Steeper Shorter and Faster

In Figure 07.05.04 the inner surface of the cone of Figure 07.05.03 is shown opened out to form a flat surface. The cross-lines shown are positioned to indicate each 30 degree strip of the conical surface. If a jet of water is projected into the lower edge of the cone at point A, at an angle of 30 degrees, then it will exit from the top of the cone at point B some 150 degrees later (sector S150). The angle of exit is also 30 degrees and the spiral track C, shown in blue, is the path followed during it's constant, steady rise though the cone.

The blue line D shows what happens when a jet of water is projected into the cone. It enters the lower edge of the cone at an angle of 30 degrees as before, but this time the water velocity is greater. As a result of this higher velocity, the water now exits from the upper edge of the cone at a steeper angle of about 35 degrees. That track D runs within a sector of the cone which spans only 120 degrees (S120) and so the track followed is shorter, steeper and covered more quickly than the jet of water flowing along the previous track C.

The diagram at the bottom right hand side of Figure 07.05.02, shows the cone as seen from the top. Track C with its constant rate of rise is shown, as is the steeper and shorter track D. The far side of the cone, shows several paths which indicate how the water flows if the angle of entry at the bottom of the cone, is increased in steps.

The diagram at the bottom left shows the cross-sectional view of the section of cone used in this discussion. It shows how the water enters at the bottom edge, moves along the inner wall and exits from the upper edge of the cone. The vector M shows the diagonal thrust of the water against the wall of the cone. This is the direct equivalent of the two forces G (against the wall) and H (upwards along the wall). Force H is much greater here than with the earlier example where the rate of upward movement was constant.

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