GATE 2026 CE (CE1) – Question 54
A wide unlined channel carries sediment-free water. The depth of water is 1 m. The specific weight of water is 10 kN/m$^3$. To prevent scouring, the maximum permissible tractive stress on bed is 10 N/m$^2$. The maximum slope of the channel bed to prevent scouring is 1 in $n$. The value of $n$ is ______ (*in integer*).
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 1000
Explanation
The tractive stress on the bed of a wide channel is $\tau = \gamma y S = 10000 \times 1 \times S$ N/m$^2$. Setting this equal to 10 gives $S = 0.001$, which is 1 in 1000.