ANS:E - all the above.

For the most economical trapezoidal section of a channel with regards to discharge, the required condition is: All the above. Let's break down each condition:

1. Half of top width = sloping side: This condition ensures that the trapezoidal section is symmetrical, which can help in achieving uniform flow and efficient hydraulic performance.
2. Hydraulic depth = half the depth: Hydraulic depth is the cross-sectional area divided by the top width. When the hydraulic depth is half the depth, it suggests an efficient distribution of flow and hydraulic forces within the channel.
3. Perpendiculars drawn from the centre of the top width onto the bottom sloping side are all equal: This condition ensures uniformity in the geometry of the trapezoidal section, contributing to consistent flow patterns and hydraulic characteristics.