GATE 2023 AG – Question 60
A 10 m concrete pipe in a drop-inlet spillway carries1 m³/s with 4 m head. Entrance-loss coefficient.5 and friction coefficient.02;g=9.81 m/s². Find neutral slope in percent, to two decimals.
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Correct answer: 4.69 to 4.80
Explanation
The official accepted range is **4.69–4.80%**. Neutral pipe grade normally equals friction slope $S_n=fv^2/(2gD)$,with $v=4Q/(\pi D^2)$,so a diameter or a complete sizing/boundary convention is needed. For example, if the4 m head supplies entrance, pipe-friction and exit-velocity heads,$4=(.5+.02L/D+1)v^2/(2g)$. This gives D=.44780 m and $100S_n=9.18\%$,not the official range. Thus the printed data do not uniquely support4.75% without an additional diameter/design convention. The official key is preserved, and the standard equation plus this unresolved source assumption are stated rather than reverse-fitting a diameter.