Section 4: Soil and Water Conservation Engineering
Fluid Mechanics
Subtopic: Flow through orifices, weirs and notches
Question Statement:
Water is discharged from a tank through a rectangular orifice of width 1.5 m and height 1.2 m. The water level in the tank is 3.5 m above the top edge of the orifice. If the coefficient of discharge of this orifice is 0.62, the discharge through the orifice in m³·s⁻¹ is ______. [round off to 2 decimal places] (Take acceleration due to gravity, g = 9.81 m·s⁻²)
Official Answer Key:
9.90 to 10.10
Step-by-Step Solution & Explanation
For a large rectangular orifice (submergence comparable to orifice height, so the standard integrated formula is used), Q = (2/3)Cd·b·√(2g)·(H₂^1.5 − H₁^1.5), where H₁ = 3.5 m (head to top edge) and H₂ = 3.5+1.2 = 4.7 m (head to bottom edge). √(2×9.81) = 4.4294. H₂^1.5 = 4.7^1.5 = 10.189; H₁^1.5 = 3.5^1.5 = 6.548; difference = 3.641. Q = (2/3)×0.62×1.5×4.4294×3.641 = 10.0 m³/s.
Section 5 — Irrigation and Drainage Engineering
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.