Pressure Drop and Flow Characteristics of Short Capillary Tubes at Low Reynolds Numbers

The pressure drop and flow characteristics of short capillary tubes have been investigated experimentally for length-to-diameter ratios varying from 0.45 to 18 at diameter Reynolds numbers ranging from 8 to 1500. In the range of the dimensionless modulus (Lμ)/(VD²ρ) from 4 × 10⁻³ to 3 to 10⁻¹, the experimental data agree within 15 per cent with a mathematical theory by Langhaar (1). At a value of (Lμ)/(VD²ρ) of about 0.3 the experimental data approach the Poiseuille laminar-flow theory (2). For very short tubes (L/D < 0.5) the experimental results deviate from Langhaar’s theory at values of Lμ/VD²ρ less than 4 × 10⁻³, and at Lμ/VD²ρ equal to 5 × 10⁻⁴, the pressure drop is twice as large as that predicted by Langhaar’s theory (1). The experimental results for tubes having very short aspect ratios are in agreement with data obtained by Zucrow (12) with short square-edged jets. It was found that the flow rate $Q˙$ through a short capillary tube can be related empirically to the over-all pressure drop $Δp¯$ raised to a power N. The exponent N is a function of the length-to-diameter ratio L/D varying from 0.5 at L/D equal to 0.45 to 0.91 at L/D of 18. The trend of the curve suggests an asymptotic approach to unity, the exponent for Poiseuille-type flow. The results of this study have application to: (a) Simulating flow through screens, doors, cracks, and fissures in small-scale model testing of buildings in atmospheric wind tunnels. (b) Automatic control devices where capillary tubes are used as hydraulic resistances in a larger line and in nozzle-flapper combinations. (c) Heat pumps and air-conditioning equipment where short capillary tubes are used as two-way control valves. (d) Flow through compact heat exchangers and porous materials.