🎯 Flow through a Circular Orifice
A constant-head tank discharges a jet through a sharp-edged 12 mm orifice. Trace the jet's parabola with the hook gauge to get the coefficient of velocity Cv, time the discharge for the coefficient of discharge Cd, and split out the coefficient of contraction Cc = Cd/Cv — the signature of the vena contracta.
Aims
To determine, for a sharp-edged circular orifice, the coefficient of velocity, the coefficient of contraction and the coefficient of discharge — maintaining a constant head, measuring the jet trajectory (x, y) and the discharge.
Theory
Torricelli: Videal = √(2gH) • trajectory: Cv = x / (2√(y·H)) • Cd = Qactual / (A·√(2gH)) • Cc = Cd/Cv
The streamlines converge on the opening from all directions, so the jet keeps contracting to the vena contracta just outside the plate — the real jet is both slightly slower (friction → Cv ≈ 0.96–0.98) and markedly narrower (contraction → Cc ≈ 0.64) than the ideal, giving Cd ≈ 0.62. The jet centreline is a projectile parabola: measuring a fall y over a horizontal run x recovers its launch velocity.
Apparatus
Constant-head tank with a sharp-edged side orifice; hook gauge and scale on a traversing rail; collector tank and stopwatch; vernier calliper.
Orifice d = 12 mm (sharp, bevel outward) Datum at orifice centre-line Typical: Cv ≈ 0.96 · Cd ≈ 0.62 · Cc ≈ 0.64
Procedure — perform it here
Observations & Computations
Repeat for several heads. A = 1.131×10⁻⁴ m². Cv = x/2√(yH); Cd = Q/(A√(2gH)); Cc = Cd/Cv.
| No. | H (cm) | x (cm) | y (cm) | Cv | Vol (L) | t (s) | Q (L/s) | Qth (L/s) | Cd | Cc |
|---|---|---|---|---|---|---|---|---|---|---|
| No readings yet — set the head, read the hook gauge, collect, then Record. | ||||||||||
Results
Calibration — Q vs √H
Torricelli makes Q linear in √H; the fitted slope gives Cd·A·√(2g).
Discussion
Why is Cc so much smaller than Cv?
Friction at a sharp edge is minimal, so the jet loses little speed (Cv near 1). But the streamlines approach the opening radially and cannot turn a sharp corner instantly — they keep converging past the plate, shrinking the jet to the vena contracta at roughly 64% of the orifice area. Contraction, not friction, is what limits the discharge.
Why use a sharp edge with the bevel outward?
It gives the fluid a single, well-defined separation line and minimum contact with the plate, so the contraction is repeatable and the frictional loss negligible — which is what makes tabulated coefficients reliable.
Main error sources
Head fluctuation if the overflow is overwhelmed, judging the jet centre-line with the hook gauge (the jet thickens and wobbles downstream), timing errors over short collections, and the jet's slight spread from air drag at large x.
Precautions: keep the head truly constant (steady overflow) before every reading; measure x from the vena contracta plane and y from the orifice centre-line datum; take trajectory readings at several x and use the farther ones cautiously; collect for at least 60 s.