where h is the depth of the plane below the free surface. The external layers of fluid subjected throughout, after leaving the orifice, to the atmospheric pressure will attain the velocity v, and will flow away with this velocity unchanged except by friction. The layers towards the interior of the jet, being subjected to a pressure greater than atmospheric pressure, will attain a less velocity, and so much less as they are nearer the centre of the jet. But the pressure can in no case exceed the pressure v2/2g or h measured in feet of water, or the direction of motion of the water would be reversed, and there would be reflux. Hence the maximum intensity of the pressure of the jet on the plane is h ft. of water. If the pressure curve is drawn with pressures represented by feet of water, it will touch the free water surface at the centre of the jet.
| Fig. 167. |
Suppose the pressure curve rotated so as to form a solid of revolution. The weight of water contained in that solid is the total pressure of the jet on the surface, which has already been determined. Let V = volume of this solid, then GV is its weight in pounds. Consequently
GV = (G/g) ωv1v;
V = 2ω √ (hh1).
We have already, therefore, two conditions to be satisfied by the pressure curve.
| Fig. 168.—Curves of Pressure of Jets impinging normally on a Plane. |
Some very interesting experiments on the distribution of pressure on a surface struck by a jet have been made by J. S. Beresford (Prof. Papers on Indian Engineering, No. cccxxii.), with a view to afford information as to the forces acting on the aprons of weirs. Cylindrical jets 1⁄2 in. to 2 in. diameter, issuing from a vessel in which the water level was constant, were allowed to fall vertically on a brass plate 9 in. in diameter. A small hole in the brass plate communicated by a flexible tube with a vertical pressure column. Arrangements were made by which this aperture could be moved 1⁄20 in. at a time across the area struck by the jet. The height of the pressure column, for each position of the aperture, gave the pressure at that point of the area struck by the jet. When the aperture was 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 v2/2g. 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 diameter of the jet. Hence, roughly, the pressure due to the jet extends over an area about four times the area of section of the jet.
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.
| Height from Free Surface to Brass Plate in inches. | Distance from Axis of Jet in inches. | Pressure in inches of Water. |
| Experiment 1. Jet .475 in. diameter. | ||
| 43 | 0 | 40.5 |
| ” | .05 | 39.40 |
| ” | .1 | 37.5-39.5 |
| ” | .15 | 35 |
| ” | .2 | 33.5-37 |
| ” | .25 | 31 |
| ” | .3 | 21-27 |
| ” | .35 | 21 |
| ” | .4 | 14 |
| ” | .45 | 8 |
| ” | .5 | 3.5 |
| ” | .55 | 1 |
| ” | .6 | 0.5 |
| ” | .65 | 0 |
| Experiment 2. Jet .988 in. diameter. | ||
| 42.15 | 0 | 42 |
| ” | .05 | 41.9 |
| ” | .1 | 41.5-41.8 |
| ” | .15 | 41 |
| ” | .2 | 40.3 |
| ” | .25 | 39.2 |
| ” | .3 | 37.5 |
| ” | .35 | 34.8 |
| ” | .45 | 27 |
| 42.25 | .5 | 23 |
| ” | .55 | 18.5 |
| ” | .6 | 13 |
| ” | .65 | 8.3 |
| ” | .7 | 5 |
| ” | .75 | 3 |
| ” | .8 | 2.2 |
| 42.15 | .85 | 1.6 |
| ” | .95 | 1 |
| Experiment 3. Jet 19.5 in. diameter. | ||
| 27.15 | 0 | 26.9 |
| ” | .08 | 26.9 |
| ” | .13 | 26.8 |
| ” | .18 | 26.5-26.6 |
| ” | .23 | 26.4-26.5 |
| ” | .28 | 26.3-26.6 |
| 27 | .33 | 26.2 |
| ” | .38 | 25.9 |
| ” | .43 | 25.5 |
| ” | .48 | 25 |
| ” | .53 | 24.5 |
| ” | .58 | 24 |
| ” | .63 | 23.3 |
| ” | .68 | 22.5 |
| ” | .73 | 21.8 |
| ” | .78 | 21 |
| ” | .83 | 20.3 |
| ” | .88 | 19.3 |
| ” | .93 | 18 |
| ” | .98 | 17 |
| 26.5 | 1.13 | 13.5 |
| ” | 1.18 | 12.5 |
| ” | 1.23 | 10.8 |
| ” | 1.28 | 9.5 |
| ” | 1.33 | 8 |
| ” | 1.38 | 7 |
| ” | 1.43 | 6.3 |
| ” | 1.48 | 5 |
| ” | 1.53 | 4.3 |
| ” | 1.58 | 3.5 |
| ” | 1.9 | 2 |
As the general form of the pressure curve has been already indicated, it may be assumed that its equation is of the form