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The discharge coefficient - experimental measurement of a dependence on density contrast

Synopsis At sufficiently high Reynolds numbers, the discharge coefficient C d associated with a sharply contracting flow through a square-edged opening is, in general, taken to be constant. The effect of buoyancy forces, due, for example, to temperature differences between the air on either side of the opening, is ignored. We hypothesise that the buoyancy force may result in a significant reduction in the discharge coefficient associated with the flow through a square-edged opening in a horizontal surface. We test this hypothesis by deducing C d from laboratory measurement of the two-layer stratification produced by a localised buoyancy source in an enclosure which ventilates passively in a displacement mode. Experiments were performed at small scale in a water tank using saline solutions to generate buoyancy forces. In the absence of a buoyancy contrast, the discharging flow contracts due to inertial effects giving C d ≈ 0.6. In the presence of a buoyancy contrast, our results show that the discharge through a horizontal vent takes the form of a rising plume-like flow, which may contract further giving a smaller value of C d . The plume-like discharge is characterised by conditions at the discharge opening, which we represent by a single dimensionless parameter Γ d - the discharge parameter . Our results demonstrate that once a critical value of Γ d is exceeded, C d exhibits a strong dependence on the density contrast and rapidly decreases with increasing Γ d . implications of a dependence of C d on density contrast are for potentially serious errors in the prediction of airflow rates if a constant value of C d is assumed.