To summarise, in Figure 07.05.10 the complete 360 degree surface of the cone is shown four times one below the other. Since the wide part of the cone has a radius of 24 cm it has a circumference of about 150 cm (R24 and U150), while the narrow part has a radius of 16 cm and hence a circumference of about 100 cm (R16 and U100). The length of the side-surface is about 24 cm (H24). Using this example with these dimensions, the upward flow is along the indentations in the cone and along the walls of the cone.
The angle of entry of the water at the narrow circumference was assumed to be 30 degrees. Maintaining this steady angle would cause the water flow to cover an angular sector of about 150 degrees, exiting at that same angle. Due to the centrifugal force of water striking the wall at an angle, an upward force is generated which causes the water to follow a steeper track and exit after crossing a sector which spans only 120 degrees or so (S120) and exit at an increased angle of about 35 degrees. That track D (drawn in blue) is shown several times in the top diagram.
Water flowing in indentations will follow this track. However, this water can't follow the faster moving wider circumference at the top of the cone. In order to achieve the 'neutral-force' track for the complete path across the cone, the indentations need to have an increased backward curvature of one third. This indentation track H is shown in red and is contained within a sector of 40 degrees (S40) and this path is also drawn several times in the top diagram.
In order to have the turbine generate a mechanical turning force, the indentations need to be curved backwards more strongly. Here, for example, that sector was extended to cover 90 degrees (S90) so water is channelled outwards faster, and exits after covering only 70 degrees (S70). In the second diagram that indentation L (shown in red) and water track K (shown in blue) are drawn several times.
The indentations of the turbine are shown here as saw tooth-like notches which are open on their outer side. This arrangement results in two separate flows: on the one hand, there is forced flow within the indentations and on the other hand there is the free flow of water on the wall of the cone. In the third diagram, these indentations L (shown in red) are drawn several times as are the tracks of the free-flowing water D (shown in blue). These two paths cross each other at an angle of about 90 degrees.
Because free-flowing water projected upwards is too slow for the turbine-surface which is moving rather fast, but the water movement will be fast enough if it flows along the indentations L which are curved backwards as shown in the bottom diagram. In this diagram, both track D (shown in blue) taken by the free-flowing water and the indentation-forced track K (shown in red) are shown. Again, both flows are drawn several times and it can be seen clearly that these paths cross each other at an acute angle. The free-flowing water 'brushes' across the water which is flowing
forwards in the indentations. It does this in the direction of rotation and this causes the water flowing in the indentations to start revolving.
Water within the indentations becomes redirected backwards and transfers it's inertia to the pressure-sides of the indentations, thus decelerating it's forward motion. This water still has centrifugal force, but the further out it progresses, the faster the pressure-sides run away ahead of it. This water which is flowing 'too slowly' can only apply pressure to the walls if they were much more strongly curved backwards, and even in that case it would only be by a small angle which would impart practically no additional turning momentum.
Also, free-flowing water can't keep up with the faster movement of the turbine at its larger exit circumference. However, the outward water flow is easily fast enough to fill the grooves with water and produce additional rotation around its longitudinal axis. This revolving-water-cylinder effectively works like a gear wheel as it applies the pressure of the free flowing water on to the pressure-sides of the grooves. The water flowing along the cone-wall is not pressed into the grooves, and so it is not redirected and its forward motion is not decelerated. So the centrifugal forces of that free-flowing water can go on contributing to the turning momentum of the turbine, but only indirectly, by driving that water-cylinder within the grooves.
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