📐 Operation Characteristics of Three Flow Meters
A virtual re-creation of the flow-measurement apparatus: a venturi meter, orifice plate and rotameter installed in series, read from an air-pressurised manometer bank. Compare each meter against the catch-tank-and-stopwatch standard, and measure the energy loss each device — plus the wide-angle diffuser and 90° bend — costs you.
Objectives
(1) Familiarise with common flow-measurement devices; (2) compare each meter with the standard timed volumetric collection; (3) determine the energy loss incurred by each device; (4) determine the loss in a rapid enlargement and a 90° elbow.
Theory
For steady incompressible flow, Bernoulli's equation with a loss term between two tappings gives each meter's working formula:
Venturi: Q = A_B·√( 2g(h_A−h_B) / (1−(A_B/A_A)²) ) • Orifice: Q = C·A_F·√( 2g(h_E−h_F) / (1−(A_F/A_E)²) ), C = 0.601 • Rotameter: l ∝ Q (linear calibration)
The venturi accelerates the flow gradually, so its loss is small; the orifice plate is cheap but its abrupt contraction and vortices cost a large loss (ΔH ≈ 0.83(h_E−h_F)); the rotameter's float rides in a tapered tube, and the head loss across it (h_H−h_I) is nearly constant ≈ 100 mm regardless of discharge — which is exactly why its scale is linear.
Apparatus
Hydraulics bench with volumetric tank & stopwatch; flow-measurement apparatus with pressure tappings to an air-pressurised manometer bank (tubes A–I); flow-control valve; hand pump for purging.
Venturi: A = 26 mm, throat B = 16 mm Orifice: pipe E = 51.9 mm, C = 0.601, vena contracta F = 20 mm Diffuser C→D: area 1:4 Bend G→H: 51.9 → 40 mm
Procedure — perform it here
Observations & Computations
Take ~10 tests at increasing valve openings. Q from each meter is back-computed from the manometer readings using the theory equations; the error is relative to the bench timed collection. ΔH columns are the measured energy losses (mm of water): venturi h_A−h_C, orifice 0.83(h_E−h_F), rotameter h_H−h_I, diffuser and bend from the kinetic-head-corrected piezometric drops.
| No. | l (mm) | Vol (L) | t (s) | Qbench (L/s) |
Qventuri | Qorifice | Qrotameter | ΔHvent | ΔHorif | ΔHrot | ΔHdiff | ΔHbend |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| No tests yet — set the valve, run a timed collection, then press “Record test”. | ||||||||||||
Meter calibration vs the bench standard
Each meter's computed discharge plotted against Qbench. Points on the 1:1 line mean perfect agreement — see which meter tracks it best.
Discussion & Conclusions
Which device would you recommend for flow measurement?
The venturi is the most accurate (typically within ~2%, and even that bias comes from neglecting its discharge coefficient C ≈ 0.98) and wastes the least energy — but it is long and expensive. The orifice plate is compact and cheap and, once its C is known, also accurate — but it dissipates by far the most head. The rotameter reads directly and linearly but is a fragile, vertical-only glass instrument of moderate accuracy. Choose by constraint: accuracy & low loss → venturi; cost & retrofit → orifice; convenience → rotameter.
Advantages and disadvantages of each device
Venturi: + low permanent loss, accurate, no moving parts; − long, costly, fixed installation. Orifice: + cheapest, fits between existing flanges, easily replaced; − large permanent head loss, C sensitive to wear and installation. Rotameter: + direct linear reading, good rangeability, cheap; − must be vertical, glass tube fragile, float sticks with dirty fluids, constant head loss even at low flow.
Why must the rotameter have a slightly diverging (tapered) cross-section?
The float rests where the upward drag equals its submerged weight — which requires a fixed velocity through the annular gap around the float. To pass a larger discharge at that same gap velocity, the gap area must grow, so the tube bore must increase with height. The taper makes the float's equilibrium height — and hence the scale reading — approximately proportional to discharge.
Precautions: purge all air from the manometers and pressurise the bank to a convenient level before starting; keep the purge valve closed during readings (levels creeping upward mean it leaks); wait for steady flow before each timed collection; tap the manometers gently to dislodge trapped air.