Verify the equation given in Table 11.1 for the hydraulic radius of a circular channel. Evaluate and plot the ratio R/D, for liquid depths between 0 and D.
The expression for the hydraulic radius of the circular channel and plot the ratio
Explanation of Solution
Calculation:
The area of the circular channel can be molded as the summation of two triangles and the segment of the chord.
Calculate the area of the circular channel
Calculate the hydraulic radius of the circular channel
Thus, the hydraulic radius of the circular channel is
Calculate the ratio between the hydraulic radius and the depth of the circular channel.
Calculate the relation between the height of the channel and the angle made by the channel surface.
For plotting the graph between
The values of
0.0000 | 0 | 0.0000 |
0.3927 | 0.0125 | 0.0096 |
0.7854 | 0.0498 | 0.0381 |
1.1781 | 0.1079 | 0.0843 |
1.5708 | 0.1817 | 0.1464 |
1.9635 | 0.2647 | 0.2222 |
2.3562 | 0.3499 | 0.3087 |
2.7489 | 0.4304 | 0.4025 |
3.1416 | 0.5000 | 0.5000 |
3.5343 | 0.5541 | 0.5975 |
3.9270 | 0.5900 | 0.6913 |
4.3167 | 0.6069 | 0.7778 |
4.1724 | 0.6061 | 0.8536 |
5.1051 | 0.5905 | 0.9157 |
5.4978 | 0.5643 | 0.9619 |
5.8905 | 0.5325 | 0.9904 |
6.2832 | 0.5000 | 1.0000 |
Plot the ratio
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