Page:Encyclopædia Britannica, Ninth Edition, v. 12.djvu/533

517 HYDRAULICS.] HYDROMECHANICS 517 To determine the remaining constant, the other condition may be used, that the solid formed by rotating the pressure curve represents the total pressure on the plane. The volume of the solid is v , = 2n7( lo &quot;&quot;log. 6 Using the condition already stated, xdx b- w /A 2^ v ^ (2). Putting the value of b in (2) in eq. (1), and also r for the radius of the jet at the orifice, so that ca = irr 2, the equation to the pressure curve is 154. Resistance of a Plane moving through a Fluid, or Pressure of a Current on a Plane. When a thin plate moves through the air, or through an indelinitely large mass of still water, in a direction normal to its surface, there is an excess of pressure on the anterior definiteness to be moving through the fluid, receive from it forward momentum. Portions of this forward moving water are thrown oil laterally at the edges of the plate, and diffused through the surround ing fluid, instead of falling to their original position behind the plate. Other portions of comparatively still water are dragged into motion to fill the space left behind the plate ; and there is thus a pressure less than hydrostatic pressure at the back of the plate. The whole resistance to the motion of the plate is the sum of the excess of pressure in front and deficiency of pressure behind. This resistance is independent of any friction or viscosity in the fluid, and is due simply to its inertia resisting a sudden change of direction at the edge of the plate. Experiments made by a whirling machine, in which the plate is fixed on a long arm and moved circularly, gave the following values of the coefficient/. The method is not free from objection, as the centrifugal force causes a flow outwards across the plate. Approximate Area of Plato in sq. ft. Values of /. Borda. Hutton. Tliibault. 0-13 1-39 1-24 0-25 1-49 1-43 1 525 0-63 1-64 1-11 1 -784 Wiiler Level in. Ttescr oirlL. 0-5 Distance from Axis of Jet in Inches. FIG. 171. Carves of Pressure of Jets impinging normally on a Plane. face and a diminution of pressure on the posterior face. Let v be the relative velocity of the plate and fluid, 12 the area of the plate, G the density of the fluid, h the height due to the velocity, then the total resistance is expressed by the equation R=/Gft ~ pounds =/CflA ; where /is a coefficient having about the value 1 &quot;3 for a plate moving instill fluid, and 1 8 for a current impinging on a fixed plane, whether the fluid is air or water. The difference in the value of the coefficient in the two cases is perhaps due to errors of experiment. There is a similar resistance to motion in the case of all bodies of &quot;unfair&quot; form, that is, in which the surfaces over which the water slides are not of gradual and continuous curvature. The stress between the fluid and plate arises chiefly in this way. The streams of fluid deviated in front of the plate, supposed for There is a steady increase of resistance with the size of the plate ; in part or wholly due to centrifugal action. Dubuat made experiments on a plane one foot square, moved in a straight line in water at 3 to 6^ feet per Fecond. Calling m the coefficient of excess oi pressure in front, and n the coefficient of de ficiency of pressure behind, so that /= m + n, he found the following values : m=l: ? 3 ; /=1 433. The pressures were mea sured by pressure columns. Experiments by Morin, Piobert, and Didion on plates of 3 to 27 square s: feet area, drawn vertically g through water, gave b /=2 18; but the experi- v ments were made in a o., reservoir of comparatively 4; small depth. For similar ,s plates moved through air , they found/= 1 36, a result ~ more in accordance with &quot;g those which precede. For a fixed plane in a moving current of water Mariotte found /-I -25.. Dubuat, in experiments in&amp;gt; a current of water like- those mentioned above,, obtained the values ?n = 1-186; 7( = 670; /= 1-856. Tliibault ex posed to wind pressure planes of I ] 7 and 2 5- square feet area, and found /to vary from 1 568 to 2 &quot;125, the mean value being /=1 834, a result agreeing well with Ihi- buat. 155. Case when the Direction of Motion oblique to the Plane. The determination of the pressure between a fluid and surface in this case is of importance in many practical questions, for instance, in assigning the load due to wind pressure on sloping and curved roofs, and experiments have been made by Hutton, Yince, and Tliibault on planes moved circularly through air and water on a whirling machine. Let AB (fig. 172) be a plane moving in the direction R making an angle &amp;lt;p with the plane. The resultant pressure Ivtwcen the fluid and the plane will be a normal pressure N. The component R of this normal pressure is the resistance to the motion of the plane and the other component L is a lateral force resisted by the guides which support the plane. Obviously R = X sin (/&amp;gt; ; L = N cos q&amp;gt;. In the case of wind pressure on a sloping roof surface, R is the