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Encyclopedia Britannica - Main :: HOR-I25 |
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HYDRAULICS (Gr. iS&,p, water, and ai,Xos, a pipe) , the branch of engineering science which deals with the practical
I. THE DATA OF HYDRAULICS' r. Properties of Fluids.The fluids to which the laws of practical
great
change of figure are always small compared with the weight, inertia, pressure, &c., which produce the visible motions it is the object of hydraulics to estimate. On the other hand, while a fluid passes easily from one form to another, it opposes considerable resistance to change of volume.It is easily deduced from the absence or smallness of the tangential stress that contiguous portions of fluid 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 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 element
2. Fluids are divided into liquids, or incompressible fluids, and gases, or compressible fluids. Very great
In 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, 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 short time, and yet may be deformed considerably by a small stress acting for a long period. A block
hammer
All actual fluids are viscous. They oppose a resistance to the relative 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 influence too great to be neglected. Measurement of Viscosity. Coefficient of Viscosity.Suppose the plane ab, fig. r of 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- mined
Except where other 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 face, forwards in the direction of motion if we consider the upper layer, backwards if we consider the lower layer. Now suppose the original
R=K'w(nV). (2) But equations (I) and (2) may both be expressed in one equation if K and K' are replaced by a constant varying inversely as the thickness of the layer. Putting K =%T, K' =/nT, R =mV/T ; or, for an indefinitely thin layer, R =wdV /dt, (3) an expression first proposed by L. M. H. Navier. The coefficient is termed the coefficient of viscosity. According to J. Clerk Maxwell, the value of for air at 0 Fahr. in pounds, when the velocities are expressed in feet per second, is =0.000 000 025 6(461+0); that is, the coefficient of viscosity is proportional to the absolute temperature and independent of the pressure. The value of u for water at 77 Fahr. is, according to H. von Helmholtz and G. Piotrowski, =o 000 oi8 8, the units being the same as before. For water decreases rapidly with increase of temperature. 4. When a fluid flows in a very regular manner, as for instance when it flows in a capillary 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 developed by these regular movements is very small. if in large pipes and open channels there were a similar regularity of movement
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