Question

A trapezoidal open channel with a base width of 4 m and side slope 1 horizontal to 2 vertical carries water at a depth of 2 m. The flow area of section is

• A. 16 m$^2$
• B. 12 m$^2$
• C. 10 m$^2$
• D. 8 m$^2$

Hint:

The most common error in trapezoidal channel problems is misinterpreting the side slope.
Always be sure what 'm' represents. The standard formula $A=(B+my)y$ assumes $m$ is the horizontal component for a 1-unit vertical component.
If the slope is given as "X horizontal to Y vertical," then $m = X/Y$.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
Trapezoidal channel: base 4m, depth 2m, side slope 1H:2V. Find flow area.

Step 2: Key Formula (Alternate):
A = (B + my)y. m = horizontal per unit vertical. Given 1H:2V → m=0.5.

Step 3: Detailed Explanation:
A = (4 + 0.5×2)×2 = (4+1)×2 = 10m². Top width = B+2my = 4+2=6m. Wetted perimeter = B+2y√(1+m²).

Step 4: Final Answer:
10 m².