CN104297099B - A Method of Measuring Air Specific Heat Capacity Ratio by Vibration Method - Google Patents
A Method of Measuring Air Specific Heat Capacity Ratio by Vibration Method Download PDFInfo
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- CN104297099B CN104297099B CN201410585318.0A CN201410585318A CN104297099B CN 104297099 B CN104297099 B CN 104297099B CN 201410585318 A CN201410585318 A CN 201410585318A CN 104297099 B CN104297099 B CN 104297099B
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- 238000005553 drilling Methods 0.000 abstract description 10
- 230000010355 oscillation Effects 0.000 abstract description 6
- 230000008901 benefit Effects 0.000 abstract description 2
- 238000005259 measurement Methods 0.000 abstract description 2
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Abstract
A kind of vibratory drilling method measures the method for air specific heat ratio, relates to the measurement of physical constant, and for the problem overcoming prior art to exist, the technical solution used in the present invention is: a cylinder, and its upper end seals, lower ending opening, has a spirit bubble in the medial plane of upper surface；The side surface upper part of cylinder has one or more pore, and pore can realize sealing by sealing nut；Cylinder is vertically fixed on support；A spring, one weight of the lower surface suspension line of piston is connected between cylinder inner top side plane and piston；When pore is opened, weight vibration period T1=2π(m/k)0.5, seal all pores, weight vibration period T；Then air specific heat ratio γ=4 π mh (T1 2‑T2)/(r 2P T2 T1 2), wherein π is pi, and m is the quality sum of piston and weight, and k is the coefficient of elasticity of spring, and P is for sealing gas pressure intensity, and r is barrel bore.Provide the benefit that: seal air and possess elasticity；Experimental principle is more rigorous；It it is strict simple harmonic oscillation；Do not have rotation phenomenon；Apparatus structure is simpler, and cost is less expensive.
Description
Technical field
The present invention relates to the measurement of physical constant, a kind of method using vibratory drilling method to measure air specific heat ratio is particularly provided.
Background technology
It is a kind of conventional specific heat ratio measuring method that vibratory drilling method measures air specific heat ratio, the measuring method used in physics laboratory, experimental principle refers to " 2 experiment " of " vibratory drilling method surveys the improvement of Ratio of Specific Heats of Air experimental technique; Taizhou University's journal, in December, 2010 the 6th phase of volume 32, the 39-42 page ", and " the 1.1 former experimental principle " of " vibratory drilling method Experiment of Determining Air Specific Heat Ratio principle analysis; laboratory science, the 3rd phase of volume 16 in June, 2013,35-37 ".
nullThe principle that prior art uses，Refer to Fig. 1，Gas inlet injects gas continuously and stably，The steel ball A that the pressure of gas increases in the vertical glass tubing that promotion is connected with gas container moves up，(this gap is a theoretical value the gap of 0.01-0.02mm between the tube wall of steel ball A and glass tubing B，Refer to the internal diameter of the vertical glass tubing big 0.02-0.04mm of diameter than steel ball A)，When steel ball A rises to the upper end of aperture，Portion gas flows out from aperture，The pressure of gas suffered by steel ball A reduces，The thrust of the gas that steel ball A is subject to reduces，The kinetic energy of steel ball A gradually weakens，After arriving high point，By action of gravity，Steel ball A falls，Transform gravitational energy is kinetic energy，Drop to below aperture at steel ball A，The gas pressure intensity of steel ball A lower end is more than the gas pressure intensity of steel ball A upper end，The thrust of the gas being subject to，Kinetic energy gradually weakens，After kinetic energy is zero，The thrust that steel ball A produces in the gas pressure intensity difference suffered by spheroid upper and lower side，Steel ball A moves again up，Back and forth carry out，Realize vibration.
The problem that prior art exists, also mentions at aforementioned two documents:
(1) aperture is not the space symmetr center of vibration, is not the time symmetrical centre of vibration, does not possess the mathematical form of simple harmonic oscillation；Steel ball A is typically shorter than the distance of aperture moved beneath in the distance of aperture upper direction, steel ball A is typically less than the time of aperture moved beneath in the time of aperture upper direction, and the motion of steel ball A is substantially subjected to the size control of steel ball A and the gap size of tube wall, aeration speed and aperture；
(2) unequal character of stress above and below aperture, do not possesses the mechanical condition of simple harmonic oscillation: steel ball A is different in the thrust suffered by aperture top and bottom, thrust big in the thrust of the gas suffered by the lower end of aperture, suffered by upper end (gas is from small hole leaking) is little, air-flow environment residing for steel ball A motion is sudden change, and its principle is all held the suspicious attitude by two documents；If, do not has foraminate existence, the thrust that steel ball A is produced by pressure difference, steel ball A will rise always, will not vibrate, although, in document " improvement of vibratory drilling method survey Ratio of Specific Heats of Air experimental technique ", propose to search out the equilbrium position of steel ball A below aperture, then the vibration of amplitude an about 1cm is produced, owing to lacking the effect of external force, regulation only by air-flow, it is difficulty with, reason is that air-flow little then steel ball A declines, the big then steel ball A of air-flow rises, suitable then steel ball A is stable for air-flow, after so steel ball A is stable, must strengthen air-flow just can promote it to rise, after rising certain distance, aforementioned appropriate gas flow must be immediately returned to, the thrust making pressure difference produce is equal with gravity, the step for be difficult to；
(3) steel ball A there will be rotation in motor process and collides with tube wall: when in steel ball A hovering or vibrating by a small margin, it is easier to observe.nullDocument " improvement of vibratory drilling method survey Ratio of Specific Heats of Air experimental technique " have also discovered rotation (being referred to as spin in document) and collision phenomenon，Steel ball A we have found that in vibration processes change occurs in its reflection light，Then，We use red symbol pen to draw a cross on the surface of steel ball A，Find that the cross of steel ball A occurs rotating in vibration processes，And difference instrument、The different time, its rotation direction also changed，What this result presented to us is, and the surface of tube wall or steel ball A is not uniform，And the asymmetry quantum dot of air-flow at aperture，The asymmetric stress of steel ball A is caused to occur rotating，It has been found that，Its frequency rotated also shows difference at different instruments and different time，In other words，Steel ball A is not at laminar flow environment，But have certain turbulent flow，The precision that impact is measured by its rotational kinetic energy，And，Due to the uncertainty rotated，Also cannot quantitatively be revised.
Summary of the invention
For the problem overcoming prior art to exist, the present invention designs a kind of method that novel vibratory drilling method measures air specific heat ratio.
The present invention realizes a kind of method that goal of the invention the technical scheme is that vibratory drilling method measures air specific heat ratio, it is characterized in that: a cylinder, its upper end seals, lower ending opening, and cylinder outer upper end face is a plane, described plane is vertical with cylinder axis, has a spirit bubble in described plane；The side surface upper part of cylinder has one or more pore, and pore realizes sealing by sealing nut and sealing gasket；Cylinder is vertically fixed on support, the altitude mixture control foot of regulation support, makes the level that is in of the spirit bubble of upper transverse plane outside cylinder, thus reach cylinder and be in vertical state；The upper end of spring is fixed at the center of cylinder inner top side plane, the upper transverse plane of the lower end fixed piston of spring, the side of piston is in close contact with the inner side of cylinder, the friction between piston and cylinder inner surface is reduced by the side coating lubricating oil at piston, the upper end of suspension line is fixed at the center, lower surface of piston, the lower end system weight of suspension line；When pore is opened, traction weight stretches downwards spring, after decontroling weight, under the action of the spring, will vibrate, its vibration period T1=2π(m/k)0.5, wherein T1For the vibration period, π is pi, and m is the quality sum of piston and weight, and k is the coefficient of elasticity of spring；Then, sealing all pores, traction weight stretches downwards spring, after decontroling weight, under the common effect of spring and sealing air, will vibrate, and its vibration period is T, then air specific heat ratio γ=4 π mh (T1 2- T2)/( r 2P T2
T1 2), wherein, pi=3.14159；H is piston distance of transverse plane when being in equilbrium position, on piston upper surface to cylinder interior, is read by the millimeter rule outside hard transparent cylinder；R is the inner radial of cylinder；T and T1For the vibration period, wherein T is vibration period during port sealing, T1For vibration period during pore unsealing；P is piston when being in equilbrium position, seals the pressure of gas, equal to atmospheric value P measuring air from air gauge.
The had the benefit that air of the present invention is in sealing state, seals air and possesses elasticity, and the use of air spring (seal air, use at automobile etc., play damping effect) also demonstrate that air has good elasticity；The air of prior art is constantly in inflation--and leak condition, the experimental principle of the present invention is more rigorous；The pore gas leakage of prior art, is not a strict simple harmonic oscillation；The pore of the present invention is opened, only the vibration of spring effect, port sealing, vibrates under the common effect of spring and air spring, and two kinds of vibrations are all strict simple harmonic oscillations；Prior art is due to the imperfection, the most rigorous of principle, and in the case of cannot quantitatively revising its gas leakage impact, its result similarly is with fortune, to the sensation of a kind of coincidence of people；The piston of the present invention is translation, does not haves the rotation phenomenon of prior art；Relative to prior art, the present invention need not pump-up device, and structure is simpler, and cost is less expensive.
Accompanying drawing explanation
Fig. 1 is the device schematic diagram of prior art；Fig. 2 is the device schematic diagram that the present invention uses.
Wherein, 1, weight；2, suspension line, 3, cylinder, 4, piston, 5, pore, 6, spring.
Detailed description of the invention
One cylinder 3, its upper end seals, lower ending opening, the outer upper end face of cylinder 3 is a plane, described plane vertical with cylinder 3 axis (completed by maker manufacture and ensure that it is vertical), a spirit bubble is had in described plane, there are one or two or more pore 5 in the upper end of the side of cylinder 3, and pore 5 can seal (pore 5 opening is close to a circle sealing gasket side, be in close contact realization sealing inside sealing gasket opposite side and sealing nut) by sealing nut；Cylinder 3 is vertically fixed on support, the most fixing cylinder 3 can weld a screw in cylinder upper end, screw pierces into the screw of support, then fixed by nut, or use the fixing means that other is conventional, such as cylinder 3 is fixed on support by a holder, the altitude mixture control foot of regulation support, makes cylinder 3 vertical (judging whether cylinder 3 is in vertical state by the spirit bubble of the upper transverse plane outside cylinder 3).
The upper end of spring 6 is fixed at the center of cylinder 3 inner top side plane, and the upper transverse plane of a piston 4 is fixed in the lower end of spring 6, and the side of piston 4 is in close contact with the inner side of cylinder 3, reduces friction by the side coating lubricating oil at piston 4；The upper end of suspension line 2 is fixed at the center, lower surface of piston 4, and suspension line 2 is preferably soft line, the lower end system weight 1 of suspension line 2.
When pore is opened, traction weight 1 stretches downwards spring 6, after decontroling weight 1, under the effect of spring 6, will vibrate, and its vibration period is T1=2π(m/k)0.5, wherein T1For the vibration period, π is pi, and m is the quality sum (ignoring spring 6 and the quality of suspension line 2, prior art the most all uses this approximation method) of piston 4 and weight 1, and k is the coefficient of elasticity (also known as the coefficient of stiffiness, stiffness factor) of spring.
Then, seal all pores 5, traction weight 1 stretches downwards spring 6, after decontroling weight 1, under the common effect of spring 6 and sealing air, to vibrate, vibration the most now to be acted on (seal air and can constitute an air spring, the damping device of automobile just uses air spring) by sealing air；
Area (the π * r of device static (being now in dynamic balance state), distance h of the upper surface of piston 4 to cylinder 3 inner upper end plane and piston 42) be multiplied, obtain seal air volume (impact of volume can be ignored by pore 5 under certain condition, such as seal inside cap and fix a stopper, sealed by screw thread and sealing gasket, before sealing, there is micro gap that air-flow can be allowed to pass through between stopper and pore, port sealing is made by being in close contact sealing gasket, from sealing nut contact sealing gasket to fully sealing, the distance that sealing nut moves is the shortest, when sealing completes, the volume of stopper is equal to inside pore, the volume of enclosed space outside cylinder and bottom sealing nut, this can determine this relation during fabrication according to the size of the size of pore and stopper), it seals the volume V=π * r of air2* h, uses clear glass or clear hard plastic cylinder 3, preferably clear rigid plastics, at the outer surface labelling millimeter rule of transparent cylinder 3, then can record parameter h, and r can be given by manufacturing firm or measure at cylinder opening end；
According to adiabatic equation PVγ=C,
Wherein, P is the pressure values sealing air, and V is the volume sealing air, and γ is air specific heat ratio (being also called the adiabatic coefficent of air), and C is a constant；
Both sides are carried out differential, obtains dP* Vγ+P*dVγ=dP* Vγ+P*(γVγ -1)*dV
=dC=0,
So, dP=-(P* γ/V) dV；
When piston 4 moves, the pressure sealing air will be caused to change, if piston 4 moves down distance x from equilbrium position, the pressure difference at piston two ends is dP, and pressure difference produces a directed force F 1 upwards and is:
F1=S*dP=π*r2*dP
Spring 6 also will produce directed force F 2=-kx upwards simultaneously, and F=F1+ F2 is the most with joint efforts
F=π*r2*dP- kx
This active force acts on piston 4 and weight 1, will produce acceleration a, and acceleration is equal to displacement x second-order derivative dx to time t2/dt2, (defined when x is motion the position of piston relative to the displacement of equilbrium position during piston rest), then
F=π* r2*dP- kx
=m dx2/dt2
V=π* r2*h
dV=π* r2*x
F=π*r2*dP- kx=-π* r 2*(P*γ)*x/h-kx=m
dx2/dt2
So
dx2/dt2+[π* r 2* P* γ/(m h)+k/m] * x=0
The above is a simple harmonic oscillation equation, and its circular frequency ω is
ω=2πf=2π/T=[π* r 2* P* γ/(m h)+k/m]0.5
Wherein f is frequency of vibration, the T vibration period, T1=2π(m/k)0.5, so 2 π/T1=( k/m) 0.5
Therefore (2 π/T)2-(2 π/T1)2=π* r 2* P* γ/(m h)
Then air specific heat ratio γ is
γ=4πmh(T1 2- T2)/( r 2P T2
T1 2)
In above formula, pi=3.14159；M is the quality sum of piston 4 and weight 1；H is piston 4 when being in equilbrium position, the distance of piston 4 upper surface to cylinder 3 inner upper end plane；R is the inner radial of cylinder 3；T and T1For the vibration period, measuring (method that background technology uses) by the photogate arranged outside cylinder 3 or stopwatch is measured, wherein T is the vibration period (to consider to seal the impact of air) during port sealing, T1For the vibration period (not considering the impact of air) during pore unsealing；P is piston when being in equilbrium position (piston 4 is static), seals the pressure of gas, equal to atmospheric value P measuring air from air gauge.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| GB1202281A (en) * | 1966-09-20 | 1970-08-12 | Cie Des Compieurs | Improvements in or relating to testing apparatus for gases |
| FR2389129A1 (en) * | 1977-04-26 | 1978-11-24 | Elf Aquitaine | METHOD AND DEVICE FOR MEASURING THE SPECIFIC HEAT RATIO AT CONSTANT PRESSURE AND VOLUME FOR A REAL FLUID |
| CN101718726A (en) * | 2009-11-30 | 2010-06-02 | 河海大学 | Device and method for measuring gas specific heat ratio |
| CN203720124U (en) * | 2014-03-06 | 2014-07-16 | 滨州学院 | Device for measuring air specific heat ratio at different temperature |
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