CN100562740C - Rotary liquid comprehensive experimental instrument and experimental technique - Google Patents

Abstract

A kind of rotary liquid comprehensive experimental instrument, comprise by rotating mechanism, speed controlling and adjusted module, test the speed and display module, laser instrument and measurement component are formed, rotating mechanism places in the casing, disk on the casing upper surface is fixed on the motor bearings, can follow the motor smooth rotation, cabinet panel is provided with speed-regulating switch, rotating toggle switch, the digital demonstration of speed, laser power supply, on the casing vertical fixing two support bars that have scale, support bar is used to measure and the fixing required measurement component of different experiments content and make its locality adjustable.The invention provides and a kind ofly collect that carried out acceleration of gravity, the coefficient of viscosity that mechanics, electricity, optics are one are measured and the comprehensive physics facility of rotating liquid of Research on Optical System.

Description

Rotary liquid comprehensive experimental instrument and experimental technique

Technical field

The present invention relates to a kind of physics facility, particularly relate to the rotary liquid comprehensive experimental instrument that to measure acceleration of gravity and coefficient of viscosity quantitatively.

Background technology

Acceleration of gravity is a very important physical quantity, in college physical experiment teaching, and method and instrument to following measurement acceleration of gravity commonly used:

I, freely falling body method, it is to be that a kind of initial velocity is zero according to the movement of falling object, acceleration is the uniformly accelrated rectilinear motion of g, promptly $h=\frac{1}{2}{\mathrm{<figure-callout\; id="2"\; label="gt"\; filenames="C2006100517770013H1.png,C2006100517770014H1.png"\; state="\{\{state\}\}">gt</figure-callout>}}^2$ If it is v that object falls to the speed that a certain height place has ₀, so, be at this height of highly locating t object whereabouts in the time $h=v_{0}t+\frac{1}{2}{\mathrm{<figure-callout\; id="2"\; label="gt"\; filenames="C2006100517770013H1.png,C2006100517770014H1.png"\; state="\{\{state\}\}">gt</figure-callout>}}^2,$ By the freely falling body instrument in experiment, measure a series of nt (n=1,2,3 ...) pairing height h _i(i=1,2,3 ...), just can derive gravity acceleration g according to secondary by difference method principle by following formula.

II, air track method are adjusted into air track and have a pitch angle, and slide block is done uniformly accelrated rectilinear motion from top to bottom, respectively puts a photogate at two places up and down of gas rail, measures the speed of slide block respectively, obtains acceleration of gravity by respective formula.

III, single pendulum method, when the pivot angle amplitude hour, ignore air resistance, the swing of single pendulum in vertical plane is simple harmonic oscillation, the vibration period $T=2\mathrm{\&pi;}\sqrt{L/g}$ In the formula, L is the single pendulum pendulum length; G is an acceleration of gravity.Measured T and L, can calculate g:g=4 π by following formula ²L/T ²Referring to: patent " measuring the acceleration of gravity experiment instrument "＜application number with single pendulum〉02219720.

The coefficient of viscosity is a physical quantity that is used for characterizing the moving fluid glutinousness, and the selection of the lubricating oil that uses in all kinds of machineries in hydrostatic transmission and the research to the real fluid characteristics of motion, all needs to measure the coefficient of viscosity.What use always in college physical experiment teaching is falling ball method.When a bead moves, be subjected to the effect of gravity, buoyancy, three power of viscous force in liquid.If liquid is unlimited extension, and do not produce vortex at the volley, then according to Stokes' law, the viscous force that bead is subjected to is that d is little bulb diameter in the f=3 π η dv formula, and v is the bead falling speed, and η is the coefficient of viscosity of liquid.Bead falls with uniform velocity after decline a period of time, and this moment, viscous force and buoyancy sum equaled the gravity of bead.Can be according to the formula of deriving $\mathrm{\&eta;}=\frac{(\mathrm{\&rho;}-{\mathrm{\&rho;}}_0){\mathrm{<figure-callout\; id="2"\; label="gd"\; filenames="C2006100517770013H1.png,C2006100517770014H1.png"\; state="\{\{state\}\}">gd</figure-callout>}}^2}{18v}$ (ρ and ρ ₀Be respectively bead and density of liquid) measurements and calculations.Experiment content is mainly measured the required time of bead whereabouts certain distance, calculates the bead falling speed, and the substitution formula is obtained the coefficient of viscosity.Referring to: patent " falling ball method coefficient of viscosity analyzer "＜application number〉02215782.

Existing acceleration of gravity surveying instrument and coefficient of viscosity surveying instrument are independently two experimental provisions in experimental teaching is used, both experiment contents and the physical quantity of surveying few, as an independent experiment, the student only needs the experimental period of half just can finish experiment, will cause waste and the decrease in efficiency of learning time like this.If do not possess this two kinds of instruments in the teaching, just can't carry out the measurement of the acceleration of gravity and the coefficient of viscosity.

Summary of the invention

The object of the invention provides and a kind ofly collects that carried out acceleration of gravity, the coefficient of viscosity that mechanics, electricity, optics are one are measured and the comprehensive physics facility of rotating liquid of Research on Optical System.

Rotary liquid comprehensive experimental instrument provided by the invention is by rotating mechanism, speed controlling and adjusted module, test the speed and display module, laser instrument and measurement component are formed.Rotating mechanism places in the casing, and the disk on the casing upper surface is fixed on the motor bearings, can follow the motor smooth rotation.Cabinet panel is provided with speed-regulating switch, rotating toggle switch, the digital demonstration of speed, laser power supply.On the casing vertical fixing two support bars that have scale.Support bar is used to measure and the fixing required measurement component of different experiments content and make its locality adjustable.Measurement component comprises: millimeter scale horizontal screen, horizontal graticule, horizontal protractor, millimeter scale vertical screen, pull spring suspended cylinder.Cylindrical experiment container fixed placement is on rotating disk.It is characterized in that: by speed-regulating switch, make to be placed on the experiment container rotation that fills liquid on the rotating disk, reach the rotation of liquid, the digital liquid rotating speed that shows is measured various relevant physical quantitys, carries out different Physical Experiments.

Comprehensive physics experimental principle provided by the invention and method:

A, measurement acceleration of gravity

The parabolic derivation of equation of rotating liquid: during quantitative Analysis, choose the reference frame with the hydrostatic column rotation, this is the non inertial reference frame of a rotation.Liquid phase is static for reference frame, an optional fritter liquid P, and it is stressed as Fig. 2.F _iBe radially outside inertial centrifugal force, mg is a gravity, and N is this fritter liquid surrounding liquid to the making a concerted effort of its acting force, and by symmetry as can be known, N is inevitable perpendicular to liquid surface.P under the X-Y coordinate (x y) then has:

Ncosθ-mg＝0

Nsinθ-F _i＝0

F _i＝mω ²x

$\tan \mathrm{\&theta;}=\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{{\mathrm{\&omega;}}^{2}x}{g}$

Have according to Fig. 2: $y=\frac{{\mathrm{\&omega;}}^2}{2g}{x}^2+y_0---\left(1\right)$

ω is an angular velocity of rotation, y ₀Y value for the x=0 place.This is a parabolic equation, and visible liquid level is the paraboloid of revolution.

In experimental system, one fill the liquid radius be the cylindrical experiment container of R around this cylindrical axis of symmetry with angular velocity omega at the uniform velocity during stable rotation, the surface of liquid forms parabola, as Fig. 3.

If liquid level was not h when liquid rotated, the volume of liquid is:

V＝πR ²h (2)

Because of volume before and after the liquid in rotation remains unchanged, liquid volume can be expressed as during rotation:

$V={\&Integral;}_0^{R}y\left(2\mathrm{\&pi;x}\right)\mathrm{dx}=2\mathrm{\&pi;}\&Integral;(\frac{{\mathrm{\&omega;}}^2{x}^2}{2g}+y_0)\mathrm{xdx}---\left(3\right)$

Get by (2), (3) formula:

$y_0=h-\frac{{\mathrm{\&omega;}}^2{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="C2006100517770013H1.png,C2006100517770014H1.png"\; state="\{\{state\}\}">R</figure-callout>}}^2}{4g}---\left(4\right)$

Simultaneous (1), (4) can get, when $x=x_0=R/\sqrt{2}$ The time, y (x ₀)=h, promptly liquid level is at x ₀The height at place is a steady state value.

Method one: the height difference measuring gravity acceleration g of and lowest part the highest with the rotating liquid liquid level

According to shown in Figure 3, establish the rotation liquid level the highest with difference in height lowest part be Δ h, point (R, y ₀+ Δ h) on the para-curve of (1) formula, has $y_0+\mathrm{\&Delta;h}=\frac{{\mathrm{\&omega;}}^2{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="C2006100517770013H1.png,C2006100517770014H1.png"\; state="\{\{state\}\}">R</figure-callout>}}^2}{2g}+y_0,$

: $g=\frac{{\mathrm{\&omega;}}^2{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="C2006100517770013H1.png,C2006100517770014H1.png"\; state="\{\{state\}\}">R</figure-callout>}}^2}{2\mathrm{\&Delta;h}}$

Again $\mathrm{\&omega;}=\frac{2\mathrm{\&pi;n}}{60},$ Then

$g=\frac{{\mathrm{\&pi;}}^2{D}^2{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="C2006100517770013H1.png,C2006100517770014H1.png"\; state="\{\{state\}\}">n</figure-callout>}}^2}{7200\&CenterDot;\mathrm{\&Delta;h}}---\left(5\right)$

D is the experiment container diameter, n be rotational speed (rev/min).

Method two, slope method check weighing power acceleration

As shown in Figure 3, the incident of laser beam parallel shaft through the BC transparent screen, is beaten $x_0=R/\sqrt{2}$ Liquid level A point on reflection light point be C, the angle of A place tangent line and x direction is θ, ∠ BAC=2 θ then measures transparent screen to the distance H of container bottom, height h when liquid level is static, and between two luminous point BC apart from d, then $\tan 2\mathrm{\&theta;}=\frac{d}{H-h},$ Obtain the θ value.

Because $\tan \mathrm{\&theta;}=\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{{\mathrm{\&omega;}}^{2}x}{g},$ $x_0=R/\sqrt{2}$ The place has $\tan \mathrm{\&theta;}=\frac{{\mathrm{\&omega;}}^{2}R}{\sqrt{2}g}$

Because $\mathrm{\&omega;}=\frac{2\mathrm{\&pi;n}}{60},$

Then $\tan \mathrm{\&theta;}={\left(\frac{2\mathrm{\&pi;n}}{60}\right)}^2\frac{R}{\sqrt{2}g}=\frac{{4\mathrm{\&pi;}}^2{\mathrm{<figure-callout\; id="2"\; label="Rn"\; filenames="C2006100517770013H1.png,C2006100517770014H1.png"\; state="\{\{state\}\}">Rn</figure-callout>}}^2}{3600\sqrt{2}g}=\frac{{2\mathrm{\&pi;}}^2{\mathrm{<figure-callout\; id="2"\; label="Dn"\; filenames="C2006100517770013H1.png,C2006100517770014H1.png"\; state="\{\{state\}\}">Dn</figure-callout>}}^2}{3600\sqrt{2}g}$

$g=\frac{{2\mathrm{\&pi;}}^{2}D}{3600\sqrt{2}\tan \mathrm{\&theta;}}---\left(6\right)$

Maybe can make tan θ～n ²Curve is asked slope k, can get $k=\frac{{2\mathrm{\&pi;}}^{2}D}{3600\sqrt{2}g},$ Obtain $g=\frac{{2\mathrm{\&pi;}}^{2}D}{3600\sqrt{2}k}$

The relation of B, the parabolic focal length of checking and rotating speed

The parabola that the rotating liquid surface forms can be regarded a concave mirror as, meets the rule of optical imaging system, if light is parallel to the incident of curved surface axis of symmetry, reflected light will all converge at paraboloidal focus.

According to parabolic equation (1), paraboloidal focal length $f=\frac{\mathrm{<figure-callout\; id="2"\; label="g"\; filenames="C2006100517770013H1.png,C2006100517770014H1.png"\; state="\{\{state\}\}">g</figure-callout>}}{2{\mathrm{\&omega;}}^2}.$

C, measurement coefficient of viscosity

Put into the right cylinder that pull spring hangs along the experiment container center, be immersed in the liquid, the cylinder height is L, and radius is R ₁, the experiment container radius is R, as shown in Figure 4.

Experiment container is with constant angular velocity omega ₀Rotation, under the less situation of rotating speed, fluid can rotate regularly from level to level very much, and right cylinder is static when stablizing, and angular velocity is zero.

1, establish when experiment container is stable to be rotated, the moment of resistance that cylindrical object bore is M, then

The moment of resistance M of M=cylindrical side institute liquid body ₁+ cylinder bottom surface suffered fluid friction moment M ₂(deriving slightly)

${\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="C2006100517770017H1.png"\; state="\{\{state\}\}">M</figure-callout>}}_1=4\mathrm{\&pi;\&eta;L}{\mathrm{\&omega;}}_0\frac{{{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="C2006100517770017H1.png"\; state="\{\{state\}\}">R</figure-callout>}}_1}^2{R}^2}{{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="C2006100517770017H1.png"\; state="\{\{state\}\}">R</figure-callout>}}_1^2-R^2}---\left(7\right)$

${\mathrm{<figure-callout\; id="2"\; label="M"\; filenames="C2006100517770013H1.png,C2006100517770014H1.png"\; state="\{\{state\}\}">M</figure-callout>}}_2=\frac{{\mathrm{\&pi;\&eta;<figure-callout\; id="2"\; label="R"\; filenames="C2006100517770013H1.png,C2006100517770014H1.png"\; state="\{\{state\}\}">R</figure-callout>}}^2{\mathrm{\&omega;}}_0}{2\mathrm{\&Delta;z}}---\left(8\right)$

The liquid resistance square M that cylindrical object bore

$M={\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="C2006100517770017H1.png"\; state="\{\{state\}\}">M</figure-callout>}}_1+{\mathrm{<figure-callout\; id="2"\; label="M"\; filenames="C2006100517770013H1.png,C2006100517770014H1.png"\; state="\{\{state\}\}">M</figure-callout>}}_2=4\mathrm{\&pi;\&eta;L}{\mathrm{\&omega;}}_0\frac{{{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="C2006100517770017H1.png"\; state="\{\{state\}\}">R</figure-callout>}}_1}^2{R}^2}{{{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="C2006100517770017H1.png"\; state="\{\{state\}\}">R</figure-callout>}}_1}^2-{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="C2006100517770013H1.png,C2006100517770014H1.png"\; state="\{\{state\}\}">R</figure-callout>}}^2}+\frac{\mathrm{\&pi;\&eta;}{\mathrm{<figure-callout\; id="4"\; label="R"\; filenames="C2006100517770017H1.png"\; state="\{\{state\}\}">R</figure-callout>}}^4{\mathrm{\&omega;}}_0}{2\mathrm{\&Delta;z}}---\left(9\right)$

2, pull spring torsional moment M '.

The pull spring of suspended cylinder is a steel wire, and its shear modulus is G, and the pull spring radius is r, and pull spring length is L '.Rotating torque is: $M^{\&prime;}=\frac{{\mathrm{\&pi;<figure-callout\; id="4"\; label="Gr"\; filenames="C2006100517770017H1.png"\; state="\{\{state\}\}">Gr</figure-callout>}}^4}{2L^{\&prime;}}\mathrm{\&theta;}---\left(10\right)$

This formula represents that moment M ' is directly proportional with windup-degree θ.

When the liquid in rotation system stability, the moment of resistance that liquid produces and the suspension torsional moment balance that pull spring produced make cylindrical object reach static.

So M=M '

Can solve viscosity coefficient from (9), (10) formula is:

$\mathrm{\&eta;}=\frac{{\mathrm{<figure-callout\; id="4"\; label="Gr"\; filenames="C2006100517770017H1.png"\; state="\{\{state\}\}">Gr</figure-callout>}}^4}{2L^{\&prime;}{\mathrm{\&omega;}}_0}\mathrm{\&theta;}\left[\frac{2\mathrm{\&Delta;z}({{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="C2006100517770017H1.png"\; state="\{\{state\}\}">R</figure-callout>}}_1}^2-R^2)}{8\mathrm{L\&Delta;<figure-callout\; id="1"\; label="z\; R"\; filenames="C2006100517770017H1.png"\; state="\{\{state\}\}">z</figure-callout>}{R_{}}^{}{{}_1}^2{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="C2006100517770013H1.png,C2006100517770014H1.png"\; state="\{\{state\}\}">R</figure-callout>}}^2+({{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="C2006100517770017H1.png"\; state="\{\{state\}\}">R</figure-callout>}}_1}^2-R^2)R^4}\right]---\left(11\right)$

Wherein:

The shear modulus of G metal pull spring: r pull spring radius: L ' pull spring length: θ is deflection angle: ω ₀The experiment container rotating speed: the distance of experiment container bottom surface is arrived in Δ z cylinder bottom surface: L cylinder height: R ₁Cylindrical radius: R experiment container radius.

The present invention adopts above-mentioned experimental principle and technical method to constitute a kind of rotary liquid comprehensive experimental device, this device is in college physical experiment teaching, can not only observe the phenomenon of centrifugal action qualitatively, also the upper recess surface of rotating liquid can be studied as an optical system, can be measured acceleration of gravity and coefficient of viscosity quantitatively.This experiment combines many-sided knowledge such as fluid mechanics, geometrical optics and physical optics, and content is very abundant, and the experiment manipulative ability and the analysis ability of exercise student ' improve the physics experiment teaching quality preferably.

Description of drawings:

Fig. 1 is an Experimental equipment of the present invention

Fig. 2 is experimental principle figure

Fig. 3 is for measuring gravity acceleration g experimental principle figure

Fig. 4 is coefficient of viscosity measuring principle figure

Fig. 5 is for measuring gravity acceleration g embodiment 2 Experimental equipment

Fig. 6 is for measuring gravity acceleration g embodiment 3 Experimental equipment

Fig. 7 is the Experimental equipment that concerns of parabolic focal length of checking and rotating speed

Fig. 8 is for measuring the coefficient of viscosity Experimental equipment

Fig. 9 is the graph of a relation of parabolic focal length of the checking of embodiment 3 and rotating speed

1, the support bar 2, laser instrument 3, the horizontal transparent screen 4 of millimeter scale, horizontal graticule 5, level meter 6, casing 7, laser power supply jack 8, rotating toggle switch 9, speed-regulating switch 10, speed display window 11, rotating disk 12, cylindrical experiment container 13, horizontal protractor 14, the vertical transparent screen 15 of millimeter scale, pull spring suspended cylinder 16, the pull spring that have millimeter scale

Embodiment

Embodiment 1

Experimental provision of the present invention is seen Fig. 1: by rotating mechanism, speed controlling and adjusted module, test the speed and display module, laser instrument and measurement component are formed.Rotating mechanism places in the casing 6, and the rotating disk 11 on casing 6 upper surfaces is fixed on the motor bearings, can follow the motor smooth rotation.Cabinet panel is provided with speed-regulating switch 10, rotating toggle switch 9, the digital demonstration 10 of speed, laser power supply.Vertical fixing has the support bar 1 of scale on the instrument box 6, the direction adjustable required parts of different experiments content in fixed position on the support bar 1, described parts comprise: laser instrument 2, millimeter scale horizontal screen 3, horizontal graticule 4, horizontal protractor 13, millimeter scale vertical screen 14, pull spring suspended cylinder 15, pull spring 16; The cylindrical experiment container 12 of fixed placement on the rotating disk 11 of casing 6; Speed-regulating switch 9 and rotating toggle switch 8 connection speed control circuits also pass through display window 10 demonstration rotary speeds.

By the fast switch that experimental provision of the present invention is transferred, make to be placed on the experiment container rotation that fills liquid on the rotating disk, reach the rotation of liquid, digital demonstration liquid rotating speed, thus carry out the measurement of each physical quantity, with different Physical Experiments.

Embodiment 2

The height difference measuring gravity acceleration g of and lowest part the highest with the rotating liquid liquid level, experimental procedure is as follows:

Referring to accompanying drawing 5, fill the cylindrical experiment container 12 of liquid, by speed-regulating switch 9, with a certain rotating speed rotation, the liquid surface of interior Sheng forms parabola, and rotating speed shows 10 by number;

Change experiment container rotation speed n (revolutions per second) (ω=2 π n), aim at rotating liquid respectively with horizontal graticule 4 and present paraboloidal bottom and highest point, and read the highest value with lowest part of liquid level at the support bar 1 that has scale, computed altitude difference Δ h, with the diameter D of vernier caliper measurement experiment container, according to formula $g=\frac{{\mathrm{\&pi;}}^2{D}^2{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="C2006100517770013H1.png,C2006100517770014H1.png"\; state="\{\{state\}\}">n</figure-callout>}}^2}{7200\&CenterDot;\mathrm{\&Delta;h}}$ Calculate gravity acceleration g.

Experimental data:

Number of times	1	2	3	4	5	6
							Rotation speed n (rev/min)	110	115	120	125	130	135
Difference in height Δ h (cm)	1.70	1.80	1.90	2.10	2.20	2.4
							g(cm/s 2)	936.08	966.28	996.75	978.54	1010.28	998.70

G=981.11 (cm/s ²) the generally acknowledged value of area, Hangzhou acceleration of gravity: g=979.30cm/s ²Experiment relative error: E=0.18%

Embodiment 3

With slope method check weighing power acceleration g, referring to accompanying drawing 6.Millimeter scale horizontal screen 3 is placed cylindrical experiment container 12 tops that fill liquid, and laser instrument 2 laser beam parallel shaft incidents through millimeter scale horizontal screen 3, are aimed at 12 ends of container $x_0=R/\sqrt{2}$ The mark at place is measured the distance H of transparent screen 3 to container 12 bottoms, height h when liquid level is static;

Cylindrical experiment container 12 rotation speed n of speed-regulating switch 9 changes (rev/min) $(\mathrm{\&omega;}=\frac{2\mathrm{\&pi;n}}{60}),$ Reading between incident light and reflection light point BC apart from d, then on the millimeter scale horizontal screen 3 $\tan 2\mathrm{\&theta;}=\frac{d}{H-h},$ Obtain tan θ value, according to formula $g=\frac{{2\mathrm{\&pi;}}^{2}D}{3600\sqrt{2}\tan \mathrm{\&theta;}},$ Obtain gravity acceleration g.

Experimental data:

Height difference H-the h=92.0mm of transparent screen and inactive liquid liquid level

G=987.55 (cm/s ²) the generally acknowledged value of area, Hangzhou acceleration of gravity: g=979.30cm/s ²Experiment relative error: E=0.75%

Embodiment 4

Verify the relation of parabolic focal length and rotating speed,

With reference to accompanying drawing 7, millimeter scale vertical screen 14 is crossed rotating shaft put into the experiment container central authorities that fill liquid, by speed-regulating switch 9, with a certain rotating speed rotation, the liquid surface of interior Sheng forms parabola, and rotating speed shows 10 by number;

The laser beam parallel shaft is incident to the rotation liquid level, after focus on the vertical screen, can change incoming position and observe the focusing situation, by change rotation speed n (rev/min) $(\mathrm{\&omega;}=\frac{2\mathrm{\&pi;n}}{60}),$ Observe the focal position that is on vertical screen after the incident of laser beam parallel shaft, the distance that reads focus and liquid concave bottom with scale on horizontal graticule 4 and the vertical screen 14 and the scale on the support bar 1 is a real focal length; Use paraboloidal focal length $f=\frac{\mathrm{<figure-callout\; id="2"\; label="g"\; filenames="C2006100517770013H1.png,C2006100517770014H1.png"\; state="\{\{state\}\}">g</figure-callout>}}{2{\mathrm{\&omega;}}^2}$ Formula, the focal length and the real focal length that calculate under each rotating speed compare.

Experimental data:

Number of times	1	2	3	4	5	6
							Rotation speed n (revolutions per second)	70	80	90	100	110	120
The focal distance f of surveying ' (cm)	8.59	6.77	5.32	4.50	3.62	3.00
							Calculated value focal distance f (cm)	9.12	6.98	5.39	4.47	3.69	3.10

The focal length that is obtained and the graph of a relation of rotating speed are seen Fig. 9

Embodiment 5

Measure coefficient of viscosity, with reference to accompanying drawing 8, in cylindrical experiment container 12, pour certain amount of fluid into, right cylinder 15 vertical immersion that pull spring is hung are in liquid, cylindrical center is consistent with rotation, the center hole of horizontal protractor 13 is aimed at steel wire, make steel wire just in time pass aperture, can not collide on every side; Right cylinder 15 upper surfaces have a scale mark mark, and the position of adjusting laser instrument 2 makes laser beam vertically pass through protractor 13 back alignment liquids scale mark on cylinder when static, record laser this moment pairing angle on horizontal protractor 13; Open speed-regulating switch 9 then, low speed rotation, rotating speed shows 10 by number; Cylindrical experiment container 12 is with constant angular velocity omega ₀Rotation, under the less situation of rotating speed, fluid rotates regularly from level to level, right cylinder repose angle speed is zero when stablizing, adjust the position of laser instrument 2 this moment again, make the scale mark of laser beam on vertically aiming at the cylinder face static through protractor 13 back, recording laser is pairing angle on horizontal protractor 13; Two differential seat angles of front and back record are the deflection angle theta of cylinder; Measure the cylinder deflection angle theta under the different rotating speeds in the experiment respectively.

With the spiral dial gauge measure the pull spring radius r, with vernier caliper measurement pull spring length L ', horizontal graticule 4 measures the cylinder bottom surfaces to the distance, delta z of experiment container bottom surface, with vernier caliper measurement cylinder height L, with vernier caliper measurement cylindrical radius R ₁, with vernier caliper measurement experiment container radius R, find the shear modulus G of metal pull spring,

Can be according to formula: $\mathrm{\&eta;}=\frac{{\mathrm{<figure-callout\; id="4"\; label="Gr"\; filenames="C2006100517770017H1.png"\; state="\{\{state\}\}">Gr</figure-callout>}}^4}{2L^{\&prime;}{\mathrm{\&omega;}}_0}\mathrm{\&theta;}\left[\frac{2\mathrm{\&Delta;z}({{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="C2006100517770017H1.png"\; state="\{\{state\}\}">R</figure-callout>}}_1}^2-R^2)}{8\mathrm{L\&Delta;<figure-callout\; id="1"\; label="z\; R"\; filenames="C2006100517770017H1.png"\; state="\{\{state\}\}">z</figure-callout>}{R_{}}^{}{{}_1}^2{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="C2006100517770013H1.png,C2006100517770014H1.png"\; state="\{\{state\}\}">R</figure-callout>}}^2+({{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="C2006100517770017H1.png"\; state="\{\{state\}\}">R</figure-callout>}}_1}^2-R^2)R^4}\right],$ Calculate the coefficient of viscosity η of liquid.

Experimental data:

Castor oil, T=18 ℃

η=1.30537Pas is formula η=5.75e rule of thumb ^-0.0837t[1]Get η=1.27455Pas

Experiment relative error: E=2.4%

The shear modulus r=0.1213mm pull spring radius of G=81GPa metal pull spring

L '=30.0cm pull spring length θ is a deflection angle

ω ₀Container rotating speed Δ z=2.3cm cylinder bottom surface is to the distance of experiment container bottom surface

L=3.0cm cylinder height R ₁=1.5cm cylindrical radius

R=4.9cm experiment container radius

Claims (7)

1, a kind of rotary liquid comprehensive experimental instrument, comprise by rotating mechanism, speed controlling and adjusted module, test the speed and display module, laser instrument and measurement component are formed, rotating mechanism places in the casing, disk on the casing upper surface is fixed on the motor bearings, can follow the motor smooth rotation, cabinet panel is provided with speed-regulating switch, the rotating toggle switch, speed is digital to be shown, laser power supply, on the casing vertical fixing two support bars that have scale, support bar is used to measure and the fixing required measurement component of different experiments content and make its locality adjustable, measurement component comprises: millimeter scale horizontal screen, horizontal graticule, horizontal protractor, millimeter scale vertical screen, the pull spring suspended cylinder, cylindrical experiment container fixed placement is on rotating disk.

2, rotary liquid comprehensive experimental instrument according to claim 1 is characterized in that laser instrument (2) is fixed on the support bar (1), and position and direction are adjustable, by laser power supply jack (7) power supply on the panel.

3, rotary liquid comprehensive experimental instrument according to claim 1 is characterized in that two of the both sides vertical fixing of the cylindrical experiment container (12) on the casing (6) have the support bar (1) of scale.

4, the described rotary liquid comprehensive experimental instrument measurement method for viscosity coefficient of liquid of claim 1, its experimental procedure is:

In cylindrical experiment container (12), pour certain amount of fluid into, right cylinder (15) vertical immersion that pull spring is hung is in liquid, and cylindrical center is consistent with rotation, with the center hole aligning steel wire of horizontal protractor (13), make steel wire just in time pass aperture, can not collide on every side; Right cylinder (15) upper surface has a scale mark mark, and the position of adjusting laser instrument (2) makes laser beam vertically pass through protractor (13) back alignment liquid scale mark on cylinder when static, and record laser this moment is gone up pairing angle at horizontal protractor (13); Open speed-regulating switch (9) then, low speed rotation, rotating speed shows (10) by number; Cylindrical experiment container (12) is with constant angular velocity omega ₀Rotation, under the less situation of rotating speed, fluid rotates regularly from level to level, right cylinder repose angle speed is zero when stablizing, adjust the position of laser instrument (2) this moment again, make laser beam vertically pass through scale mark on the cylinder face of protractor (13) back aiming at static, recording laser is gone up pairing angle at horizontal protractor (13); Two differential seat angles of front and back record are the deflection angle theta of cylinder; Measure the cylinder deflection angle theta under the different rotating speeds in the experiment respectively;

With the spiral dial gauge measure the pull spring radius r, with vernier caliper measurement pull spring length L ', horizontal graticule (4) measures the cylinder bottom surface to the distance, delta z of experiment container bottom surface, with vernier caliper measurement cylinder height L, with vernier caliper measurement cylindrical radius R ₁, with vernier caliper measurement experiment container radius R, find the shear modulus G of metal pull spring,

Can be according to formula: $\mathrm{\&eta;}=\frac{{\mathrm{Gr}}^4}{2L^{\text{'}}{\mathrm{\&omega;}}_0}\mathrm{\&theta;}\left[\frac{2\mathrm{\&Delta;z}({R_1}^2-R^2)}{8\mathrm{L\&Delta;z}{R_1}^2{R}^2+({R_1}^2-R^2)R^4}\right],$ Calculate the coefficient of viscosity η of liquid.

5, the described rotary liquid comprehensive experimental instrument of claim 1 is measured the gravity acceleration g measuring method, it is characterized in that the steps include: with slope method check weighing power acceleration g

Millimeter scale horizontal screen (3) is placed cylindrical experiment container (12) top that fills liquid, and the incident of laser instrument (2) laser beam parallel shaft through millimeter scale horizontal screen (3), is aimed at container (12) end $x_0=R/\sqrt{2}$ The mark at place, R is the radius of experiment container in the formula, measures the distance H of transparent screen (3) to container (12) bottom, height h when liquid level is static;

Speed-regulating switch (9) changes cylindrical experiment container (12) rotation speed n, and n is rev/min angular velocity $\mathrm{\&omega;}=\frac{2\mathrm{\&pi;n}}{60},$ Reading between incident light and reflection light point BC apart from d, then on the millimeter scale horizontal screen (3) $\tan 2\mathrm{\&theta;}=\frac{d}{H-h},$ Obtain tan θ value, according to formula $g=\frac{2{\mathrm{\&pi;}}^{2}D}{3600\sqrt{2}\tan \mathrm{\&theta;}},$ D is the diameter of experiment container in the formula, obtains gravity acceleration g.

6, the described rotary liquid comprehensive experimental instrument of claim 1 is measured the gravity acceleration g measuring method, it is characterized in that height difference measuring gravity acceleration g the highest with the rotating liquid liquid level and lowest part, and experimental procedure is as follows:

Fill the cylindrical experiment container (12) of liquid, by speed-regulating switch (9), with a certain rotating speed rotation, the liquid surface of interior Sheng forms parabola, and rotating speed shows (10) by number;

Change rotation speed n, n be revolutions per second, angular velocity omega=2 π n, and with horizontal graticule (4) with have the difference in height Δ h of the highest and lowest part of support bar (1) the measurement liquid level of scale, the diameter D of usefulness vernier caliper measurement experiment container is according to formula $g=\frac{{\mathrm{\&pi;}}^2{D}^2{n}^2}{7200\&CenterDot;\mathrm{\&Delta;h}}$ Calculate gravity acceleration g.

7, the described rotary liquid comprehensive experimental instrument of claim 1 is verified the relation of parabolic focal length and rotating speed, and experimental procedure is as follows:

Millimeter scale vertical screen (14) is crossed rotating shaft and is put into the experiment container central authorities that fill liquid, and by speed-regulating switch (9), with a certain rotating speed rotation, the liquid surface of interior Sheng forms parabola, and rotating speed shows (10) by number;

The laser beam parallel shaft is incident to the rotation liquid level, after focus on the vertical screen, change rotation speed n, n is rev/min angular velocity $\mathrm{\&omega;}=\frac{2\mathrm{\&pi;n}}{60},$ Observe the focal position that is on vertical screen after the incident of laser beam parallel shaft, the distance that reads focus and liquid concave bottom with scale on horizontal graticule (4) and the vertical screen (14) and the scale on the support bar (1) is a real focal length;

Use paraboloidal focal length $f=\frac{g}{2{\mathrm{\&omega;}}^2}$ Formula, the focal length and the real focal length that calculate under each rotating speed compare.

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