HYDRODYNAMICS. 373 HYDBO-FERROCYANIC ACID. flowing in a steady state where the velocity 13 small the pressure is large, and conversely if friction is supposed to he excliuled. This general principle is illustrated by the 'ball nozzle,' the injector of a boiler, the common atomizer, the 'ball in the fountain' experiment, and many others. If a fluid is flowing through a long pipe, e.g. water or gas in city mains, there is of course always a great amount of friction between the moving fluid and the layer that sticks to the tube. Owing to this, the pressure decreases along the pipe, and the velocity of flow is decreased also. If an opening is made in the side of a vessel ■containing a liquid, the latter will make a jet out into air. If the opening is a small one in a thin wall, it may be observed that the cross- section of the jet a short distance from the wall is less than that of the opening itself: this place of smallest cross-section is called the 'vena contracta.' If a quantity of liquid of mass m escapes having a velocity t', its kinetic energy is i/imu'. This energy is evidently due to the fact that the effect inside the vessel is just as if these ni grams had been taken oflf from the free surface; and so. if the centre of the opening is at a depth h below the free surface, the m grams have lost an amount of potential energy mgh. Therefore ■mgh= imv^i or v^ = 2f/h. This value of the velocity of eftlux was first tleduced by Torricelli, the pupil of Galileo. This theorem may be stated in a slightly diff'erent way. The liquid is forced out owing to a differ- ence of pressure on the two sides of the opening equal to pgh. (See Hydrostatics.) Calling this diff'erence of pressure P, the formula for v' be- comes In this form it may be applied to the rate of escape of a gas from a vessel through a small opening in a thin wall. It is seen that the square of the velocity of efllux varies inversely as the density of the gas and directly as the pressure forcing the gas out, that is as the difl'er- cnee of the partial pressures of that particular gas on the two sides of the opening, regardless of what other gases are present or what their pressures are. (See Effusion.) If the escape of the fluid takes place through a thick wall or throujrh a tube, the phenomena are entirely diff'erent, owing to friction. It is ob.served that the rate of escape is independent — within certain limits — of the material of the tube, showing that there is a layer of the fluid adhering to the inner walls of the tube, thus forming a tube of the fluid through which the flow takes place. The following formula has been found by experi- ment to hold approximately for capillary tubes: »' = 6V' ■nhere r is the internal radius of the tube, I is its length, and 7; is a constant. If an obstacle is placed in a stream of liquid or of gas, it experiences certain forces. One of the most interesting cases is that of an oblong solid in a fluid stream ; it will tend to place itself ■with its length at right angles to the current. This is illustrated by the fact that when a small piece of paper falls it does not do so edge down, but face down ; if a coin is dropped in water, it falls face down, 'wabbling' as it sinks. (See Projectile.) Other cases of fluid motion are too diflicult for discussion here. It should be noted, however, that there are two great divisions of such motions: irrotational and rotational. The former is such that, if a small portion of the fluid were suddenly solidified and freed from the rest of the fluid, it would have simply motion of translation, no rotation. The latter is such that if a small portion of the fluid were suddenly solidified and freed from the rest of the fluid, it would be spinning round a definite axis. It was proved theoretically by Lagrange that if a certain portion of a perfect fluid free from viscosity was set in irrotational motion, it would never have its character changed (if certain con- ditions are satisfied, as they would be in gen- eral). Helmholtz has proved, further, that if a portion of a perfect fluid is moving rotationally, it will always do so; and that it is as impo.ssible to produce this motion in a perfect fluid as it is to destroy it. He showed, too, how lines can be imagined drawn in the fluid so that at each of their points they coincide with the axis of rotation of the portion of fluid at that point. Such a line is called a 'vortex-line;' and a solid tube made up of such lines is called a 'vortex.' A vortex once existing in a perfect fluid moves through it, keeping its identity, i.e. always being made up of the same particles and preserving certain other properties. If two vortices were to collide they would rebound, being perfectly elastic. It is possible to devise many forms of vortices which are stable and can keep their gen- eral shape. Many of the properties of vortices can be imitated by smoke-rings, but the air is. of course, not a perfect fluid, and so the vortices do not persist. HY'DRO-FER'RICYANIC ACID ( from hydro-gen -- ferricyanic) , H3Fe(CX)a. A brown crystalline substance obtained by decomposing potassium ferrieyanide with dilute mineral acids, in aqueous solution. Potassium ferrieyanide, or red prussiate of potash, K,Fe(CX)„, is a dark-red soluble crys- talline salt obtained by passing chlorine-gas into solutions of potassium ferrocyanide (see Hydro- FERROCY.xic Acin), the transformation of the latter taking place according to the following chemical equation : K.Fe(C]Sr), + a = K,Fe(CN), + KCl Potassium ferroo.vanide Potassium ferrio.vanide Potassium ferrieyanide is used principally for making Turnbuil's blue, or ferrous ferrieyanide, Fe,[Fe(CN)ol;, which is prepared by mixing po- tassium ferrieyanide with ferrous salts in aqueous solution. HYDRO-FERROCYANIC ACID (from 7.;/- dro-gon + fcrrocjifitiic) . H,Fo(('X),. A white crystalline substance readily soluble in water and in alcohol. If exposed to the air. it soon as- sumes a blue coloration. It m.iy be obtained in the free state by decomposing an aqueous solu- tion of its potassium salt with dilute mineral acids. The ferrocyanide of potassium, K.Fe(CN),-l- SH,0. often called yellow prussiate of potash, is a yellow crystalline substance produced when a
