Center of pressure

“ Then dividing this sum of the momenta by the sum of the pressure there will be 2λ ( ( (b - a) (b - a) + a2 - aλ + 1/3λ2) / (2λ (b - a) ) ) = b + p (a (a2 - aλ + 1/3λ2) / (b - a) ) the distance of the314 center of the pressure from the level of the fluid, that is, to the distance of the result of all the pressure from that level. ”

“ The pressure in the bounding surface of the internal medium is also zero, and there is no resistance, therefore it is zero throughout; but the pressure in the third case is the difference of pressures in the two given cases, therefore these are equal, and there is only one distribution of pressure which is possible, namely, that due to the imaginary distribution of sources and sinks.
(25) When the resistance is infinite in the internal medium, there can be no passage of fluid through it or into it. ”

“ If, then, the vertical depth of the earthy particles or sand above the bottom is so small that the arching effect against the sides is negligible, the full weight of the particles in contact, directly or vicariously, with the bottom acts as pressure on the bottom, while the full pressure of the water acts through the voids or on them, or is transmitted through material in contact with the bottom. ”

“ The immediate and perfect distribution of a pressure applied on any one part, however small, of a fluid surface through the whole mass, enables us to communicate at one instant the same pressure to any number of such parts by merely increasing the surface of the fluid, which may be done by enlarging the containing vessel; and if the vessel be so constructed that a large portion of its surface shall be moveable together, the pressures on all the similar parts of this portion will be united into one consentient force, which may thus be increased to any extent we please. ”

“ If the pressure at every point of a closed surface be the same and equal to p, and if there be no sources or sinks within the surface, then there will be no motion of the fluid within the surface, and the pressure within it will be uniform and equal to p. ”

“ This theory shows that, when pressure is applied at a point of the edge of a plate in any direction in the plane of the plate, the stress developed in the plate consists exclusively of radial pressure across any circle having the point of pressure as centre, and the magnitude of this pressure is the same at all points of any circle which touches the edge at the point of pressure, and its amount at any point is inversely proportional to the radius of this circle. ”

“ In the case of wind pressure on a sloping roof surface, R is the horizontal and L the vertical component of the normal pressure.
In experiments with the whirling machine it is the resistance to motion, R, which is directly measured. Let P be the pressure on a plane moved normally through a fluid. ”

“ If this material is under water, and is so soft as to be considered semi-aqueous, the pressure per square foot will increase in diminishing proportion to the depth, and the pressure per area will soon approach and become a constant, due to the resistance offered by the lateral arching of the solid material ”

“ The explanation is found in the uniform distribution of the pressure, the influence of which is thus counteracted, and by the fact that the tissues themselves contain everywhere a certain amount of air at the same pressure. The familiar experiment of holding the hand over an exhausted glass cylinder—which experiment is indeed but a modification of the use of the cupping glass above referred to—illustrates very forcibly the insupportable difficulties which the human body would encounter were not its entire surface uniformly subjected to the atmospheric pressure. ”

“ This pressure, it should be noted, is the net or effective pressure, the pressure with which the gas raises the liquid in a water-gauge glass out of the level while the opposite end of the water column is exposed to the atmosphere. The absolute pressure in a vessel containing gas at an effective pressure of 12 inches of water is 7 oz. plus the normal, insensible pressure of the atmosphere itself--say 15-1/4 lb. ”

“ Pressure on a Curved Surface when the Water is deviated wholly in one Direction.—When a jet of water impinges on a curved surface in such a direction that it is received without shock, the pressure on the surface is due to its gradual deviation from its first direction. ”

“ The pressure in the central portions of such a mass of gas would, of course, be greater than the pressure in the outer portions, just as the pressure rises as we penetrate from above downward into our terrestrial atmosphere. ”

“ A pressure exerted upon a body at rest is resisted and balanced by another pressure; when the pressure of one body puts another in motion, the body, though it yields to the force, nevertheless exerts upon the pressing body a force like that which it suffers. ”

“ The pressure exerted by the plunger in the small cylinder, being transmitted according to the principles already explained, produces on each portion of the area of the large plunger equal to that of the smaller an exactly equal pressure. ”

“ C1 is then the centre of pressure for the joint bb, and R1 is the total force acting there. Repeating this process for each block in succession there will be found the centres of pressure C2, C3, &c., and also the resultant pressures R2, R3, &c., acting at these respective centres. The centres of pressure at the joints are also called centres of resistance, and the curve passing through these points is called a line of resistance. Let all the resultants acting at the several centres of resistance be produced until they cut one another in a series of points so as to form an unclosed polygon. ”

“ The pressure of the air is a convenient unit to employ in practical work, where it is called an “atmosphere”; it is made the equivalent of a pressure of one kg/cm2; and one ton/inch2, employed as the unit with high pressure as in artillery, may be taken as 150 atmospheres.
12. Theorem.—A body immersed in a fluid is buoyed up by a force equal to the weight of the liquid displaced, acting vertically upward through the centre of gravity of the displaced liquid. ”

“ Thus, the weight of each separate piece in a machine is treated as acting wholly at its centre of gravity, and each pressure applied to it as acting at a point called the centre of pressure of the surface to which the pressure is really applied. ”

“ Pressure for Forced Fits.—The pressure required for assembling cylindrical parts depends not only upon the allowance for the fit, but also upon the area of the fitted surfaces, the pressure increasing in proportion to the distance that the inner member is forced in. ”

“ We see from these curves that for very short arcs the potential difference increases continuously with the pressure, but for longer ones there is a critical pressure at which the potential difference is a minimum, and that critical pressure seems to increase with the length of arc. ”

“ But when we are so prepared, the truth appears to be manifest, even independent of experience, and is seen to be a rule to which experience must conform. What, then, is the leading idea which thus enables us to reason effectively upon mechanical subjects? By attention to the course of such reasonings, we perceive that it is the idea of Pressure; Pressure being conceived as a measurable effect of heavy bodies at rest, distinguishable from all other effects, such as motion, change of figure, and the like. ”

“ The stress considered in hydro-mechanics is always a pressure, as liquids are in general capable of sustaining only a slight tension without disruption: the intensity of the pressure is measured by the number of units of force per unit of area. Thus we say, one thousand pounds of pressure per square inch of piston—the pounds and the square inches are the units used in these calculations. ”

“ Weight is the name of a particular species of pressure; pressure towards the centre of the earth. Pressure, as we have already fully seen, is the name we apply, when we have certain sensations in the muscles, just as green is the name we apply when we have a certain sensation in the eye. As green is the name of the sensation in the eye, pressure is the name of the sensation in the muscles. Pressure upwards, is one thing; pressure downwards, is another; pressure of a body, when that body is urged by another body, is one thing ”

“ The pressure arising from the motion of the body is spent in generating a motion in the parts of the fluid, and this creates the resistance. But the pressure arising from the compression of the fluid, be it ever so forcible, if it be propagated in an instant, generates no motion in the parts of a continued fluid, produces no change at all of motion therein ”

“ If we stretch a tape upon a flat table, whatever be the tension of the tape it obviously exercises no pressure upon the table below. But if we stretch it over a curved surface, a cylinder for instance, it does exercise a downward pressure; and the more curved the surface the greater is this pressure, that is to say the greater is this share of the entire force of tension which is resolved in the downward direction. In math­e­mat­i­cal language, the pressure (p) varies directly as the tension (T) , and inversely as the radius of curvature (R) : that is to say, p = T ⁄ R, per unit of surface. ”

“ PRESSURE AT DIFFERENT ANGLES.—What every one wants to know, and a subject on which a great deal of experiment and time have been expended, is to determine what the pressures are at the different angles between the horizontal, and laws have been formulated which enable the pressures to be calculated. ”

“ Only in minus-pressure means, which serve as a partial vacuum in some cases, to [Pg 34] disturb the equilibrium of pressure, is motion, or change of place of the elements of bodies, or of bodies themselves promoted: without such means there is nothing to promote the blowing of a wind, or to put the medium of space into action. Cause being given, the General Pressure in the production of every physical effect, the sole province of philosophy consists in tracing out the minus-pressure means which promote the occasional and partial action of the medium of pressure. ”

“ In like manner, when the solid is not in a state of isotropic stress, the difference of the two pressures in question will not sensibly affect the values of and , and the value of the second member of the equation may be calculated as if represented the true pressure in the solid in the direction of the normal to the surface. ”

“ We all know that air or any other gas placed in a vessel presses against the sides of the vessel, and against the surface of any body placed within it. On the kinetic theory this pressure is entirely due to the molecules striking against these surfaces, and thereby communicating to them a series of impulses which follow each other in such rapid succession that they produce an effect which cannot be distinguished from that of a continuous pressure. ”

“ For this Elastical power, according to the Experiment, has no less force of pressure then an hundred pound weight or more: which pressure (as in all flexible bodies that have a Spring power in them) is perpetual and every where in the Aire, if it be there at all. And therefore any Cylinder of Aire in the same height from the ground, and of the same diameter with that of the Sucker of the Pump, will press as forcibly as an hundred pound weight. ”

“ Whence neither will a motion of the parts of the fluid among themselves, be changed by a pressure communicated to the external superficies, except so far as either the figure of the superficies may be somewhere alter'd, or that all the parts of the fluid, by pressing one another more intensely or remissly, may slide with more or less difficulty among themselves. ”

“ Pneumatics relates to the equilibrium or movements of aërial fluids under all circumstances of pressure, density, and elasticity. The weight of the air, and its pressure on all the bodies on the earth’s surface, were quite unknown to the ancients, and only first perceived by Galileo, on the occasion of a sucking-pump refusing to draw water above a certain height. ”

“ The reason why a satisfactory quantitative experimental demonstration of the principle of the equality of pressure cannot be given is that the influence of the weight of the liquid and of the friction of the pistons cannot be altogether eliminated. ”

“ Now, as one may easily convince himself, a mass having components is capable of only independent variations in nature and state. Hence, if the fluid on one side of the diaphragm remains without change, that on the other side cannot (in general) vary in nature or state. Yet the pressure will not necessarily be the same on both sides. For, although the pressure is a function of the temperature and the n potentials, it may be a many-valued function (or any one of several functions) of these variables. ”