For a fixed plane in a moving current of water E. Mariotte found f = 1.25. Dubuat, in experiments in a current of water like those mentioned above, obtained the values m = 1.186; n = 0.670; f = 1.856. Thibault exposed to wind pressure planes of 1.17 and 2.5 sq. ft. area, and found f to vary from 1.568 to 2.125, the mean value being f = 1.834, a result agreeing well with Dubuat.
| Fig. 169. |
§ 167. Stanton’s Experiments on the Pressure of Air on Surfaces.—At the National Physical Laboratory, London, T. E. Stanton carried out a series of experiments on the distribution of pressure on surfaces in a current of air passing through an air trunk. These were on a small scale but with exceptionally accurate means of measurement. These experiments differ from those already given in that the plane is small relatively to the cross section of the current (Proc. Inst. Civ. Eng. clvi., 1904). Fig. 169 shows the distribution of pressure on a square plate. ab is the plate in vertical section. acb the distribution of pressure on the windward and adb that on the leeward side of the central section. Similarly aeb is the distribution of pressure on the windward and afb on the leeward side of a diagonal section. The intensity of pressure at the centre of the plate on the windward side was in all cases p = Gv2/2g ℔ per sq. ft., where G is the weight of a cubic foot of air and v the velocity of the current in ft. per sec. On the leeward side the negative pressure is uniform except near the edges, and its value depends on the form of the plate. For a circular plate the pressure on the leeward side was 0.48 Gv2/2g and for a rectangular plate 0.66 Gv2/2g. For circular or square plates the resultant pressure on the plate was P = 0.00126 v2 ℔ per sq. ft. where v is the velocity of the current in ft. per sec. On a long narrow rectangular plate the resultant pressure was nearly 60% greater than on a circular plate. In later tests on larger planes in free air, Stanton found resistances 18% greater than those observed with small planes in the air trunk.
§ 168. Case when the Direction of Motion is 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, Vince, and Thibault on planes moved circularly through air and water on a whirling machine.
| Fig. 170. |
Let AB (fig. 170) be a plane moving in the direction R making an angle φ with the plane. The resultant pressure between 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 = N sin φ;
L = N cos φ.
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. Then, for the same plane inclined at an angle φ to its direction of motion, the resistance was found by Hutton to be