T-shaped three-way pipe is made up of transparent material, such as T-shaped glass tube.
The length of the supervisor of wherein T-shaped three-way pipe (6) is 30-100cm, preferably 40-90cm, more preferably 50-80cm.Work as T
When type three-way pipe (6) is along its supervisor's rotation, its radius of turn is 3-50cm, preferably 4-40cm, more preferably 4.5-20cm, more excellent
Select 5-10cm.
Second embodiment of the invention, there is provided a kind of method that use said apparatus verify Bernoulli equation,
The method comprises the following steps：
1) the VERTICAL TUBE radius r of T-shaped three-way pipe is measured；
2) motor is connected with power supply, appropriate water is loaded onto in beaker, addition red ink is in beaker；
3) switch on power, while starting time set, T-shaped three-way pipe rotation, water level rises, and measures water level lifting height h,
Timing stops while deenergization, by revolution recorder and stopwatch record revolution n and time t；
4) the revolution n and time t rotated according to T-shaped three-way pipe, can obtain angular velocity omega：So as to calculate
The VERTICAL TUBE mouth of pipe relative velocity v of corresponding T-shaped three-way pipe：
5) ρ is calculatedWatergh、It is compared, draws experiment conclusion.
Preferably, the method also includes：6) change the height of voltage, that is, change the rotary speed (rotation of T-shaped three-way pipe
Speed is general in the range of 1600~9200 revs/min), above steps may be repeated multiple times calculates and record data, relatively and draws
Experiment conclusion.
In the present invention, its mentality of designing is：
Bernoulli equationHere constant is P0(atmospheric pressure).
1. analysis of the vertical inner air tube (pressure is P) of T-shaped three-way pipe to the mouth of pipe：
Atmospheric density very little, so that the influence of gas difference in height is not notable, it is negligible,
I.e.：
2. the vertical inner air tube (pressure is P) of T-shaped three-way pipe is to the analysis of the water surface in beaker：
VERTICAL TUBE inner fluid speed is zero, i.e.,：P+ρWaterGh=P0
By 1. and 2. obtaining：
And v=ω r (ω --- angular speed, the r of the T-shaped three-way pipe rotation --- radius that T-shaped three-way pipe top rotates),
I.e.：ρWaterGh=ρAirω2r2
From above formula：As long as measuring h, ω, r can just verify Bernoulli equation.
Compared with prior art, the device have the advantages that：
1st, this experiment instrument submerges in water by by the vertical tube portion of T-shaped three-way pipe, allows T-shaped three-way pipe to rotate with motor, T
The linear velocity of the VERTICAL TUBE mouth of pipe of type three-way pipe is flow velocity of the air with respect to the mouth of pipe, as long as measuring the linear velocity of mouth of pipe rotation and not having
Enter in water water level lifting height in VERTICAL TUBE, just demonstrate the establishment of Bernoulli equation, this experiment instrument simple structure, low cost,
Systematic error is small；
2nd, this experiment instrument qualitative can demonstrate fluid pressure and flow velocity relation, and can quantitative verification Bernoulli equation.
Brief description of the drawings
Fig. 1 is the installation drawing of prior art Bernoulli equation experimental instrument
Fig. 2 is the structural representation of Bernoulli equation experimental instrument of the present invention
Reference：1：Support；2：Carrier base；3：Beaker；4：First support piece；5：Clutch shaft bearing；6：T-shaped three-way pipe；
7：Motor；8：Revolution recorder；9：Digitisation laser tachometer；10：Laser aperture；11：Photosensitive scraps of paper patch；12：Measurement apparatus；
13：Second support piece；14：Second bearing.
Specific embodiment
A kind of the first embodiment of the invention, there is provided Bernoulli equation experimental instrument：
A kind of Bernoulli equation experimental instrument, it include support 1, carrier base 2, beaker 3, first support piece 4, clutch shaft bearing 5,
T-shaped three-way pipe 6, motor 7, revolution recorder 8, digitisation laser tachometer 9, laser aperture 10, photosensitive scraps of paper patch 11 and measurement
Device 12, its medium-height trestle 1 is arranged on carrier base 2.The side of carrier base 2 (such as left side) is placed with beaker 3, support 1 with burning
3 same upper lateral parts of cup are provided with the outwardly directed first support piece 4 of vertical bar perpendicular to support 1.First support piece 4 is provided with
One bearing 5, the VERTICAL TUBE of T-shaped three-way pipe 6 is submerged beaker 3 straight down through clutch shaft bearing 5 and first support piece 4.Motor 7,
Revolution recorder 8 and digitisation laser tachometer 9 are arranged on the cross bar on the top of support 1.Motor 7 connects with T-shaped three-way pipe 6
Connect, revolution recorder 8 is connected with motor 7, laser aperture 10 is provided with the cross bar that digitisation laser tachometer 9 is set on support 1.
The transverse tube of T-shaped three-way pipe 6 is being provided with photosensitive scraps of paper patch 11 with the place of being vertically aligned of laser aperture 10.Measurement apparatus 12 are used to measure T
Water level lifting height in the VERTICAL TUBE of type three-way pipe 6.
Preferably, support 1 is provided with second alignd with first support piece 4 in the same side for being provided with first support piece 4
Frame piece 13, the height of the height less than first support piece 4 of second support piece 13.
Preferably, second support piece 13 is provided with second bearing 14.
In the present invention, the center of first support piece 4, clutch shaft bearing 5, second support piece 13 and second bearing 14 4 exists
On same vertical curve, the VERTICAL TUBE of T-shaped three-way pipe 6 sequentially passes through clutch shaft bearing 5, first support piece 4, second bearing 14 and second
Rack plate 13 submerges beaker 3 straight down.
In the present invention, digitisation laser tachometer 9, laser aperture 10 and the photosensitive scraps of paper paste the center of 11 threes same
On vertical curve.
Preferably, T-shaped three-way pipe 6 is made up of transparent material (such as glass, plastics).
Preferably, motor 7 is direct current generator.
In the present invention, the experiment instrument also includes time set, the time for recording the rotation of T-shaped three-way pipe 6.
Second embodiment of the invention, there is provided a kind of method that use said apparatus verify Bernoulli equation,
The method comprises the following steps：
1) the VERTICAL TUBE radius r of T-shaped three-way pipe 6 is measured；
2) motor 7 is connected with power supply, appropriate water is loaded onto in beaker 3, addition red ink is in beaker 3；
3) switch on power, while starting time set, T-shaped three-way pipe 6 rotates, and water level rises, and measures water level lifting height
H, timing stops while deenergization, and revolution n and time t is obtained by revolution recorder and stopwatch；
4) the revolution n and time t rotated according to T-shaped three-way pipe 6, can obtain angular velocity omega：So as to calculate
The VERTICAL TUBE mouth of pipe relative velocity v of corresponding T-shaped three-way pipe 6：
5) ρ is calculatedWatergh、It is compared, draws experiment conclusion.
Preferably, the method also includes：6) change the height of voltage, that is, change the rotary speed of T-shaped three-way pipe 6, it is many
Secondary repeat the above steps calculating and record data, relatively and draw experiment conclusion.
Embodiment 1
Such as Fig. 2, a kind of Bernoulli equation experimental instrument, it includes a support 1, and support 1 is arranged on carrier base 2.Support
The left side of seat 2 is placed with beaker 3, and support 1 is provided with the outwardly directed first support piece of vertical bar perpendicular to support 1 in left upper portion
4.First support piece 4 is provided with clutch shaft bearing 5, the center of first support piece 4 and clutch shaft bearing 5 on same vertical curve, T-shaped glass
The VERTICAL TUBE of glass pipe 6 is submerged beaker 3 straight down through clutch shaft bearing 5 and first support piece 4.Direct current generator 7, revolution recorder
8 and digitisation laser tachometer 9 be arranged on the cross bar on the top of support 1.Direct current generator 7 is connected with T-shaped glass tube 6, revolution
Logger 8 is connected with direct current generator 7, and laser aperture 10 is provided with the cross bar that digitisation laser tachometer 9 is set on support 1.It is T-shaped
The transverse tube of glass tube 6 is being provided with photosensitive scraps of paper patch 11 with the place of being vertically aligned of laser aperture 10.Digitisation laser tachometer 9, laser
Aperture 10 and the photosensitive scraps of paper paste the center of 11 threes on same vertical curve.Measurement apparatus 12 are used to measure the perpendicular of T-shaped glass tube 6
Water level lifting height in straight tube.The experiment instrument also includes time set, the time for recording the rotation of T-shaped glass tube 6.
Embodiment 2
Embodiment 1 is repeated, simply the support 1 of the experiment instrument is provided with the second support alignd with first support piece 4 in left side
Piece 13, the height of the height less than first support piece 4 of second support piece 13.Second support piece 13 is provided with second bearing 14.The
The center of one rack plate 4, clutch shaft bearing 5, second support piece 13 and second bearing 14 4 on same vertical curve, T-shaped glass
The VERTICAL TUBE of pipe 6 sequentially passes through clutch shaft bearing 5, first support piece 4, second bearing 14 and second support piece 13 and submerges straight down
Beaker 3.
Embodiment 3 (practical application example)
A kind of method for verifying Bernoulli equation, using the experiment instrument in embodiment 2, the method comprises the following steps：
1) T-shaped three-way pipe top radius of gyration r (=5cm) of T-shaped glass tube 6 is measured；
2) direct current generator 7 is connected with power supply, appropriate water (200mL) is loaded onto in beaker 3 (capacity 300mL), added
20 drop red ink are in beaker 3；
3) switch on power, while starting time set, T-shaped glass tube 6 rotates, and water level rises, measurement water level lifting height h
=11.0cm, timing stops while deenergization, and revolution n (=31203 turns) and time t are drawn by revolution recorder and stopwatch
(=240 seconds)；
4) " DT2234C digitisation laser tachometer " is used, according to revolution n and time t that T-shaped glass tube 6 rotates, angle can be obtained
Speed omega：(unit：Rev/min, the test scope of this " tachometer "：2.5-99999RPM. is differentiated
Power：0.1RPM(2.5-999RPM))., so as to calculate the VERTICAL TUBE mouth of pipe relative velocity v of corresponding T-shaped glass tube 6：
5) ρ is calculatedWaterGh=1078.0,(g=9.8m/s2、ρWater=103kg/m3、ρAir=
1.293kg/m3), it is compared, draw experiment conclusionChecking Bernoulli equation is set up, and tests accuracy
Height, experimental error about 3 ‰.
Embodiment 4
Embodiment 3 is repeated, simply the method also includes：6) change the height of voltage, that is, change the rotation of T-shaped glass tube 6
Speed omega (=4475.7 revs/min), water level rises, and measures water level lifting height h=3.7cm, at this moment mouth of pipe relative velocity v：Calculate ρWaterGh=352.8,(g=9.8m/s2、ρWater
=103kg/m3、ρAir=1.293kg/m3), it is compared, draw experiment conclusionChecking Bernoulli equation
Set up, experiment accuracy is high, and experimental error is approximately less than 1%.
Above steps may be repeated multiple times calculates and record data, relatively and draws experiment conclusion.
The result of embodiment 3 and 4 shows that the experiment effect accuracy that checking Bernoulli equation is set up is high, and experimental error is about
Less than 1%.
Claims (10)
1. a kind of Bernoulli equation experimental instrument, it is characterised in that：It include support (1), carrier base (2), beaker (3), first
Frame piece (4), clutch shaft bearing (5), T-shaped three-way pipe (6), motor (7), revolution recorder (8), digitisation laser tachometer (9), swash
Light aperture (10), the photosensitive scraps of paper patch (11) and measurement apparatus (12), its medium-height trestle (1) on carrier base (2), carrier base
(2) side (such as left side) is placed with beaker (3), and support (1) is provided with perpendicular to support (1) with beaker (3) same upper lateral part
The outwardly directed first support piece (4) of vertical bar, first support piece (4) is provided with clutch shaft bearing (5), T-shaped three-way pipe (6)
VERTICAL TUBE is submerged beaker (3), motor (7), revolution recorder (8) straight down through clutch shaft bearing (5) and first support piece (4)
And digitisation laser tachometer (9) is arranged on the cross bar on support (1) top, motor (7) is connected with T-shaped three-way pipe (6), turns
Number logger (8) is connected with motor (7), and laser aperture is provided with the cross bar that digitisation laser tachometer (9) is set on support (1)
(10), the transverse tube of T-shaped three-way pipe (6) is being provided with photosensitive scraps of paper patch (11), measurement apparatus with laser aperture (10) place of being vertically aligned
(12) for the water level lifting height in the VERTICAL TUBE for measuring T-shaped three-way pipe (6).
2. Bernoulli equation experimental instrument according to claim 1, it is characterised in that：Support (1) is being provided with first support piece
(4) the same side is provided with the second support piece (13) alignd with first support piece (4), and the height of second support piece (13) is less than the
The height of one rack plate (4).
3. Bernoulli equation experimental instrument according to claim 2, it is characterised in that：Second support piece (13) is provided with second
Bearing (14).
4. Bernoulli equation experimental instrument according to claim 3, it is characterised in that：First support piece (4), clutch shaft bearing
(5), the center of second support piece (13) and second bearing (14) four is on same vertical curve, the VERTICAL TUBE of T-shaped three-way pipe (6)
Clutch shaft bearing (5), first support piece (4), second bearing (14) and second support piece (13) is sequentially passed through to submerge straight down burning
Cup (3).
5. the Bernoulli equation experimental instrument according to any one of claim 1-4, it is characterised in that：Digitisation laser rotating speed
The center of meter (9), laser aperture (10) and the photosensitive scraps of paper patch (11) three is on same vertical curve.
6. the Bernoulli equation experimental instrument according to any one of claim 1-5, it is characterised in that：T-shaped three-way pipe (6) by
Transparent material (such as glass, plastics) is made.
7. the Bernoulli equation experimental instrument according to any one of claim 1-6, it is characterised in that：Motor (7) is direct current
Motor.
8. the Bernoulli equation experimental instrument according to any one of claim 1-7, it is characterised in that：The experiment instrument also includes
Time set, the time for recording T-shaped three-way pipe (6) rotation.
9. the method that the Bernoulli equation experimental instrument any one of a kind of usage right requirement 1-8 verifies Bernoulli equation,
The method comprises the following steps：
1) the VERTICAL TUBE radius r of T-shaped three-way pipe (6) is measured；
2) motor (7) is connected with power supply, appropriate water is loaded onto in beaker (3), addition red ink is in beaker (3)；
3) switch on power, while starting time set, T-shaped three-way pipe (6) rotation, water level rises, and measures water level lifting height h,
Timing stops while deenergization, records revolution n and time t；
4) the revolution n and time t rotated according to T-shaped three-way pipe (6), draw angular velocity omega：It is right so as to calculate
The VERTICAL TUBE mouth of pipe relative velocity v of the T-shaped three-way pipe (6) answered：
5) ρ is calculatedWatergh、It is compared, draws experiment conclusion.
10. method according to claim 9, the method also includes：6) change the height of voltage, that is, change T-shaped three-way pipe
(6) rotary speed, above steps may be repeated multiple times calculates and record data, relatively and draws experiment conclusion.
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| CN106816065B (en) | 2023-01-13 |
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