χ = 2a + b.
Putting these values in (1),
ac + 1⁄2 bd = (a + 1⁄2 b) d; and hence c = d.
| Fig. 115. |
| Fig. 116. |
That is, EF, EG, EH are all equal, hence a semicircle struck from E with radius equal to the depth of the stream will pass through F and H and be tangential to the sides of the channel.
To draw the channel, describe a semicircle on a horizontal line with radius = depth of channel. The bottom will be a horizontal tangent of that semicircle, and the sides tangents drawn at the required side slopes.
The above result may be obtained thus (fig. 116):—
χ = b + 2d / sin β.
(1)