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90
[IMPACT AND REACTION
HYDRAULICS


Fig. 168 shows the pressure curves obtained in three experiments with three jets of the sizes shown, and with the free surface level in the reservoir at the heights marked. on a brass plate 9 in. in diameter. small hole in the brass plate

of the jet on the plane is h ft. of water. If the pressure curve is l H '75 3 '73 2l'8 drawn with pressures represented by feet of water, it will touch the H '3 2'2 '73 21 free water surface at the centre of the jet. 42'15 '85 V6 1 '33 20'3 Suppose the pressure curve rotated so as to form a solid of revolu- H '95 I '83 I9'3 tion. The weight of water contained in that solid IS the total H '93 I3 pressure of the jet on the surface, which has already been deter- H ~93 17 1 mined. Let V =volume of this solid, then GV is its weight in pounds. 26'5 V13 I3'5 Consequently 77 V13 12'5 G¥=“'£'2zG”'3" ~ is “ai =2L»J 11 - P ° We have already, therefore, two conditions to be satisfied by the ' V33 8 pressure curve ' V38 7 1 Some very interesting experiments on the distribution of pressure I 8 on a surface struck by a jet have been made by ]. Beresford ' 1 4 5, (Prof. Papers on Indzan Engrneerzng, No. cccxxu.), with aview to ' I 5§ 4 3 afford information as to the forces acting on the aprons of welrs. ' I 5 3 5 Cylindrical jets 5 in. to 2 in. diameter, issuing from a vessel in "V 9 2 which the water level was constant, were allowed to fall vertically As the general form of the pressure curve has been already indicommumcated by a flexible tube with a vertical pressure column. Arrangements were made by which this aperture could be moved 215 in. at a time across the area struck by the jet. The height of the pressure column for each osition of the a erture ave th r p p, g e p essure, at that point of the area struck by the jet. When the aperture was l E -Diana.-4Bz> ' j;

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I 1 i I Q 2 1 I | |; 1 1 } 1-o ofs o o~5 1'° 1'5 ° Distance from axis of jet in inches. FIG. 168.-Curves of Pressure of jets impinging normally on a Plane. exactly in the axis of the jet, the pressure column was very nearly level with the free surface in the reservoir supplying the jet; that is, the pressure was very nearly v2/2 g. As the aperture moved away from the axis of the jet, the pressure diminished, and it became insensibly small at a distance from the axis of the jet about equal to the dia meter of the jet. Hence roughly the pressure due to the jet extends cated, it may be assumed that its equation is of the form y=ab"2- (I) But it has already been shown that for x-=o, y=h, hence a=h. To determine the remaining constant, the other condition ma b Y e used, that the solid formed by rotating the pressure curve represents the total pressure on the plane The volume of the solid is ® V= Ozrrxydx °° 2 =21rh ob zxdx 2 Q = oh/10g.1>> [-ff' jo -=-irh/log, b. Using the condition already stated, 2w/(hhi)=1rh/log Bb, log e b = (1r/2w)x/ (h/hr). Putting the value of b in (2) in eq. (1), and also r for the radius of the jet at the orifice, so that w=1rr2, the equation to the pressure curve is T22 y==he§ li;- § 166. Resistance of a Plane moving through a Fluid, or Pressure of a Current on 0, Plane.-When a thin plate moves through the air, or through an indefinitely large mass of still water, in a direction normal to its surface, there is an excess of pressure on the anterior face and a diminution of pressure on the posterior face. Let vbe the relative velocity of the plate and fluid, SZ 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 =fG§ 2 D2/2g pounds ==fG§ 2h; where f is a coefficient having about the value 1 -3 for a plate moving in still 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 “ unfair ” form, fthat is, lin which the surfaces over which the water slides are t d | no o gra ua and continuous curvature.

over an area about four times the area of section of the jet. The stress between the fluid and plate arises chiefly in this way.