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INJE-TP-00-05U(1)Gauge Field of the Kaluza-Klein Theory in the Presence of Branes Gungwon Kang ?and Y.S.Myung ?Department of Physics,Inje University,Kimhae 621-749,Korea Abstract We investigate the zero mode dimensional reduction of the Kaluza-Klein uni?cations in the presence of a single brane in the in?nite extra dimension.We treat the brane as ?xed,not a dynamical object,and do not require the orbifold symmetry.It seems that,contrary to the standard Kaluza-Klein models,the 4D e?ective action is no longer invariant under the U(1)gauge transformations due to the explicit breaking of isometries in the extra dimen-sion by the brane.Surprisingly,however,the linearized perturbation analysis around the RS vacuum shows that the Kaluza-Klein gauge ?eld does possess the U(1)gauge symmetry at the linear level.In addition,the graviscalar also behaves di?erently from the 4D point of view.Some physical implications of our results are also discussed.
I.INTRODUCTION
In the standard?ve-dimensional Kaluza-Klein(KK)approach where the full spacetime manifold is factorized as M4?S1,the?ve-dimensional gravitation theory which has the reparametrization invariance on S1can be interpreted as a gauge theory of the Virasoro group from the four-dimensional point of view(see[1]and references therein).After the geometric spontaneous symmetry breaking of the Virasoro invariance,the excitations of the 5D gravitational?elds are split into4D massless gravitational?elds,massless gauge?elds, massless scalar?eld,and an in?nite tower of massive spin-2?elds[1,2].In particular,the U(1)gauge symmetry of the vector?elds in the4D e?ective action is originated from the translational isometries in the extra dimension.
Recently,there have been lots of interest in the phenomenon of localization of gravity proposed by Randall and Sundrum(RS)[3,4](for previous relevant work see references therein).RS[4]assumed a single positive tension3-brane and a negative bulk cosmological constant in the?ve-dimensional spacetime.There have been developed a large number of brane world models afterwards[5,6].The introduction of branes usually gives rise to the“warping”of the extra dimensions,resulting in non-factorizable spacetime manifolds. More importantly,the presence of branes breaks the translational isometries in the extra dimensions.Therefore,it would be very interesting to see how the conventional Kaluza-Klein picture changes in the brane world scenarios.
Dobado and Maroto[7]recently have incorporated the e?ect of the presence of the brane in the Kaluza-Klein(KK)reduction by introducing Goldstone bosons(GB)?elds.The GB?elds parameterize the excitations of the brane[8]and so the GB correspond to the spontaneous symmetry breaking of the translational isometries of the compacti?ed extra dimensions by the brane.It has been shown that in the dimensional reduction of the KK uni?cations a sort of Higgs mechanism related to the GB[9]gives mass to the KK graviphotons.(see also the appendix of Ref.[10]although it has the opposite sign for the mass term.)
On the other hand,there are other approaches to con?ne standard model particles on the brane by allowing the?elds to live in the bulk spacetime.For example,bulk gauge bosons have been considered in Ref.[11,12].It is important to derive the zero mode e?ective action because its zero modes(massless modes)correspond to the standard model particles localized on the brane.
In this paper,contrary to the approach mentioned above where the brane is treated as a dynamical object,we have treated the brane as?xed,and investigate the zero mode dimensional reduction of the Kaluza-Klein uni?cations.The brane world model considered in this paper is the RS one with a single3-brane in the in?nite?fth dimension[4].As expected, the breaking of isometries in the extra dimension by the brane makes the4D e?ective action not being invariant under U(1)gauge transformations.Interestingly,however,the analysis of the linearized equation around the RS background shows that the KK gauge?eld does possess the U(1)gauge symmetry at the linear level.
In section2,we carry out the dimensional reduction of the KK uni?cations in the pres-ence of a single brane with some ansatz for the zero mode excitations.In section3,the linearized perturbations of the4D e?ective action obtained are analyzed around the RS vacuum solution.Some physical implications of our results are discussed in section4.
II.KALUZA-KLEIN REDUCTION
The RS model with a single brane can be described by the following action in5D space-times[4,5,13]
I= d4x ∞?∞dz √
16πG5
(?R?2Λ)? d4x
??xμ?xβ
??xμ
Aα+κ?1
?f ??x M
?x Q
thus we ?nd h 0μν(x,z )=c h ?h μν(x )with a constant c h .Other examples are the form of
the zero modes for the bulk spin-0and spin-1?elds on the RS background [14].For the spin-0?eld Φ(x,z )=H 3/2χ(z )?φ(x ),we have χ=c ΦH ?3/2for the zero mode and hence its localized zero mode is given by Φ0(x,z )=c Φ?φ
(x ).In the case of the spin-1?eld V μ(x,z )=H 3/2σ(z )v μ(x ),one ?nds σ=c V H ?3/2for the zero mode and hence its zero
mode is given by V 0μ(x,z )=c V v μ(x ).From the observations mentioned above,we may pro-
pose that the zero modes are constants with respect to “z ”.Furthermore we stress that for h μ5=0,h 55=0,it may be not a correct way to obtain the zero modes from the linearized equations.This is because their forms are too complicated to analyze the zero modes [13].Even if we choose the gauge-?xing,it is hard to obtain the consistent zero mode solutions.Hence the integration of Eq.(1)over z could be a good starting point to obtain the zero modes.
Note ?rst that
?γ,
(6)
?γ H ?20?P H ?P H
2
A μγαβ?μγαβ+?μA μ),(9)we have
8?P ?P H
H 2= 8H ′′
H )2
(φ?2+κ2A ·A )+8κH ′2A μγαβ?μγαβ+?μA μ),(10)
where the prime (′)denotes the di?erentiation with respect to z .
Then,the ?ve-dimensional action Eq.(1)is given by
I =1
?γφ R (g ) dzH ?3+(φ?2+κ2A ·A )
dzH ?3 8H ′′H 2 +8κ(φ?1A μ?μφ+
1H 4?2Λ dzH ?5 ? d 4x √|δμν+κ2φ2A μA ν|σ.(11)It should be pointed out that the 5D Ricci scalar curvature constructed from g MN ,R (g ),is
independent of z -coordinate since the metric elements g MN are functions of x μhttps://www.doczj.com/doc/9b3776422.html,ing H ′=kθ(z ),H ′′=2kδ(z ), ∞?∞dzH ?3=1/k ,and ∞?∞dzH ?5=1/2k for the RS model with
a single brane,one gets the 4D e?ective action
I KK=1
k
d4x√
|δμν+κ2φ2AμAν| (12)
=1
?γ φR(g)+6k2 φ?1+φ?2
?γφR(g)=
d4x√
4
φ2F2 + [···].(14)
The last term is the
surface term.
The?eld strength is de?ned as Fμν=?μAν??νAμand
F2=FμνFμν.Using Eq.(14),one?nally obtains
I KK=1
?γ φR(γ)?κ2
|δμν+κ2φ2AμAν|+κ2φA·A ,(15)
where we have ommitted the surface terms.
We observe that the zero mode gravitational degrees of freedom in the5D spacetime are split into the4D gravitational?eldsγμν,a vector?eld Aμ,and a graviscalar?eldφas usual. However,the properties of the vector?eld and the scalar?eld are very di?erent from those in the conventional KK reduction.The?rst two terms in this e?ective action are the same form as in the ordinary dimensional reduction of the Kaluza-Klein uni?cations,and they have the U(1)gauge symmetry.The di?erence from the conventional KK reduction is only the last term which is proportional to the brane tension squared.If one started from the KK metric decomposition with Aμ=0andφ=1in Eq.(3),this“potential”term would disappear and one obtains the ordinary Einstein gravity on the brane with zero e?ective cosmological constant as well known.As can be easily seen in Eq.(12),this happens because of the?ne tunning between the brane tensionσand the5D bulk cosmological constantΛ. The appearance of the non-linear term(e.g.,
16πG4 d4x√
4
φ3F2+6k2 φ?1+φ?2+κ2φ(1?φ)A·A .(16)
Here we used 2κ2φ2A·A.
In order to explicitly see how the dynamical aspect of theφ?eld comes out,let us conformally transform the metric as
γμν→ˉγμν=φγμν.(17) Then,the zero-mode e?ective action Eq.(15)is written by
I KK=
1
?ˉγ R(ˉγ)?κ22φ?2ˉ?μφˉ?μφ
+6k2φ?2 φ?1+φ?2
16πG4
d4x√
4
φ3F2?3
2
φ3 FμαFνα?1
2
φ?2 ˉ?μφˉ?νφ?2k2ˉγμν(φ?1+φ?2) ,(20)
ˉ?μFμν+12k2κ2φ?3(1?φ)Aν=?3φ?1ˉ?μφFμν,(21)ˉ?μˉ?μφ?φ?1ˉ?μφˉ?μφ+2k2 φ?1(4?φ?3φ?1)?κ2φ2A·A =κ2
ˉγRN
μν
=diag[1?2M/r+Q′2/r2,(1?2M/r+Q′2/r2)?1,r2,r2sin2θ](23) with Q′=κQ/2,F tr=Q/r2,andφ=1,satis?es Eqs.(20)and(21).In this case we have F tr=??r A0with A0=Q/r.However it does not satisfy Eq.(22)(i.e.,?2k2A·A=F2/4). This is so because of the presence of both brane andφ.Thus,the4D Reissner-Nordstr¨o m black hole withφ=1cannot be embedded in the brane world.In the absence of the brane (i.e.,k=0),there exist charged black hole solutions with non-trivialφ?eld.However,such charged black hole is very di?erent from the Reissner-Nordstr¨o m black hole[18].It does not seem that the presence of the brane changes this feature of the Kaluza-Klein theory much. On the other hand,however,if the scalar?eld were frozen somehow from the beginning in Eq.(3)(e.g.,φ=1),there would be no equation like Eq.(22).Consequently,by observing Eqs.(20)and(21),one can easily?nd that the Reissner-Nordstr¨o m black hole is a solution.
III.LINEARIZED PERTURBATION
In this section we consider the linearized perturbations around the RS vacuum solution (ˉγμν=ημν,Aμ=0,φ=1)for the dimensionally reduced e?ective action in Eq.(18). Actually,at the linear level,the truncated e?ective action in Eq.(19)is equivalent to the non-truncated one in Eq.(18).Let us introduce the perturbations around the RS solution γμν=ημν+κhμν,Aμ=0+aμ,φ=1+κ?.(24) Consequently,
ˉγμν=ημν+κˉhμν,ˉhμν=hμν+?ημν.(25) Then the bilinear action of Eq.(18)or(19)which governs the perturbative dynamics is given by
I0KK=κ2
4 ?μˉhαβ?μˉhαβ??μˉh?μˉh+2?μˉhμν?νˉh?2?μˉhμα?νˉhαν
?12?μ??μ?+6k2?2 ,(26)
whereˉh=ημνˉhμν=h+4?.Surprisingly,it turns out that the bilinear e?ective action is invariant under the U(1)gauge transformation.The U(1)gauge symmetry breaking term in Eq.(19)appears as higher order term than the squared order:i.e.,6k2κ2(1?φ)A·A??6k2κ3?aμaμ.
In order to understand what physical states there are,let us analyze the?eld equations as below.From the action Eq.(26)we have the equations of motion
2ˉhμν+?μ?νˉh? ?μ?αˉhαν+?ν?αˉhαμ ?ημν 2ˉh??α?βˉhαβ =0,(27)
2aμ??μ(?νaν)=0,(28)
2?+4k2?=0.(29) By taking the trace of Eq.(27),we have
2ˉh??α?βˉhαβ=0.(30) Hence Eq.(27)becomes
2ˉhμν+?μ?νˉh? ?μ?αˉhαν+?ν?αˉhαμ =0.(31) So far we have not chosen any gauge forˉhμν.Now let us choose the transverse(or harmonic)gauge in the?ve-dimensional spacetime.Since
,(32)
g MN=ηMN+κ?MN, ?MN = hμν?aμ
?aν2?
the?ve-dimensional harmonic gauge?M?MN=1
?νˉh,?μaμ=0.(33)
2
That is,the5D harmonic gauge is split into the harmonic gauge for the4D gravitational ?eld and the Lorenz gauge for the4D KK gauge?https://www.doczj.com/doc/9b3776422.html,ing these gauge conditions above, Eq.(31)and Eq.(28)become
2ˉhμν=0,2aμ=0,(34) respectively.Therefore,it proves thatˉhμνand aμindeed represent the massless spin-2 gravitons and the massless spin-1graviphotons on the brane,respectively.
On the other hand,the spin-0scalar?eld?uctuation?in Eq.(29)appears to be massive. However,it has a tachyonic mass m2?=?4k2proportional to the brane tension squared. It seems to indicate that the scalar?uctuation of the5D gravitational degrees of freedom corresponds to the unstable mode in the RS background.
IV.DISCUSSION
We have investigated the KK zero mode e?ective action in the presence of a single brane in the extra dimension.Although the four-dimensional gravitational modes behaves as usual, the vector and scalar modes behave quite di?erently.In the4D e?ective action,it seems that the vector?eld Aμdoes not possess the U(1)gauge symmetry and that KK photons are not massless any more.The scalar?eldφis also no longer massless and couples to the vector?eld.
However,this is not all of the story.The linearized perturbation analysis around the RS background spacetime shows that the5D massless gravitational degrees of freedom are split into spin-2,spin-1,and spin-0modes as the standard KK model up toκ2-order.We have observed that the massive propagation of the vector mode in the4D e?ective action is not revealed in the linearized perturbation.In order to observe the e?ect of the brane(k=0), thus,one needs to study one-loops correction rather than the linearized one.For example, we expect the relevant vertex correction(k2κ3?aμaμ)from the last term of Eq.(19).
We also have observed that the spin-0mode propagation has a tachyonic mass,indicating some instability of the RS background spacetime through the“radion”or“modulus”?eld.
Presumably,it suggests that some stabilization mechanism for the55-metric component is
necessary in order to have the stable RS background spacetime with a single brane as in the case of the two branes.On the other hand,if one requires the R/Z2orbifold symmetry in
the brane world model,there will be no vector zero mode propagations as mentioned above. Thus,the R/Z2orbifold symmetry with the“modulus”?eld stabilization establishes the
usual localization of gravity on the brane in the RS model[4].
In deriving the U(1)Maxwell term from the5D RS brane model,we use the conventional Kaluza-Klein approach.Apparently,we?nd a non-linear term as well as A·A.This
arises from a sort of brane-Higgs e?ect:Here the isometry of extra dimension was broken
spontaneously by the presence of the brane.Hence we expect that the gauge?eld becomes massive.However,we have found that the massive propagation of the KK gauge?eld does
not reveal at the linear level.Fortunately,instead we?nd the massless vector propagation. What will happen if we take a z-coordinate dependent or other form of ansatz for the“zero
modes”?We still expect there should be non-linear or mass terms in the reduced e?ective
action due to the broken isometry in the extra dimension.However,in order to answer whether or not the gauge?eld becomes massless when linearized,some further work in
detail is needed.There were other attempts to achieve the4D U(1)symmetry from the5D U(1)bulk gauge?elds[11,19].
On the other hand,the RS solution can be extended to accommodate the Schwarzschild
black hole solution on the brane as a zero mode solution.This is possible because the RS solution is Ricci-?at.Hence the Ricci-?at Schwarzschild solution can be embedded into the
brane world by introducing the spherically symmetric spacetime.Now it is very important to
check whether or not the RS brane world allows to have the Reissner-Nordstr¨o m black hole on the brane.As is shown above,the Reissner-Nordstr¨o m black hole cannot be embedded
in the brane world,because this case of A0=0cannot be a solution to the e?ective action of Eq.(15)including the non-linear term and A·A.To obtain this black hole on the brane,
it seems to be necessary to introduce some U(1)bulk gauge?eld in the?ve-dimensional
spacetime whose dynamics is localized on the brane[20].
We have observed that the naive propagations of the scalar?eld gives rise to the tachyonic
mass proportional to the tension of the brane.It may induce the instability of the RS
vacuum.In the linearized gravity,by using the residual gauge freedom,one can also impose the traceless gauge in a source-free region in addition to the harmonic gauge.It follows mainly because“2Trace”vanishes in a source-free region.What will happen if such traceless gauge is imposed in our linearized analysis?The?ve-dimensional trace is?=ηMN?MN= h+2?=ˉh?2?.Hereˉh=h+4?is used.By combining the trace of Eq.(34)and Eq.(29), we have
2(5)?=2ˉh?22?=8k2?,(35) where2(5)=2+?25.Thus,imposing the?ve-dimensional traceless gauge(i.e.,?=0)directly results in?=0,that is,no graviscalar?uctuation.Since h=??2?andˉh=?+2?,it also means the four-dimensional traceless gauge(i.e.,h=ˉh=0).In other words,we notice that the existence of the tachyonic graviscalar?uctuation is mutually inconsistent with imposing the traceless gauge condition.Therefore,the resolution of the instability of the RS background spacetime due to the graviscalar transforms to whether or not one can impose the traceless gauge.In the linearized gravity,the trace of metric?uctuations can be
set to be zero by using remaining gauge freedom provided that there is no matter source in the region in consideration[21].In our analysis,however,since the graviscalar?eld?plays like a matter source in the trace equation above,it does not seem to be plausible imposing such gauge condition in the?rst place.Presumably such traceless gauge condition can be imposed onˉh(2ˉh=0),but not on h(2h=16k2?).
As mentioned above,another possible caveat of our result is that the tachyonic graviscalar ?uctuation is merely an artifact of the ansatz for the zero mode we used in this paper.For instance,instead of H(z)=k|z|+1in Eq.(2),let us assume H(x,z)=k|z|φ(x)+1for the zero mode.This ansatz is analogous to the form used in Ref.[22]for the case of RS model with two branes.Then the4D e?ective action is given by
I KK=1
?γ R(γ)?κ2
|δμν+κ2φ2AμAν|+κ2φ2A·A
?1?γ R(γ)?κ2
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[23]D.A.Demir,hep-ph/0006344.
Are you blind when you're born? Can you see in the dark? 你出生时是目盲的吗？你能在黑暗处看到事物吗？ Dare you look at a king? Would you sit on his throne? 你敢目室国王吗？你想坐在王位上吗？ Can you say of your bite that it's worse than your bark? 你能说你的咬力不如你的叫声吗？ Are you cock of the walk when you're walking alone? 当你独自行走时你很自信自傲吗？ Because jellicles are and jellicles do 因为杰利克是杰利克能 Jellicles do and jellicles would 杰利克能杰利克会 Jellicles would and jellicles can 杰利克会杰利克能 Jellicles can and jellicles do 杰利克能杰利克做 When you fall on your head, do you land on your feet? 当你头朝下落下时，你能用脚着地吗？ Are you tense when you sense there's a storm in the air? 当你感到风暴来临时，你会很紧张吗？ Can you find your way blind when you're lost in the street? 当你迷路时，你能本能的找到正确的方向吗？ Do you know how to go to the heaviside layer? 你知道如何升向九重天吗？ Because jellicles can and jellicles do 因为杰利克能杰利克做 Jellicles do and jellicles can 杰利克做杰利克能 Jellicles can and jellicles do 杰利克能杰利克做 Jellicles do and jellicles can 杰利克做杰利克能 Jellicles can and jellicles do 杰利克能杰利克做 Can you ride on a broomstick to places far distant? 你能骑着扫把去很远的地方吗？ Familiar with candle, with book, and with bell? 你喜爱玩耍蜡烛，书籍或是铃铛吗？ Were you Whittington's friend? The Pied Piper's assistant? 你是惠廷顿的朋友？或是吹笛手的助理吗？ Have you been an alumnus of heaven and hell? 你能自由的通往天堂和地狱吗？ Are you mean like a minx? Are you lean like a lynx? 你是一个爱出风头的姑娘吗？你瘦的像一只山猫吗？ Are you keen to be seen when you're smelling a rat? 当你闻到一只老鼠你会努力的寻找吗？ Were you there when the pharaoh commissioned the Sphinx? 当法老委派做狮身人面像时你在场吗？ If you were, and you are, you're a jellicle cat 如果你在并且你是，你是一只杰利克猫． Jellicle songs for jellicle cats 杰利克歌咏杰利克猫 Jellicle songs for jellicle cats 杰利克歌咏杰利克猫 Jellicle songs for jellicle cats 杰利克歌咏杰利克猫
我的歌声里 没有一点点防备 也没有一丝顾虑 你就这样出现 在我的世界里带给我惊喜情不自己可是你偏又这样 在我不知不觉中悄悄地消失 从我的世界里没有音讯 剩下的只是回忆 你存在我深深的脑海里 我的梦里我的心里我的歌声里 你存在我深深的脑海里 我的梦里我的心里我的歌声里 还记得我们曾经 肩并肩一起走过那段繁花巷口 尽管你我是陌生人是过路人 但彼此还是感觉到了 对方的一个眼神一个心跳 一种意想不到的快乐 好像是一场梦境命中注定 你存在我深深的脑海里 我的梦里我的心里我的歌声里 你存在我深深的脑海里 我的梦里我的心里我的歌声里 世界之大为何我们相遇 难道是缘分难道是天意 你存在我深深的脑海里 我的梦里我的心里我的歌声里 你存在我深深的脑海里 我的梦里我的心里我的歌声里 你存在我深深的脑海里 我的梦里我的心里我的歌声里 如水 期待过我们似细水 可惜蒸发出眼泪 明白你最近有些暂时伴侣偷一刻午睡彷佛专一使你极空虚 怀疑被你抱着我念着谁 无论你再好亦舍得失去 难过亦过难道我 嫌损失未够多
早放手可减轻痛楚 不等泡沫给吹破 不想去知谁填补我 无悔在我还是我 任你多么差错 无谓去追问为何 深知告别损失非我 让情人离别 似水清洗我 原谅你对着我说谎 出于好意的作状 明白你最近已经避谈近况 早不敢寄望 心中早把相爱如观光 情如瀑布泻下也未惊慌 心境已随着那水花得到释放 难过亦过难道我 嫌损失未够多 早放手可减轻痛楚 不等泡沫给吹破 不想去知谁填补我 无悔在我还是我 任你多么差错 无谓去追问为何 深知告别损失非我 让情人离别 似水清洗我 难过亦过难道我 嫌损失未够多 早放手可减轻痛楚 不等泡沫给吹破 不想去知谁填补我 无悔在我还是我 任你多么差错 无谓去追问为何 深知告别损失非我 让情人离别 似水清洗我 心中有涟漪吹过又回到最初平静去做我
各种单位换算及公式 长度单位面积单位 1 in = 25.4 mm 1 in 2 = 6.45 cm2 1 ft = 0.3048 m 1 ft2 = 0.09 3 m2 1 micron = 0.001 mm 体积单位 1 litre = 0.001 m3 1 cu.ft. = 0.0283 m3 1 cu.in. = 16.39 cm3 1 fluid oz.(imp) = 28.41 mL 1 fluid oz.(us) = 29.57 mL 1 gal(imp) = 4.546 L 1 gal(us) = 3.79 L 温度单位 (°F-32)X5/9=℃K-273.15 = ℃ 功及能量单位 1 Nm = 1 J 1 kgm = 9.807 J 1 kW/hr = 3.6 MJ 1 lbft = 1.356 J 功率单位 1 Nm/sec = 1 W 1 lbft/sec = 1.356 W 1 kgm/sec = 9.807 W 1 Joule/sec = 1 W 1 H.P.(imp) = 745.7 W 质量单位 1 lb = 453.6 g 1 tonne = 1000 kg 1 ton(imp) = 1016 kg 1 ton(us) = 907. 2 kg
流量计算公式 Q = Cv值X 984 = Kv值X 1100 Cv = So ÷ 18 力单位 1 kgf = 9.81 N 1 lbf = 4.45 N 1 kp(kilopound) = 9.81 N 1 poundal = 138.3 mN 1 ton force = 9.964 kM 力矩单位 1 kgm = 9.807 Nm 1 ft. poundal = 0.0421 Nm 1 in lb = 0.113 Nm 1 ft lb = 1.356 Nm 压力单位 1 psi = 6.89 kPa 1 kgf/cm 2 = 98.07 kPa 1 bar = 100 kPa 1 bar = 14.5 psi 1 mm mercury = 133.3 Pa 1 in mercury = 3.39 kPa 1 Torr = 133.3 Pa 1 ft water = 0.0298 bar 1 bar = 3.33 ft water 1 atmosphere = 101.3 kPa 1 cm water = 97.89 Pa 1 in water = 248.64 Pa 换算表 1psi=6.895kPa=0.07kg/cm2=0.06895bar=0.0703atm 1standard atmosphere=14.7psi=101.3kPa=1.01325bar 1kgf/cm2 = 98.07kPa=14.22psi = 28.96ins mercury 1m3 = 1000000cm3 1cu ft/min = 28.3 l/min
歌曲背景 "Hallelujah" is a song written by Canadian singer Leonard Cohen, originally released on his album Various Positions (1984). Achieving little initial success, the song found greater popular acclaim through a recording by John Cale, which inspired a recording by Jeff Buckley. It has been viewed as a "baseline" for secular hymns. "Hallelujah"为加拿大著名游吟诗人、民谣歌手Leonard Cohen在1985年创作的歌曲，收录在其专辑"Various Positions"中。其歌词充满诗意，内涵丰富，曲调缓慢忧伤，加上Leonard沧桑嗓音的低吟浅唱，演绎出了一种清淡而悠长的回味。 Hallelujah的版本很多，其中最有影响力的还是美国著名创作型歌手Jeff Buckley的翻唱版本，被收录在其1994年的专辑"Grace"中。Jeff被U2的Bono形容为“噪海中的纯净一滴”，他的声音明丽甜蜜又性感飘渺，诠释起悲伤和记忆来却更令人印象深刻。 中国歌手邓紫棋在现场演唱会上翻唱了本曲。 英文歌词 Now I've heard there was a secret chord 我曾听闻一曲传奇中的旋律 That David played, and it pleased the Lord 是大卫弹奏来取悦上帝的赞颂 But You don't really care for music, do You? 但祢真正喜悦的(是人的作为，而)不是音乐，对吧？ Well it goes like this 旋律是这样的 The fourth, the fifth F和弦，G和弦(复杂的心情无可言喻) The minor fall, the major lift 大小调起承转合(指戴维泣不成声的祷告颂唱，至五音不全) The baffled king composing Hallelujah
1A 1.Are You Sleeping? Are you sleeping? Are you sleeping? Brother John, Brother John? Morning bells are ringing, Morning bells are ringing. Ding, ding, dong! Ding, ding, dong! 2.Ten Little Indians One little, two little, three little Indians,
Four little, five little, six little Indians, Seven little, Eight little, Nine little Indians, Ten little Indian boys. One little, two little, three little Indians, Four little, five little, six little Indians, Seven little, Eight little, Nine little Indians, Ten little Indian girls. 3.Happy Birthday to You Happy birthday to you. Happy birthday to you. Happy birthday, dear friend. Happy birthday to you.
4.Hot Potato One potato, two potatoes, Three potatoes, four, Five potato, six potatoes, Seven potatoes, more. 5.Hot Cross Buns Hot cross buns! Hot cross buns! One a penny, two a penny. Hot cross buns! If you have no daughters, Give them to you sons!
歌名：As Long As You Love Me 歌手：Justin Bieber 所属专辑：Believe Acoustic 作曲 : Persson Svensson 作词 : Persson Svensson As long as you love me yeah 只要你爱我就好 I'm under pressure, seven billion people in the world trying to fit in 我们在压力下跟着全世界70亿人适应这个社会 Keep it together, smile on your face even though your heart is frowning 紧紧相依，你心有困懑却面带笑容 But hey now, you know girl, we both know it's a cruel world 但是现在，宝贝你知道，我们都知道世界多么残酷 But I will take my chances 但我愿意（搏一搏）抓住我的机会 As long as you love me, we could be starving, 只要你爱我，我们可以挨饿（饥肠辘辘） We could be homeless, we could be broke 可以流离失所，也可以支离破碎 As long as you love me I'll be your platinum, I'll be your silver, i'll be your gold 只要你爱我，我是你的铂金，我是你的银，我是你的财富（我会不离不弃，无坚不摧，所向披靡）
工程上常用的是兆帕（MPa）：1MPa=1000000Pa。 1个标准大气压力=1.00336×0.098MPa=0.10108MPa≈0.1Mpa。 1bar=0.1MPa 压力的法定单位是帕斯卡（Pa）：1Pa=1N/㎡（牛顿/平方米）。 压力单位换算： 1MPa=1000kPa 1kPa=10mbar=101.9716 mmH2O = 4.01463imH2O 10mWC＝1bar＝100kPa bar 巴= 0.987 大气压= 1.02 千克/平方厘米= 100 千帕= 14.5 磅/平方英寸 PSI英文全称为Pounds per square inch。P是磅pound，S是平方square，I是英寸inch。把所有的单位换成公制单位就可以算出：1bar≈14.5psi 1psi=6.895kPa=0.06895bar
1兆帕(MPa)=145磅/英寸2(psi)=10.2千克/厘米2(kg/cm2)=10巴(bar)=9.8大气压(atm) 1磅/英寸2(psi)=0.006895兆帕(MPa)=0.0703千克/厘米2(kg/cm2)=0.0689巴(bar)=0.068大气压(atm) 1巴(bar)=0.1兆帕(MPa)=14.503磅/英寸2(psi)=1.0197千克/厘米 2(kg/cm2)=0.987大气压(atm) 1大气压(atm)=0.101325兆帕(MPa)=14.696磅/英寸2(psi)=1.0333千克/厘米2(kg/cm2)=1.0133巴(bar) ------------------------------------------------------------------------------------- 压力单位换算方法 1. 1atm=0.1MPa=100KPa=1公斤=1bar=10米水柱＝14.5PSI 2.1KPa=0.01公斤 =0.01bar=10mbar=7.5mmHg=0.3inHg=7.5torr=100mmH2O=4inH2O 3. 1MPa=1N/mm2 14.5psi=0.1Mpa 1bar=0.1Mpa 30psi=0.21mpa,7bar=0.7mpa 现将单位的换算转摘如下： Bar---国际标准组织定义的压力单位。 1 bar=100,000Pa 1Pa=F/A, Pa: 压力单位, 1Pa=1 N/㎡ F : 力, 单位为牛顿(N) A: 面积, 单位为㎡ 1bar=100,000Pa=100Kpa 1 atm=101,325N/㎡=101,325Pa 所以,bar是一种表压力(gauge pressure)的称呼。
AWG 标准线径对照表 线径的粗细是以号数(xxAWG)来表示的，数目越小表示线径愈粗，所能承载的电流就越大，反之则线径越细，耐电流量越小。例如说：12号的耐电流量是20安培，最大承受功率是2200瓦，而18号线的耐电流量则是7安培，最大承受功率是770瓦。 为什么AWG号数越小直径反而越大？如这么解释你就会明白，固定的截面积下能塞相同的AWG线的数量，如11#AWG号数可塞11根而15#AWG号数可塞15根，自然的15#AWG的单位线径就较小。 美规线径值单一导体或群导体【各正值或负值】的线径值(Gauge)是以圆或平方厘米(mm2) 量测而得，平方厘米不常用在量测线径值，由于牵涉到不正确，因一般大部份的导体形体，包含长方形及其他怪异形状。因此我们拿全部的量测以圆平方厘米(c/m)为参考值 群导体计算的方法或公式： 加上单一导体的线径值总和，并比较上表求得。如果值落入两者之间，取比较少的值。 40股群导体线的线径值为，如每一芯为24 Guage = 40 x 405 c/m = 16，200 c/m = 9 AWG(得出值落入12960c/m和16440c/m之间) 快速求得线径值的方法： 两条(AWG)相加时，该单一线径值减3. ex. 2 x 18 AWG = (18-3=) 15 AWG 三条(AWG)相加时，该单一线径值减5. ex. 3 x 24 AWG = (24-5=) 19 AWG 四条(AWG)相加时，该单一线径值减6. ex. 4 x 10 AWG = (10-6=) 04 AWG 请记得“快速求得线径值的方法”一些案例也许边际会不正确，只采用此方式为大原则 AWG 标准线径规格对照表
各种单位换算及公式
各种单位换算及公式 长度单位面积单位 1 in = 25.4 mm 1 in 2 = 6.45 cm2 1 ft = 0.3048 m 1 ft 2 = 0.09 3 m2 1 micro n = 0.001 mm 体积单位 1 litre = 0.001 m3 1 cu.ft. = 0.0283 m3 1 cu.i n. = 16.39 cm3 1 fluid oz. (imp) = 28.41 mL 1 fluid oz. (us) = 29.57 mL 1 gal(imp) = 4.546 L 1 gal(us) = 3.79 L 温度单位 (°-32)X5/9= C K-273.15 = C 功及能量单位 1 Nm = 1 J 1 kgm = 9.807 J 1 kW/hr = 3.6 MJ 1 Ibft = 1.356 J 功率单位 1 Nm/sec = 1 W 1 lbft/sec = 1.356 W 1 kgm/sec = 9.807 W 1 Joule/sec = 1 W 1 H.P.(imp) = 745.7 W
质量单位 1 to nne = 1000 kg 1 lb = 453.6 g
流量计算公式 Q = Cv 值X 984 = Kv 值X 1100 Cv = So 48 力单位 1 kgf = 9.81 N 1 Ibf = 4.45 N 1 kp(kilopou nd) = 9.81 N 1 pou ndal = 138.3 mN 1 ton force = 9.964 kM 力矩单位 1 kgm = 9.807 Nm 1 ft. poun dal = 0.0421 Nm 1 in lb = 0.113 Nm 1 ft lb = 1.356 Nm 压力单位 1 psi = 6.89 kPa 1 kgf/cm 2 = 98.07 kPa 1 bar = 100 kPa 1 bar = 14.5 psi 1 mm mercury =133.3 Pa 1 in mercury =3.39 kPa 1 Torr = 133.3 Pa 1 ft water = 0.0298 bar 1 bar = 3.33 ft water 1 atmosphere = 101.3 kPa 1 cm water = 97.89 Pa 1 in water = 248.64 Pa 换算表 1psi=6.895kPa=0.07kg/cm2=0.06895bar=0.0703atm 1sta ndard atmosphere=14.7psi=101.3kPa=1.01325bar 1kgf/cm2 = 98.07kPa=14.22psi = 28.96i ns mercury 1m3 = 1000000cm3
1、《Mister Sun》 Oh Mister Sun, Sun, Mister Golden Sun, Please shine down on me. Oh Mister Sun, Sun,Mister Golden Sun, Hiding behind a tree… These little children ， Are asking you To please come out So we can play with you. Oh Mister Sun, Sun,Mister Golden Sun, Please shine down on me! Oh Mister Sun, Sun, Mister Golden Sun, Please shine down on me. Oh Mister Sun, Sun, Mister Golden Sun,Hiding behind a tree…These little children Are asking youTo please come out So we can play with you. Oh Mister Sun, Sun,Mister Golden Sun, Please shine down on,Please shine down on, Please shine down on me! 2、Mango Walk My brother did a tell me That you go mango walk You go mango walk(2×) My brother did a tell me That you go mango walk And pick all the numbe r ?leven 3、Mosquito Mosquito one, Mosquito two. Mosquito jump in the old man ,shoe Zzzzzzzz(clap the mosquito ) 4、Artist：harrybelafonte Songs Title：coconut woman （Coconuts, coconuts） （Coconuts, coconuts） Coconut woman is calling out And everyday you can hear her shout Coconut woman is calling out And everyday you can hear her shout Get your coconut water （Four for five） Man, it's good for your daughter （Four for five） Coco got a lotta iron （Four for five） Make you strong like a lion （Four for five） A lady tell me the other day No one can take her sweet man away I ask her what was the mystery She say coconut water and rice curry You can cook it in a pot （Four for five） You can serve it very hot （Four for five） Coco got a lotta iron （Four for five） Make you strong like a lion （Coconuts, coconuts） Coconut woman says you'll agree Coconut make very nice candy The thing that's best If you're feeling glum Is coconut water with a little rum It could make you very tipsy （Four for five） Make you feel like a gypsy （Four for five） Coco got a lotta iron （Four for five） Make you strong like a lion （Four for five） Ah, play that thing Coconut woman is calling out And everyday you can hear her shout Coconut woman is calling out And everyday you can hear her shout Get your coconut water （Four for five） Man, it's good for your daughter （Four for five） Get your coconut candy （Four for five） Make you feel very dandy （Four for five） Coco, coco, coco... Coconut, coconut Coconut, coconut... -
常用线规号码与线径对照表
线规SWG BWG BG AWG 号码英寸毫米英寸毫米英寸毫米英寸毫米 7／0 6／0 5／0 4／0 3／0 2／0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 0．500 0．464 0．432 0．400 0．372 0．348 0．324 0．300 0．276 0．252 0．232 0．212 0．192 0．176 0．160 0．144 0．128 0．116 0．104 0．092 0．080 0．072 0．064 0．056 0．048 0．040 0．036 0．032 0．0280 0．0240 0．0220 0．0200 0．0180 12．700 11．786 10．973 10．160 9．449 8．839 8．230 7．620 7．010 6．401 5．893 5．385 4．877 4．470 4．046 3．658 3．251 2．946 2．642 2．337 2．032 1．829 1．626 1．422 1．219 1．016 0．914 0．813 0．711 0．610 0．559 0．508 0．457 -- -- 0．500 0．454 0．425 0．330 0．340 0．300 0．284 0．259 0．238 0．220 0．203 0．180 0．165 0．148 0．134 0．120 0．109 0．095 0．083 0．072 0．065 0．058 0．049 0．042 0．035 0．032 0．028 0．025 0．022 0．020 0．018 -- -- 12．700 11．532 10．795 9．652 8．639 7．620 7．214 6．579 6．045 5．588 5．156 4．572 4．191 3．759 3．404 3．048 2．769 2．413 2．108 1．829 1．651 1．473 1．245 1．067 0．839 0．813 0．711 0．635 0．559 0．508 0．457 0．6666 0．6250 0．5883 0．5416 0．5000 0．1152 0．3954 0．3532 0．3147 0．2804 0．2500 0．2225 0．1981 0．1764 0．1570 0．1398 0．1250 0．1313 0．0991 0．0882 0．0785 0．0699 0．0625 0．0556 0．0495 0．0440 0．0392 0．0349 0．03125 0．02782 0．02476 0．02204 0．01961 16．932 15．875 14．943 13．757 12．700 11．308 10．069 8．971 7．993 7．122 6．350 5．652 5．032 4．481 3．988 3．551 3．175 2．827 2．517 2．240 1．994 1．775 1．588 1．412 1．257 1．118 0．996 0．887 0．794 0．707 0．629 0．560 0．498 -- 0．5800 0．5165 0．4600 0．4096 0．3648 0．3249 0．2893 0．2576 0．2294 0．2043 0．1819 0．1620 0．1443 0．1285 0．1144 0．1019 0．0907 0。0808 0．0720 0．0648 0．0571 0．0508 0．0453 0．0403 0．0359 0．0320 0．0285 0．02535 0．02010 0．01790 0．01594 0．01420 -- 14．732 13．119 11．684 10．404 9．266 8．252 7．348 6．544 5．827 5．189 4．621 4．115 3．665 3．264 2．906 2．588 2．305 2．053 1．828 1．628 1．450 1．291 1．150 1．024 0．912 0．812 0．723 0．644 0．573 0．511 0．455 0．405 常用线规号码与线径对照表
听的圣诞节英语歌曲 下面是一些圣诞节英文歌曲推荐！ 1、Everybody Knows I Love U 圣诞表白 2、Hallelujah-Alexandra Burke圣诞单曲销售冠军 3、圣诞必听英文歌曲John Lennon(Happy Christmas) 4、豌豆公主Kylie Minogue圣诞情调Santa Baby 5、小天后Taylor Swift演绎缤纷圣诞Last Christmas 6、NIKE最新圣诞广告歌曲完整版 7、Lady GaGa 欢乐圣诞单曲Christmas Tree 8、最畅销圣诞歌Mariah Carey(All I Want For Christmas Is You) 9、超人气童星Justin Bieber在奥巴马总统面前献唱圣诞歌曲 10、可爱童声贺圣诞When Christmas comes to town 欢乐合唱团相约快乐圣诞 Glee Cast - Last Christmas 美国福克斯电视台于2009年推出的热门青春音乐剧《欢乐合唱团》Glee盛邀剧中的男女主演们，包括Lea Michele, Amber Riley, Cory Monteith, Kevin McHale, Jenna Ushkowitz, Chris Colfer, Dianna Agron, Mark Salling等一席欢乐合唱团的团员们齐齐出动，为我们带来了这首欢快的经典翻唱"Last Christmas"。 绯闻女孩Queen B喊你回家过圣诞 Leighton Meester - Christmas "Christmas (Baby Please Come Home)"是Darlene Love于1963年发表的经典圣诞歌曲，后被乐队U2、乐坛天后Mariah Carey翻唱。
I've heard there was a secret chord That David played, and it pleased the Lord But you don't really care for music, do you? It goes like this The fourth, the fifth The minor fall, the major lift The baffled king composing Hallelujah Hallelujah, Hallelujah Hallelujah, Hallelujah Your faith was strong but you needed proof You saw her bathing on the roof Her beauty in the moonlight overthrew you She tied you to a kitchen chair She broke your throne, and she cut your hair And from your lips she drew the Hallelujah Hallelujah, Hallelujah Hallelujah, Hallelujah Baby I have been here before I know this room, I've walked this floor I used to live alone before I knew you. I've seen your flag on the marble arch Love is not a victory march It's a cold and it's a broken Hallelujah Hallelujah, Hallelujah Hallelujah, Hallelujah Maybe there’s a God above But all I’ve ever learned from love Was how to shoot at someone who outdrew you It’s not a cry you can hear at night It’s not somebody who has seen the light It’s a cold and it’s a broken Hallelujah Hallelujah, Hallelujah Hallelujah, Hallelujah I did my best, it wasn't much I couldn't feel, so I tried to touch I've told the truth, I didn't come to fool you And even though it all went wrong I'll stand before the Lord of Song With nothing on my tongue but Hallelujah
American Wire Gauge AWG mm2 42 0.003 1/0.06 41 0.004 1/0.07 40 0.005 1/0.08 38 0.008 1/0.10 36 0.013 1/0.127 34 0.020 1/0.16 7/0.06 32 0.032 1/0.203 7/0.08 8/0.07 11/0.06 30 0.051 1/0.26 7/0.10 11/0.08 14/0.07 19/0.06 28 0.081 1/0.32 7/0.12 11/0.10 16/0.08 21/0.07 28/0.06 26 0.129 1/0.40 7/0.16 9/0.14 11/0.12 16/0.10 25/0.08 33/0.07 45/0.06 24 0.205 1/0.50 7/0.20 14/0.14 19/0.12 26/0.10 41/0.08 53/0.07 73/0.06 22 0.326 1/0.65 7/0.26 11/0.203 13/0.18 17/0.16 22/0.14 29/0.12 42/0.10 65/0.08 20 0.518 1/0.80 7/0.30 10/0.26 12/0.23 16/0.203 20/0.18 26/0.16 34/0.14 46/0.12 66/0.10 18 0.823 1/1.02 7/0.40 10/0.32 16/0.26 20/0.23 26/0.203 33/0.18 41/0.16 54/0.14 73/0.12 65/0.127 104/0.10 16 1.309 1/1.29 7/0.50 11/0.40 17/0.32 25/0.26 32/0.23 41/0.203 52/0.18 65/0.16 85/0.14 119/0.12 165/0.10 14 2.081 1/1.63 11/0.50 17/0.40 26/0.32 40/0.26 50/0.23 65/0.203 82/0.18 103/0.16 135/0.14 183/0.12 264/0.10 12 3.309 1/2.05 17/0.50 27/0.40 41/0.32 54/0.28 80/0.23 102/0.203 130/0.18 164/0.16 10 5.261 1/2.60 27/0.50 42/0.40 65/0.32 99/0.26 126/0.23 162/0.203 206/0.18 261/0.16 8 8.366 1/3.26 26/0.65 67/0.40 104/0.32 157/0.26 6 13.30 1/4.12 27/0.80 40/0.65 68/0.50 105/0.40 165/0.32 4 21.1 5 1/5.20 26/1.02 42/0.80 64/0.65 107/0.50 168/0.40 2 33.6 3 1/6.54 4 26/1.29 42/1.02 67/0.80 101/0.6 5 171/0.50 0 53.48 1/8.254 26/1.63 41/1.29 66/1.02 106/0.80 161/0.65 1. 基准线规直径：直径5 mil（0.005 inch）为36 AWG： 2. 相邻线号之间以几何级数计算：见右框图中公式。 例如：d18 = d36 × r (36-18) = 5 × 8.06053 = 40.3mils = 1.024mm d n = d 36× r (36 - n)( mil ) = 0.127 r(36 - n)( mm ) 其中，r = (460/5) 1/39 = 1.1229322
Gauge 板材換算
钢材理论重量计算 钢材理论重量计算的计量单位为公斤（kg ）。其基本公式为： 钢的密度为：7.85g/cm3 ，各种钢材理论重量计算公式如下： 圆钢盘条（kg/m）W= 0.006165 ×d×d d = 直径mm 直径100 mm 的圆钢，求每m 重量。每m 重量= 0.006165 ×1002=61.65kg 螺纹钢（kg/m）W= 0.00617 ×d×d d= 断面直径mm 断面直径为12 mm 的螺纹钢，求每m 重量。每m 重量=0.00617 ×12 2=0.89kg 等边角钢（kg/m）= 0.00785 ×[d （2b – d ）+0.215 （R2 –2r 2 ）] b= 边宽 d= 边厚R= 内弧半径r= 端弧半径求20 mm ×4mm 等边角钢的每m 重量。从冶金产品目录中查出4mm ×20 mm 等边角钢的R 为3.5 ，r 为1.2 ，则每m 重量= 0.00785 ×[4 ×（2 ×20 – 4 ）+0.215 ×（3.52 – 2 ×1.2 2 ）]=1.15kg 不等边角钢（kg/m）W= 0.00785 ×[d （B+b –d ）+0.215 （R2 – 2 r 2 ）] B= 长边宽 b= 短边宽d= 边厚R= 内弧半径r= 端弧半径求30 mm ×20mm ×4mm 不等边角钢的每m 重量。从冶金产品目录中查出30 ×20 ×4 不等边角钢的R 为3.5 ，r 为1.2 ，则每m 重量= 0.00785 ×[4 ×（30+20 –4 ）+0.215 ×（3.52 –2 ×1.2 2 ）]=1.46kg 钢板（kg/m2）W= 7.85 ×d d= 厚厚度4mm 的钢板，求每m2 重量。每m2 重量=7.85 ×4=31.4kg 钢管（包括无缝钢管及焊接钢管（kg/m）W= 0.02466 ×S （D –S ）D= 外径 S= 壁厚外径为60 mm 壁厚4mm 的无缝钢管，求每m 重量。每m 重量= 0.02466 ×4 ×（60 –4 ）=5.52kg
线规SWG BWG BG AWG 号码英寸毫米英寸毫米英寸毫米英寸毫米 7／0 6／0 5／0 4／0 3／0 2／0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 0．500 0．464 0．432 0．400 0．372 0．348 0．324 0．300 0．276 0．252 0．232 0．212 0．192 0．176 0．160 0．144 0．128 0．116 0．104 0．092 0．080 0．072 0．064 0．056 0．048 0．040 0．036 0．032 0．0280 0．0240 0．0220 0．0200 0．0180 12．700 11．786 10．973 10．160 9．449 8．839 8．230 7．620 7．010 6．401 5．893 5．385 4．877 4．470 4．046 3．658 3．251 2．946 2．642 2．337 2．032 1．829 1．626 1．422 1．219 1．016 0．914 0．813 0．711 0．610 0．559 0．508 0．457 -- -- 0．500 0．454 0．425 0．330 0．340 0．300 0．284 0．259 0．238 0．220 0．203 0．180 0．165 0．148 0．134 0．120 0．109 0．095 0．083 0．072 0．065 0．058 0．049 0．042 0．035 0．032 0．028 0．025 0．022 0．020 0．018 -- -- 12．700 11．532 10．795 9．652 8．639 7．620 7．214 6．579 6．045 5．588 5．156 4．572 4．191 3．759 3．404 3．048 2．769 2．413 2．108 1．829 1．651 1．473 1．245 1．067 0．839 0．813 0．711 0．635 0．559 0．508 0．457 0．6666 0．6250 0．5883 0．5416 0．5000 0．1152 0．3954 0．3532 0．3147 0．2804 0．2500 0．2225 0．1981 0．1764 0．1570 0．1398 0．1250 0．1313 0．0991 0．0882 0．0785 0．0699 0．0625 0．0556 0．0495 0．0440 0．0392 0．0349 0．03125 0．02782 0．02476 0．02204 0．01961 16．932 15．875 14．943 13．757 12．700 11．308 10．069 8．971 7．993 7．122 6．350 5．652 5．032 4．481 3．988 3．551 3．175 2．827 2．517 2．240 1．994 1．775 1．588 1．412 1．257 1．118 0．996 0．887 0．794 0．707 0．629 0．560 0．498 -- 0．5800 0．5165 0．4600 0．4096 0．3648 0．3249 0．2893 0．2576 0．2294 0．2043 0．1819 0．1620 0．1443 0．1285 0．1144 0．1019 0．0907 0。0808 0．0720 0．0648 0．0571 0．0508 0．0453 0．0403 0．0359 0．0320 0．0285 0．02535 0．02010 0．01790 0．01594 0．01420 -- 14．732 13．119 11．684 10．404 9．266 8．252 7．348 6．544 5．827 5．189 4．621 4．115 3．665 3．264 2．906 2．588 2．305 2．053 1．828 1．628 1．450 1．291 1．150 1．024 0．912 0．812 0．723 0．644 0．573 0．511 0．455 0．405 常用线规号码与线径对照表