Civil Engineering > GATE 2026 SET-1 > Open Channel Flow
A wide unlined channel carries sediment-free water. The depth of water is 1 m. The specific weight of water is 10 kN/m3. To prevent scouring, the maximum permissible tractive stress on bed is 10 N/m2. The maximum slope of the channel bed to prevent scouring is 1 in n. The value of n is ______ (in integer).
Correct : 1000
The bed shear stress (tractive stress) in an open channel is given by τ = γ × R × S, where γ is the specific weight of water, R is the hydraulic radius, and S is the bed slope.
For a wide channel the hydraulic radius R equals the depth of flow y = 1 m.
Setting the tractive stress equal to the maximum permissible value:
τmax = γ × y × S
10 = 10,000 × 1 × S
S = 10/10,000 = 1/1000
Since the slope is expressed as 1 in n, we have n = 1000.
Any slope steeper than 1 in 1000 would produce a bed shear stress exceeding 10 N/m², causing scouring of the unlined channel bed. The maximum safe slope is therefore 1 in 1000.
Correct answer: n = 1000 ✓
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