volume

• n.

• 容積、体積、量、ボリューム、(書籍の)巻

関

amount、bulk、content、quantity

　 　 　 　 　

WordNet

1. a relative amount; "mix one volume of the solution with ten volumes of water"
2. the amount of 3-dimensional space occupied by an object; "the gas expanded to twice its original volume"
3. the magnitude of sound (usually in a specified direction); "the kids played their music at full volume" (同)loudness, intensity
4. a publication that is one of a set of several similar publications; "the third volume was missing"; "he asked for the 1989 volume of the Annual Review"
5. satisfy in a limited way; "He contented himself with one glass of beer per day"
6. the proportion of a substance that is contained in a mixture or alloy etc.
7. the sum or range of what has been perceived, discovered, or learned (同)cognitive content, mental object
8. everything that is included in a collection and that is held or included in something; "he emptied the contents of his pockets"; "the two groups were similar in content"
9. make content; "I am contented"
10. stick out or up; "The parcel bulked in the sack"
11. the property of something that is great in magnitude; "it is cheaper to buy it in bulk"; "he received a mass of correspondence"; "the volume of exports" (同)mass, volume
12. the property possessed by a large mass
13. the relative magnitude of something with reference to a criterion; "an adequate amount of food for four people"
14. be tantamount or equivalent to; "Her action amounted to a rebellion"
15. an adequate or large amount; "he had a quantity of ammunition"
16. the concept that something has a magnitude and can be represented in mathematical expressions by a constant or a variable
17. furnished with volumes; "a large room volumed with ancient books"
18. (often used in combination) consisting of or having a given number or kind of volumes; "the poets volumed works"; "a two-volumed history"; "multi-volumed encyclopedias"; "large-volumed editions"
19. formed or rising in rounded masses; "gasping with the volumed smoke"

PrepTutorEJDIC

1. 〈C〉(特に分厚い)『本』,書物 / 〈C〉(シリーズものの)『巻』,冊(《略》(単数形で)vol.,(複数形で)vols.) / 〈U〉(…の)『体積』,容積《+of+名》 / 〈U〉〈C〉)…の)『量』,かさ《+of+名》 / 〈U〉(…の)『音量』,音の強さ,ボリューム《+of+名》 / 《複数形で》多量(の…),たくさん(の…)《+of+名》
2. 〈C〉《複数形で》(容器などにはいっている)『中身』,内容物,(記録・書物などの)目次 / 〈U〉(書物・演説などの)趣旨 / 〈C〉《~》《修飾語を伴って》含有量,(容器の)容量
3. 『満足して』,甘んじて / 満足 / (…で)…'を'『満足させる』《+名+『with』+『名』》
4. 『かさばっていること』 / 《the bulk》(…の)大部分,大半《+『of』+『名』》 / ばら荷;(船の)積み荷 / かさばる,大きく見える
5. 〈計算・金額が〉『総計』(…に)『なる』,(…に)のぼる《+『to』+『名』》 / 〈事が〉結局(…に)なる,(…に)等しい《+『to』+『名』》 / 〈U〉《the ~》『総計』,総額,総数(sum) / (ある)『量』,額 / 〈U〉真意;要旨
6. 〈U〉『量』 / 〈C〉(…の)『量』,数,額,高《+『of』+『名』》 / 〈C〉『多量』,多数 / 〈C〉(数学で)量,数量

Wikipedia preview

出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2016/05/27 06:19:46」(JST)

wiki en

[Wiki en表示]

For other uses, see Volume (disambiguation).

A measuring cup can be used to measure volumes of liquids. This cup measures volume in units of cups, fluid ounces, and millilitres.

Volume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains. Volume is often quantified numerically using the SI derived unit, the cubic metre. The volume of a container is generally understood to be the capacity of the container, i. e. the amount of fluid (gas or liquid) that the container could hold, rather than the amount of space the container itself displaces.

Three dimensional mathematical shapes are also assigned volumes. Volumes of some simple shapes, such as regular, straight-edged, and circular shapes can be easily calculated using arithmetic formulas. Volumes of a complicated shape can be calculated by integral calculus if a formula exists for the shape's boundary. Where a variance in shape and volume occurs, such as those that exist between different human beings, these can be calculated using three-dimensional techniques such as the Body Volume Index. One-dimensional figures (such as lines) and two-dimensional shapes (such as squares) are assigned zero volume in the three-dimensional space.

The volume of a solid (whether regularly or irregularly shaped) can be determined by fluid displacement. Displacement of liquid can also be used to determine the volume of a gas. The combined volume of two substances is usually greater than the volume of one of the substances. However, sometimes one substance dissolves in the other and the combined volume is not additive.

In differential geometry, volume is expressed by means of the volume form, and is an important global Riemannian invariant. In thermodynamics, volume is a fundamental parameter, and is a conjugate variable to pressure.

Units

Volume measurements from the 1914 The New Student's Reference Work.
Approximate conversion to millilitres:

	Imperial	U.S. liquid	U.S. dry
Gill	142 mL	118 mL	138 mL
Pint	568 mL	473 mL	551 mL
Quart	1137 mL	946 mL	1101 mL
Gallon	4546 mL	3785 mL	4405 mL

Any unit of length gives a corresponding unit of volume, namely the volume of a cube whose side has the given length. For example, a cubic centimetre (cm³) would be the volume of a cube whose sides are one centimetre (1 cm) in length.

In the International System of Units (SI), the standard unit of volume is the cubic metre (m³). The metric system also includes the litre (L) as a unit of volume, where one litre is the volume of a 10-centimetre cube. Thus

1 litre = (10 cm)³ = 1000 cubic centimetres = 0.001 cubic metres,

so

1 cubic metre = 1000 litres.

Small amounts of liquid are often measured in millilitres, where

1 millilitre = 0.001 litres = 1 cubic centimetre.

Various other traditional units of volume are also in use, including the cubic inch, the cubic foot, the cubic mile, the teaspoon, the tablespoon, the fluid ounce, the fluid dram, the gill, the pint, the quart, the gallon, the minim, the barrel, the cord, the peck, the bushel, and the hogshead.

Related terms

Capacity is defined by the Oxford English Dictionary as "the measure applied to the content of a vessel, and to liquids, grain, or the like, which take the shape of that which holds them". (The word capacity has other unrelated meanings, as in e.g. capacity management.) Capacity is not identical in meaning to volume, though closely related; the capacity of a container is always the volume in its interior. Units of capacity are the SI litre and its derived units, and Imperial units such as gill, pint, gallon, and others. Units of volume are the cubes of units of length. In SI the units of volume and capacity are closely related: one litre is exactly 1 cubic decimetre, the capacity of a cube with a 10 cm side. In other systems the conversion is not trivial; the capacity of a vehicle's fuel tank is rarely stated in cubic feet, for example, but in gallons (a gallon fills a volume of 0.1605 cu ft).

The density of an object is defined as the ratio of the mass to the volume. The inverse of density is specific volume which is defined as volume divided by mass. Specific volume is a concept important in thermodynamics where the volume of a working fluid is often an important parameter of a system being studied.

The volumetric flow rate in fluid dynamics is the volume of fluid which passes through a given surface per unit time (for example cubic meters per second [m³ s⁻¹]).

Volume in calculus

Further information: Volume element

In calculus, a branch of mathematics, the volume of a region D in R³ is given by a triple integral of the constant function and is usually written as:

The volume integral in cylindrical coordinates is

and the volume integral in spherical coordinates (using the convention for angles with as the azimuth and measured from the polar axis (see more on conventions)) has the form

Volume formulas

Shape	Volume formula	Variables
Cube		a = length of any side (or edge)
Cylinder		r = radius of circular face, h = height
Prism		B = area of the base, h = height
Rectangular prism		l = length, w = width, h = height
Triangular prism		b = base length of triangle, h = height of triangle, l = length of prism or distance between the triangular bases
Sphere		r = radius of sphere which is the integral of the surface area of a sphere
Ellipsoid		a, b, c = semi-axes of ellipsoid
Torus		r = minor radius (radius of the tube), R = major radius (distance from center of tube to center of torus)
Pyramid		B = area of the base, h = height of pyramid
Square pyramid		s = side length of base, h = height
Rectangular pyramid		l = length, w = width, h = height
Cone		r = radius of circle at base, h = distance from base to tip or height
Tetrahedron		edge length
Parallelepiped	$<p>a b c \sqrt{K}$ $\begin{align} K =& 1+2\cos(\alpha)\cos(\beta)\cos(\gamma) \\ & - \cos^2(\alpha)-\cos^2(\beta)-\cos^2(\gamma) \end{align}$	a, b, and c are the parallelepiped edge lengths, and α, β, and γ are the internal angles between the edges
Any volumetric sweep (calculus required)		h = any dimension of the figure, A(h) = area of the cross-sections perpendicular to h described as a function of the position along h. a and b are the limits of integration for the volumetric sweep. (This will work for any figure if its cross-sectional area can be determined from h).
Any rotated figure (washer method) (calculus required)		and are functions expressing the outer and inner radii of the function, respectively.

Volume ratios for a cone, sphere and cylinder of the same radius and height

A cone, sphere and cylinder of radius r and height h

The above formulas can be used to show that the volumes of a cone, sphere and cylinder of the same radius and height are in the ratio 1 : 2 : 3, as follows.

Let the radius be r and the height be h (which is 2r for the sphere), then the volume of cone is

the volume of the sphere is

while the volume of the cylinder is

The discovery of the 2 : 3 ratio of the volumes of the sphere and cylinder is credited to Archimedes.

Volume formula derivations

Sphere

The volume of a sphere is the integral of an infinite number of infinitesimally small circular disks of thickness dx. The calculation for the volume of a sphere with center 0 and radius r is as follows.

The surface area of the circular disk is .

The radius of the circular disks, defined such that the x-axis cuts perpendicularly through them, is

or

where y or z can be taken to represent the radius of a disk at a particular x value.

Using y as the disk radius, the volume of the sphere can be calculated as

Now

Combining yields

This formula can be derived more quickly using the formula for the sphere's surface area, which is . The volume of the sphere consists of layers of infinitesimally thin spherical shells, and the sphere volume is equal to

=

Cone

The cone is a type of pyramidal shape. The fundamental equation for pyramids, one-third times base times altitude, applies to cones as well.

However, using calculus, the volume of a cone is the integral of an infinite number of infinitesimally thin circular disks of thickness dx. The calculation for the volume of a cone of height h, whose base is centered at (0,0,0) with radius r, is as follows.

The radius of each circular disk is r if x = 0 and 0 if x = h, and varying linearly in between—that is,

The surface area of the circular disk is then

The volume of the cone can then be calculated as

and after extraction of the constants:

Integrating gives us

Volume in differential geometry

Main article: Volume form

In differential geometry, a branch of mathematics, a volume form on a differentiable manifold is a differential form of top degree (i.e. whose degree is equal to the dimension of the manifold) that is nowhere equal to zero. A manifold has a volume form if and only if it is orientable. An orientable manifold has infinitely many volume forms, since multiplying a volume form by a non-vanishing function yields another volume form. On non-orientable manifolds, one may instead define the weaker notion of a density. Integrating the volume form gives the volume of the manifold according to that form.

Any oriented Riemannian (or pseudo-Riemannian) manifold has a natural volume (or pseudo volume) form. In local coordinates, it can be expressed as

where the are the 1-forms providing an oriented basis for the cotangent bundle of the n-dimensional manifold. Here, is the absolute value of the determinant of the matrix representation of the metric tensor on the manifold.

Volume in thermodynamics

Main article: Volume (thermodynamics)

In thermodynamics, the volume of a system is an important extensive parameter for describing its thermodynamic state. The specific volume, an intensive property, is the system's volume per unit of mass. Volume is a function of state and is interdependent with other thermodynamic properties such as pressure and temperature. For example, volume is related to the pressure and temperature of an ideal gas by the ideal gas law.

See also

• Area
• Banach–Tarski paradox
• Conversion of units
• Dimensional weight
• Dimensioning
• Length
• Mass
• Measure
• Orders of magnitude (volume)
• Perimeter
• Surface
• Volume (thermodynamics)
• Weight
• Volumography

References

External links

UpToDate Contents

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English Journal

• A computational study of systemic hydration in vocal fold collision.

• Bhattacharya P1, Siegmund T.
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• Mechanical stresses develop within vocal fold (VF) soft tissues due to phonation-associated vibration and collision. These stresses in turn affect the hydration of VF tissue and thus influence voice health. In this paper, high-fidelity numerical computations are described, taking into account fully
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• Effect of exercise on blood flow through the aortic valve: a combined clinical and numerical study.

• Bahraseman HG1, Hassani K, Navidbakhsh M, Espino DM, Sani ZA, Fatouraee N.
• Computer methods in biomechanics and biomedical engineering.Comput Methods Biomech Biomed Engin.2014 Dec;17(16):1821-34. doi: 10.1080/10255842.2013.771179. Epub 2013 Mar 26.
• The aim of this study was to measure the cardiac output and stroke volume for a healthy subject by coupling an echocardiogram Doppler (echo-Doppler) method with a fluid-structure interaction (FSI) simulation at rest and during exercise. Blood flow through aortic valve was measured by Doppler flow ec
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• Barkaoui A1, Hambli R.
• Computer methods in biomechanics and biomedical engineering.Comput Methods Biomech Biomed Engin.2014 Nov;17(14):1590-601. doi: 10.1080/10255842.2012.758255. Epub 2013 Feb 25.
• Hierarchical structures in bio-composites such as bone tissue have many scales or levels and synergic interactions between the different levels. They also have a highly complex architecture in order to fulfil their biological and mechanical functions. In this study, a new three-dimensional (3D) mode
• PMID 23439084

Japanese Journal

• Bumpy Pyramid Folding Problem

• ZacharyR.Abel ,ErikD.Demaine ,MartinL.Demaine ,Hiro Ito,Jack Snoeyink,Ryuhei Uehara
• 情報処理学会研究報告. AL, アルゴリズム研究会報告 2013-AL-145(19), 1-7, 2013-10-30
• … We also show a polynomial time algorithm that finds the crease pattern to produce the maximum volume bumpy pyramid. …
• NAID 110009614899

• Comparison between the electrokinetic properties of kaolinite and montmorillonite suspensions at different volume fractions

• Tsujimoto Y.,Chassagne C.,Adachi Y.,辻本 陽子,足立 泰久
• Journal of colloid and interface science 407, 109-115, 2013-10-00
• … The dielectric permittivity of kaolinite suspensions is linearly proportional to volume fraction up to volume fractions of 20%, whereas that of montmorillonite is deviating from a linear relationship, for volume fractions below 0.5%. … This indicates that the montmorillonite particles experience a particle–particle interaction at these low volume fractions. …
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• Fan Yanan,Chen Guangqi,Kasama Kiyonobu,Li Yange,笠間 清伸,カサマ キヨノブ
• Memoirs of the Faculty of Engineering, Kyushu University 73(2), 57-70, 2013-09-26
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Related Pictures

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★リンクテーブル★

リンク元	「100Cases 34」「content」「bulk」「体積」「量」
拡張検索	「minute volume」

「100Cases 34」

　　[★]

☆case34　てんかん発作

■症例

23歳　アフリカ-カリブ系　女性　銀行の店員

主訴：てんかん発作

現病歴：強直間代発作を2回起こしたところを母親が目撃していた。娘の行動は次第におかしくなり、また娘は自分のことを話している声が聞こえていた(幻聴)。最近、頭痛を訴えていた。体重が減少し、脱毛があった。盗汗と主に足と手の小関節に及ぶflitting 関節痛を訴えていた。服用薬なし。タバコ1日5-10本、アルコール10 unit/week(缶ビール(350ml)6本弱)

既往歴：特記なし(medical or psychiatric history)

家族歴：

生活歴：

・身体診断

意識：眠そうだが痛みに反応。頚部硬直：なし。頭髪：薄く斑状。体温38.5℃。リンパ節：たくさんの部位で触知。

心拍：104/分、整。血圧：164/102 mmHg。心血管系、呼吸器系、腹部：異常なし。

神経所見：focal anormalityなし(局所性異常)。乳頭浮腫：認めず。

・検査

(血液生化学)

上昇：erythrocyte sedimentation rate、urea、creatinine

低下：hemoglobin、white cell count、platelet

正常：mean corpuscular volume、sodium、potassium、glucose

(腰椎穿刺)

上昇：leukocytes、CSF protein

正常：CSF glucose

(尿検査)

蛋白：＋＋＋。血尿：＋＋＋。赤血球：＋＋。赤血球円柱：あり。

(その他)

胸部X線：異常なし。ECG：洞性頻脈。頭部CT：正常。CSFグラム染色：陰性(光顕レベルで細菌なし)

■glossary

fall out　(毛髪などが)抜ける

night sweat 盗汗、寝汗

tonic-clonic generalized seizure 全般性強直間代発作

flit　vi (鳥・蝶など)すいすい/ひらひら飛ぶ、飛び回る、飛翔する。(人が)軽やかに通る、行き交う。(時が)(飛ぶように)すぎる。(幻想など)去来する、よぎる、(表情が)かすめる

drowsy　adj. 眠い。眠そうな。眠気を誘う。ものうい。眠ったような

stiffness　n. 堅いこと、堅ぐるしさ、がんこさ

delirium tremens 振戦譫妄

hypertensive encephalopathy 高血圧性脳症

alopecia　脱毛症

African-Caribbean アフリカ-カリブ系

fit n.　(病気の)発作。引きつけ、痙攣。(感情の)激発、一時的興奮、気まぐれ

chorea n. 舞踏病

recreational drug 耽溺性があり乱用される脱法薬物

urgent adj. (物・事が)急を要する、緊急の、背拍質(pressing)。(～を)緊急に必要とする(in)。(S is ～ (with O1) for [in] O2)(人が)(O1(人)に)O2(物・事)をしつこく求める。(人に/～するように)催促する(for/to do)。(要求などが)執拗な。

□てんかん発作

・新規発生したてんかん発作の原因(ICU.805-806)

・薬物中毒(テオフィリンなど)

・薬物からの離脱(アルコールなど)

・感染症(髄膜炎、膿瘍など)

・頭部外傷

・虚血障害(虚血あるいはびまん性)

・占拠性病変(腫瘍あるいは血腫)

・代謝性障害(肝性脳症、尿毒症性脳症、敗血症、低血糖、低ナトリウム血症、低カルシウム血症など)

・合併症(ICU.805-806)

・全身性てんかん発作の場合：高血圧、乳酸アシドーシス、高体温、呼吸障害、誤嚥、肺水腫、横紋筋融解、自傷、不可逆性の神経学的障害(30分間以上てんかん発作が持続した場合)

■可能性の高い診断

　全身性エリテマトーデス systemic lupus erythematosus(SLE)

■鑑別診断のポイント

　自己免疫疾患は多彩な症状を示す。そのため、個々の症状に着目して鑑別診断をあげるのではなく、症状や検査値の異常を総合的に見て判断する必要がある。

■解答

　(第1パラグラフ)SLEの病態

精神症状：(SLEは脳で血管炎を呈することで生じる)うつ(depression)、統合失調症様の精神病、痙攣(fits)、舞踏病(chorea)、脳梗塞/脊髄梗塞

脳脊髄液：白血球増多(leukopenia)、蛋白増加

血液：自己免疫性溶血貧血(Coombs'-positive hemolytic anemia)がありうる。白血球減少と血小板減少症は普通にみられる。

腎症状：ループス腎炎は普通に見られ、顕微鏡的血尿・タンパク尿、ネフローゼ、あるいは腎不全が現れるかもしれない。

関節症状：変形を伴わない関節痛(PIP関節(近位指節間関節)、MP関節(中手指節関節)、手関節)

　(第2パラグラフ)SLEの確定診断のための検査・治療

　・すぐにすべきことは降圧薬、抗痙攣薬の投与

　・確定診断のために次の検査を行っていく(もっとも、症例の提示された所見で(日本の？)SLEの診断基準を満たすけど)

　　・検疫血清検査：抗DNA抗体、C3、C4

　　・腎生検：ループス腎炎の程度を把握

　・治療：活動性の感染がないことを確認　←　薬物療法ではステロイドや免疫抑制薬を使うため

　　・ステロイド静脈内投与、あるいはシクロホスファミドなどの細胞毒性薬(cytotoxic agents)の投与

　　・重症、治療抵抗性だったら血漿交換を行う。

■鑑別診断　頭痛/精神病的様態(psychiatric features)/痙攣

・髄膜炎、脳炎

・レクリエーショナルドラッグの中毒(例えばコカイン)

・脳腫瘍

・急性のアルコール禁断症状：振戦譫妄

・高血圧脳症

■KEYPOINT

・SLEは特に若いアフリカ系-カリブ系に普通に一般的

・SLEでは主に神経症状と精神症状をを伴って現れることがある

・白血球低下と血小板の低下はしばしばSLEを示唆する

□tonic-clonic seizure 強直間代発作

　意識消失とともに全身の随意筋に強直痙攣が生じ(強直痙攣期tonic convulsion)、次いで全身の筋の強直と弛緩とが律動的に繰り返される時期(間代痙攣期clonic convulsion)を経て、発作後もうろう状態を呈する一連の発作。

□350ml アルコール5%

350x0.05/10=1.75 unit

□細胞毒性薬

　免疫抑制薬や抗腫瘍薬として用いられる。

antimetabolites

アザチオプリン azathioprine

メトトレキセート methotrexate

ミコフェノール酸 mycophenolic acid, ミコフェノール酸モフェチル mycophenolate mofetil

レフルノミド leflunomide

alkylating agents

シクロホスファミド cyclophosphamide

「content」

　　[★]

• n.

• 内容、内容物、量、含有量、含量

関

amount, quantity, volume

---

(ラテン語 continereの過去分詞 contentus(中身が満たされた。conainの過去分詞に相当する語)

• adj.[叙述的]

• (～に)(ほどほどのところで)満足して、甘んじて(with)。(～と言うことに)安心する(that節)(⇔discontent)
• (be ～ to do)喜んで～する(willing)。(～であることに)満足する、甘んじる(that節)

• n.

• 満足

• vt.

• (事・人が)(人)を'(～で)満足させる

(～ oneself)(不十分な物・事で)満足する(with (doing)) 　 　 　 　 　 　 　

「bulk」

　　[★]

• n.

• バルク、容積、大量、大部分、(医薬品などの)原体、原末

関

a large fraction of、abundance、abundant、abundantly、copious、drug substance、large amount、large dose、large proportion、large scale、majority、massive、massively、profuse、technical product、volume

　 　 　 　

「体積」

　　[★]

英

volume

• 時々、ど忘れするので、メモ

103 L = 1 m3
1 L = 103 cm3
10-3 L = 1 mL = 1 cm3
10-6 L = 1 μL = 1 mm3

関

巻、容積、量、ボリューム

「量」

　　[★]

英

amount、volume、content、quantity

関

巻、含有量、含量、体積、達する、容積、内容物、内容、ボリューム

「minute volume」

　　[★]

• 分時換気量、毎分換気量、毎分呼吸量

関

respiratory minute volume