What is the discharge through the venturi flume built in a rectangular channel 1 m wide and having its throat width 0·4 m? The upstream head is 0·57 m, measured head in throat is 0·5 m and the value of Cd is 1.
- A210 L/s
- B230 L/s
- C250 L/sCorrect
- D270 L/s
Solution
Concept
Discharge through a venturi flume
Formula
Q = Cd A₁A₂ √(2g h) / √(A₁² − A₂²)
Step-by-step solution
1. A₁ = 1 × 0.57 = 0.57 m²; A₂ = 0.4 × 0.5 = 0.20 m². 2. Head difference h = 0.57 − 0.50 = 0.07 m; √(2gh) = √(1.3734) = 1.172 m/s. 3. Q = 0.57 × 0.20 × 1.172 / √(0.57² − 0.20²) = 0.1336 / 0.5338 = 0.250 m³/s = 250 L/s.
Explanation
A venturi flume works like a venturimeter in an open channel. The discharge follows from the areas at the upstream section and at the throat and the difference in water depth.
Why the other options are wrong
210, 230 and 270 L/s do not match the calculated 250 L/s.
Shortcut
Same formula as a venturimeter with A = width × depth.
Common mistake
Using the throat width in place of areas.
Correct answer: C) 250 L/s