Question

What is the value of the included angle between two adjacent sides of the absolute best hydraulic trapezoidal open channel?

• A. \(60^\circ\)
• B. \(30^\circ\)
• C. \(120^\circ\)
• D. \(90^\circ\)

Hint:

For the most economical trapezoidal channel, \[ \boxed{ \theta=60^\circ \text{ (side with horizontal)} } \] Hence, the included interior angle is \[ \boxed{120^\circ.} \]

Answer 1

The Correct Option is C

Step 1: Picture the ideal trapezoidal shape.
A trapezoidal channel carries the maximum discharge for a given area when a semicircle can be inscribed inside it, touching the bed and both sloping sides. This is the geometric signature of the most economical section, and it fixes how steep the sides must be.
Step 2: Find the slope of the sides.
For this ideal geometry, each sloping side must make an angle of $60^\circ$ with the horizontal bed, a standard result that follows from the inscribed semicircle condition.
Step 3: Get the angle between the two adjacent sloping sides.
Since each side rises at $60^\circ$ from the bed, the two sides meet the bed direction from opposite ends, so the angle included between them, measured through the channel, works out to $180^\circ - 60^\circ = 120^\circ$.
\[ \boxed{120^\circ} \]