Drainage of liquid from a small circular hole in a vertical wall

Figures & data

Figure 1. A side, cross-sectional depiction of a fluid handling component with a small circular hole of diameter (D) in one of its vertical walls. (a) Liquid with a surface tension and density of γ and ρ rises vertically past the hole to a height of h without flowing through it. (b) The liquid reaches a critical height of h_i, where θ ≥ θ_a and (c) flow through the hole begins. (d) As the hole drains, the height of the liquid eventually falls to a critical height of h_f where θ ≤ θ_r and flow ceases.

Table 1. Properties of the liquids.

Liquid	γ (mN/m)	ρ (kg/m^3)
Isopropyl alcohol (IPA)	22	789
Ethylene glycol (EG)	47	1110
Water (W)	72	998

Table 2. Advancing and receding contact angles (θ_a and θ_r) of the various liquids on the solids.

Solid	Liquid	θa (°)	θr (°)
PP	IPA	15	5
	EG	68	54
	W	90	69
FEP	W	107	93

Figure 2. Plots of the critical liquid heights to initiate and terminate flow (h_i and h_f) through a small circular hole of diameter D. The points are experimental data. The error bars represent standard deviation in the measurements. The curves are theoretical estimates from Equations (6(6) )–(9(9) ). The black, solid curves are for water (W), the green, short-dash curves are for ethylene glycol (EG) and the blue, long-dash curves are for isopropyl alcohol (IPA).