Thin Perforated Plate Head Loss
Calculates the pressure-drop loss coefficient and pressure drop across a thin perforated plate (plate thickness-to-hole-diameter ratio < 0.015) in a duct. The high Reynolds number (Re > 10⁵) regime is assumed.
Free Area Ratio
FAR=Total AreaOpen (Free) AreaThe FAR must be entered directly. For a plate with circular holes of diameter d on a square pitch p:
FAR=4π(pd)2Loss Coefficient
For thin plates (thickness / hole diameter < 0.015) at Re > 10⁵:
K=FAR2(0.7071−FAR+(1−FAR))2This expression is derived from sharp-edged orifice contraction theory. The factor 0.707 arises from the vena-contracta contraction coefficient for a sharp-edged opening (Cc ≈ 0.61–0.64), and represents viscous contraction of the jet as it enters each hole.
Pressure Drop
Δp=K⋅21ρV2where ρ is the air density and V is the mean velocity in the duct upstream of the plate.
Validity
- Plate thickness / hole diameter < 0.015 (thin plate assumption).
- Reynolds number Re > 10⁵ (high-Re, inertia-dominated regime).
References
- Idel'chik, I.E. and Fried, E., Flow Resistance, a Design Guide for Engineers, Taylor & Francis, Washington D.C., 1989, p. 260.