UNITS OF MEASUREMENT.

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A pressure of one kg/cm2 is thus 2048 lb/ft2, or 14-2 lb/in2; so that the normal atmospheric pressure, called an atmosphere, being taken as 143 or 147 lb/in2, is the same as 1033 kg/cm2; and therefore, for practical purposes, the atmosphere may be taken as one kg/cm2.

With the Gravitation Unit of Force, the weight of a body is at once the measure of the quantity of matter in the body, and also of the force with which it is apparently attracted by the Earth; and the word Weight may be used in either sense without ambiguity or confusion, when dealing with hydrostatical problems on the surface of the Earth.

We must notice however that, in consequence of the variation of g, this unit of force will vary slightly in magnitude at different points of the Earth; but the variation is so small that it makes no practical difference in engineering problems; the variation is only important when we consider tidal or astronomical phenomena, covering the Earth and extending to the Moon, Sun, and planets.

9. The Safety Valve.

To measure the pressure of a fluid in a vessel, and to prevent the pressure from exceeding a certain amount, the Safety Valve was invented by Papin, 1681.

It consists essentially of a spherical or conical plug C, fitting accurately into a circular orifice in the vessel, and kept closed against the pressure of the fluid by a lever AB, with fulcrum at A; carrying either a sliding weight W lb, when used on a steady fixed vessel; or else held down at the end B by a spiral spring S, which can be screwed to any desired pull of T lb, when the vessel is subject to shock and oscillation (fig. 1).

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THE SAFETY VALVE.

Then if the pressure of the fluid on the seat of the valve is p lb/in2, and the orifice is d inches in diameter, the thrust on the valve is d2p lb; so that, taking moments about the fulcrum A of the lever AB,

d2px AC=Wx AE or Tx AB,

when the valve is on the point of lifting.

Sometimes the valve is held down by a weight (fig. 2) or by a spiral spring, superposed directly without the intervention of a lever as in fig. 3, the form used in steamers and hydraulic machinery.

The danger of the sticking of the valve in the seat is obviated in Ramsbottom's safety valve (fig. 4), consisting of two equal conical valves, held down by a bar and a spring midway between them; then one or the other valve, or both valves, will open when the thrust of the fluid on it is half the pull of the spring.

THE SAFETY VALVE.

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Where the pressure of a fluid is exerted over a circular area or piston, it is often convenient to estimate the pressure in pounds per circular inch, written as 1b/O in, or lb/O"; and many pressure gauges attached to hydraulic machinery are graduated in this manner; a pressure of p lb/in2 being р or '7854p lb/○ in.

Then the thrust on a circular area d inches in diameter is obtained by multiplying this pressure in lb/O" by ď2.

Fig. 2.

Fig. 3.

Fig. 4.

It is important in steam boilers that the area of escape from the safety valve should be sufficiently large, so as to allow the steam to escape as fast as it is generated; according to a rule given by Rankine the area of the valve in in2 should be 0.006 times the number of lb of water evaporated per hour.

If the orifice of the safety valve is d ins diameter at the top and conical, the semi-vertical angle of the conical plug being a, then a lift of x ins of the valve will

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THE PRESSURE GAUGE.

give an annular area of internal diameter d- 2x tan a ins, and therefore of area a tan a(d-x tan a) in2.

But if we consider the valve as a flat disc, of d ins diameter, a lift of x ins will give de in2 area of escape sideways.

10. The Pressure Gauge.

To measure pressures continually without blowing off at the Safety Valve, the simplest and most efficient instrument is Bourdon's Pressure Gauge (fig. 5).

Fig. 5.

This consists essentially of a tube AB, bent into the arc of a circle, closed at one end A, and communicating at the other end B with the vessel containing the fluid whose pressure is to be measured.

The cross section of the tube AB is flattened or elliptical, the longer diameter standing at right angles to the plane of the tube AB, thus .

THE PRESSURE GAUGE.

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The working of the instrument depends upon the principle, discovered accidentally by its inventor M. Bourdon (Proc. I. C.. E., XI., 1851), that as the pressure in the interior increases and tends to make the elliptic cross section more circular, the tube AB tends to uncurl into an arc of smaller curvature and greater radius; and the elasticity of the tube AB brings it back again to its original shape as the pressure is removed.

The end B being fixed, the motion of the free end A is communicated by a lever and rack to a pointer on a dial, graduated empirically by the application of known test pressures.

By making the tube AB of very thin metal, and the cross section a very flattened ellipse or double segment, the instrument can be employed to register slight variations of pressure, such as those of the atmosphere; it is then called Bourdon's Aneroid Barometer.

But when required for registering steam pressures, reaching up to 150 or 200 lb/in2, the tube is made thicker; and when employed for measuring hydraulic pressures of 750 to 1000 lb/in2, or even in some cases to 5 or 10 tons/in2, the tube AB must be made of steel, carefully bored out from a solid circular bar, and afterwards flattened into the elliptical cross section, and bent into a circular arc.

Pressures in artillery due to gunpowder reach up to 35,000 or 40,000 lb/in2, and more, say up to 20 tons/in2; or from about 2,500 to 3,000 atmospheres, or kg/cm2; such high pressures require to be measured by special instruments called crusher gauges, depending on the amount of crushing of small copper cylinders by the pressure.