For a triangular channel having a side slope of 1.5 Horizontal: 1 Vertical, the Froude number is given by (where, V = mean velocity of flow in channel and g = acceleration due to gravity)
- AF = V√1.5 / √(gy)
- BF = V / √(1.5 gy)
- CF = V√2 / √(gy)Correct
- DF = 1.5V / √(gy)
Solution
Concept
Froude number of a triangular channel
Formula
Fr = V / √(g D), D = A/T = y/2 ⇒ Fr = V√2 / √(g y)
Step-by-step solution
1. A = z y², T = 2 z y (z = side slope). 2. Hydraulic depth D = A/T = y/2. 3. Fr = V / √(g y/2) = V √2 / √(g y).
Explanation
The Froude number uses the hydraulic depth A/T, not the flow depth. For a triangular section A/T = y/2 for any side slope z, so the result does not depend on the slope of 1.5:1.
Shortcut
Triangular: D = y/2. Rectangular: D = y.
Common mistake
Bringing the side slope 1.5 into the formula.
Correct answer: C) F = V√2 / √(gy)