See also:

• HYDRAULICS (Gr. iS&,p, water, and ai,Xos, a pipe)

HYDRAULICS (Gr. iS&,p, See also:

• WATER

water, and ai,Xos, a See also:

• PIPE

pipe)  , the See also:

• BRANCH (from the Fr. branche, late Lat. branca, an animal's paw)

branch of See also:

• ENGINEERING

engineering See also:

• SCIENCE (Lat. scientia, from scire; to learn, know)

science which deals with the See also:

• PRACTICAL

practical applications of the See also:

• LAWS

laws of See also:

• HYDROMECHANICS (Gr. ubpops avuca)

hydromechanics . I . THE DATA OF See also:

• HYDRAULICS (Gr. iS&,p, water, and ai,Xos, a pipe)

HYDRAULICS' § r . Properties of Fluids.—The fluids to which the laws of practical hydraulics relate are substances the parts of which possess very See also:

• GREAT

great mobility, or which offer a very small resistance to distortion independently of inertia . Under the See also:

• GENERAL
• GENERAL (Lat. generalis, of or relating to a genus, kind or class)

general heading Hydromechanics a fluid is defined to be a substance which yields continually to the slightest tangential stress, and hence in a fluid at See also:

• REST (O. Eng. rest, reste, bed, cognate with other Teutonic forms, e.g. Ger. Rast, Riiste, rest, and probably Gothic Rasta, league, i.e. resting or stopping place)

rest there can be no tangential stress . But, further, in fluids such as See also:

• WATER

water, See also:

• AIR (from an Indo-European root meaning " breathe," " blow ")
• AIR, or ASBEN

air, See also:

• STEAM
• STEAM (0. Eng. steam, vapour, smoke, cf. Du. steam; the origin is unknown)

steam, &c., to which the See also:

• PRESENT

present See also:

• DIVISION (from Lat. dividere, to break up into parts, separate)

division of the See also:

• ARTICLE (from Lat. articulus, a joint)

article relates, the tangential stresses that are called into See also:

• ACTION

action between contiguous portions during distortion or See also:

• CHANGE (derived through the Fr. from the Late Lat. cambium, cambiare, to barter; the ultimate derivation is probably from the root which appears in the Gr. «a urmu', to bend)

change of figure are always small compared with the See also:

• WEIGHT

weight, inertia, pressure, &c., which produce the visible motions it is the See also:

• OBJECT

object of hydraulics to estimate . On the other See also:

• HAND
• HAND (a word common to Teutonic languages; cf. Ger. Hand, Goth. handus)
• HAND, FERDINAND GOTTHELF (1786-185r)

hand, while a fluid passes easily from one See also:

• FORM (Lat. forma)

form to another, it opposes considerable resistance to change of See also:

• VOLUME

volume . It is easily deduced from the See also:

• ABSENCE (Lat. absentia)

absence or smallness of the tangential stress that contiguous portions of fluid See also:

• ACT (Lat. actus, actum)

act on each other with a pressure which is exactly or very nearly normal to the interface which separates them . The stress must be a pressure, not a tension, or the parts would See also:

• SEPARATE

separate . Further, at any point in a fluid the pressure in all directions must be the same; or, in other words, the pressure on any small See also:

• ELEMENT (Lat. elementum)

element of See also:

• SURFACE

surface is See also:

• INDEPENDENT

independent of the See also:

• ORIENTATION

orientation of the surface . § 2 . Fluids are divided into liquids, or incompressible fluids, and gases, or compressible fluids .

Very great changes of pressure change the volume of liquids only by a small amount, and if the pressure on them is reduced to zero they do not sensibly dilate . In gases or compressible fluids the volume alters sensibly for small changes of pressure, and if the pressure is indefinitely diminished they dilate without limit . In See also:

• ORDINARY (med. Lat. ordinarius, Fr. ordinaire)

ordinary hydraulics, liquids are treated as absolutely incompressible . In dealing with gases the changes of volume which accompany changes of pressure must be taken into, See also:

• ACCOUNT
• ACCOUNT (through O. Fr. acont, Late Lat. comptum, cornputare, to calculate)

account . § 3 . Viscous fluids are those in which change of form under a continued stress proceeds gradually and increases indefinitely . A very viscous fluid opposes great resistance to change of form in a See also:

• SHORT, FRANCIS JOB (1857– )

short See also:

• TIME (0. Eng. Lima, cf. Icel. timi, Swed. timme, hour, Dan. time; from the root also seen in " tide," properly the time of between the flow and ebb of the sea, cf. O. Eng. getidan, to happen, " even-tide," &c.; it is not directly related to Lat. tempus)
• TIME, MEASUREMENT OF
• TIME, STANDARD

time, and yet may be deformed considerably by a small stress acting for a See also:

• LONG, GEORGE (1800-1879)
• LONG, JOHN DAVIS (1838– )

long See also:

• PERIOD
• PERIOD (Gr. irepioSos, a going or way round, circuit, aepi, round, and &Sis, way, road)

period . A See also:

• BLOCK
• BLOCK (from the Fr. bloc, and possibly connected with an Old Ger. Block, obstruction, cf. " baulk ")
• BLOCK, MAURICE (1816–19or)

block of See also:

• PITCH
• PITCH, MUSICAL

pitch is more easily splintered than indented by a See also:

• HAMMER, FRIEDRICH JULIUS (1810-1862)

hammer, but under the action of the See also:

• MERE
• MERE, ADALBERT (1838-1909)

mere weight of its parts acting for a long enough time it flattens out and flows like a liquid . All actual fluids are viscous . They oppose a resistance to the relative See also:

• MOTION (Lat. motio, from movere, to move)
• MOTION, LAWS OF

motion of their parts . This resistance diminishes with the velocity of the relative motion, and becomes zero in a fluid the parts of which are relatively at rest . When the relative motion of different parts of a fluid is small, the viscosity may be neglected without introducing important errors .

On the other hand, where there is considerable relative motion, the viscosity may be ex- pected to have an See also:

• INFLUENCE (Late Lat. influentia, from influere, to flow in)

influence too great to be neglected . Measurement of Viscosity . Coefficient of Viscosity.—Suppose the See also:

• PLANE

plane ab, fig. r of See also:

• AREA

area w, to move with the velocity V relatively to the surface cd and parallel to it . Let the space between be filled with liquid . The layers of liquid in contact with ab and cd adhere to them . The intermediate layers all offering an equal resistance to shearing or distortion, the rectangle of fluid abed will take the form of the parallelogram a'b'cd . Further, the resistance to the motion of ab may be expressed in the form R=KWV, (I) where K is a coefficient the nature of which remains to be deter-See also:

• MINED

mined . Except where other See also:

• UNITS, DIMENSIONS OF
• UNITS, PHYSICAL

units are given, the units throughout this article are feet, pounds. pounds per sq. ft., feet per second . If we suppose the liquid between ab and cd divided into layers as shown in fig . 2, it will be clear that the stress R acts, at each dividing See also:

• FACE (from Lat. fades, derived either from facere, to make, or from a root fa-, meaning " appear "; cf. Gr. cbatvstv)

face, forwards in the direction of motion if we consider the upper layer, backwards if we consider the See also:

• LOWER

lower layer . Now suppose the See also:

• ORIGINAL

original thickness of the layer T increased to nT; if the bounding plane in its new position has the velocity etV, the shearing at each dividing face will be exactly the same as before, and the resistance must therefore be the same . Hence, R=K'w(nV) .

(2) But equations (I) and (2) may both be expressed in one See also:

• EQUATION (from Lat. aequatio, aequare, to equalize)

equation if K and K' are replaced by a See also:

• CONSTANT, BENJAMIN (1845-1902)

constant varying inversely as the thickness of the layer . Putting K =µ%T, K' =µ/nT, R =µmV/T ; or, for an indefinitely thin layer, R =µwdV /dt, (3) an expression first proposed by L . M . H . Navier . The coefficient µ is termed the coefficient of viscosity . According to J . Clerk See also:

• MAXWELL
• MAXWELL, JAMES CLERK (1831–1879)

Maxwell, the value of µ for air at 0° Fahr. in pounds, when the velocities are expressed in feet per second, is µ=0.000 000 025 6(461°+0); that is, the coefficient of viscosity is proportional to the See also:

• ABSOLUTE (Lat. absolvere, to loose, set free)

absolute temperature and independent of the pressure . The value of u for water at 77° Fahr. is, according to H. von See also:

• HELMHOLTZ, HERMANN LUDWIG FERDINAND VON (1821-1894)

Helmholtz and G . Piotrowski, µ=o 000 oi8 8, the units being the same as before . For water µ decreases rapidly with increase of temperature . § 4 .

When a fluid flows in a very See also:

• REGULAR

regular manner, as for instance when it flows in a capillary See also:

• TUBE (Lat. tuba)

tube, the velocities vary gradually at any moment from one point of the fluid to a neighbouring point . The layer adjacent to the sides of the tube adheres to it and is at rest . The layers more interior than this slide on each other . But the resistance See also:

• DEVELOPED

developed by these regular movements is very small. if in large pipes and open channels there were a similar regularity of See also:

• MOVEMENT

movement, the neighbouring filaments would acquire, especially near the sides, very great relative velocities . V . J . Boussinesq has shown that the central filament in a semicircular See also:

• CANAL
• CANAL (from Lat. canalis, " channel " and " kennel " being doublets of the word)

canal of i See also:

• METRE ((terpuc?, sc. rFxvf, from Gr. Or poi', measure)

metre See also:

• RADIUS

radius, and inclined at a slope of only o•000r, would have a velocity of 187 metres per second,2 the layer next the boundary remaining at rest . But before such a difference of velocity can arise, the motion of the fluid becomes much more complicated . Volumes of fluid are detached continually from the boundaries, and, revolving, form eddies traversing the fluid in all directions, and sliding with finite relative velocities against those surrounding them . These slidings develop resistances incomparably greater than the viscous resistance due to movements varying continuously from point to point . The movements which produce the phenomena commonly ascribed to fluid See also:

• FRICTION (from Lat. fricare, to rub)

friction must be regarded as rapidly or even suddenly varying from one point to another . The See also:

• INTERNAL

internal resistances to the motion of the fluid do not depend merely on the general velocities of See also:

• TRANSLATION

translation at different points of the fluid (or what Boussinesq terms the mean See also:

• LOCAL

local velocities), but rather on the intensity at each point of the eddying agitation .

The problems of hydraulics are therefore much more complicated than problems in which a regular motion of the fluid is assumed, hindered by the viscosity of the fluid .