UHM 2021, VOL. 48 NO. 1 – AUTOMATED FRAME SELECTION IN POST-DIVE ECHOCARDIOGRAPHY UHM 2021, VOL. 48 NO. 1 – FLOW RESISTANCE AND COST OF SNORKEL BREATHING SHORT COMMUNICATION Breathing through a diving snorkel; theory and experiment of air flow resistance and cost of breathing N.A.M. Schellart, PhD 1,2 1 Biomedical Engineering and Physics, Amsterdam University Medical Centers, University of Amsterdam, Amsterdam, The Netherlands 2 Foundation for Dive Research (SDR), Aerdenhout, The Netherlands AUTHOR EMAIL: – [email protected] ____________________________________________________________________________________________________________________________________________________________________ ABSTRACT INTRODUCTION The snorkel allows a surface swimmer to observe the The side-mounted diving snorkel is a bent breathing tube underwater world through the face mask without being with a mouthpiece used by swimmers, typically while disturbed by inhaling. The effect of a snorkel on breathing looking though a half-facemask. In addition, swim fins resistance and cost is widely held to be substantial. This are used to reduce swimming effort. The facemask allows study aims to model these parameters and to measure the snorkeler to continuously observe the underwater indirectly the actual increases. Further, resistances of scenery and to breathe while remaining facedown at the differing designs and dimensions were assessed and surface. Swimming facedown with mask but no snorkel recommendations were made concerning use and choice. is uncomfortable. Snorkeling is also used by scuba divers Maximal voluntary ventilation in 12 seconds (MVV12) on the surface, in freediving and breath-hold diving in was measured in 19 volunteers seated on dry land with and underwater sports (e.g., underwater hockey), in pool without a classic J-type snorkel (inner diameter 20.5 mm). training and in monofin swimming. The extra and total resistances and costs were calculated Half a century ago the snorkel was a compulsory using the MVV12 data and using estimated airways resistance extrapolated from subject’s demography and spirometric device of the recreational diving gear, but nowadays literature data. many divers neglect to take a snorkel. A possible explan- ation is the assumption that a snorkel substantially in- MVV12 measurements with snorkel showed a minute -1 volume of 152 ± 38 L·min , 6.0±3.7% lower than without creases breathing resistance. -6 snorkel (p = 7.0x10 ). The theoretical MVV12, calculated There is extensive literature on the respiratory effects from snorkel and airways resistances, decreased by 3.2%. of breathing though a tube. However, these studies – for -1 Experimental total breathing resistance (457 ± 83 Pa·s·L ) example reference [1] – examined the tubes of clinical -7 was 6.5 ± 3.2% higher than without snorkel (p = 2.6x10 ), ventilators. Because in outdated machines these tubes but the total mechanical breathing cost was unaffected by add a dead space of 1-1.5 liters (L), which is about five the snorkel (13.58 Watts with; 13.64 Watts without). Divers’ times that of a snorkel, the findings are not relevant to estimations of resistance increase were exaggerated (8.8% at this study. rest, 23% swimming). Classical J-type snorkels with an inner Although snorkel resistance is dependent on the di- diameter ≥19.5 mm add 3-16% resistance . There is no risk mensions of the snorkel, snorkels for adults do not of hypercapnia. differ much in length or inner diameter (< 8%). Scuba divers are recommended to use their snorkel to The use of a snorkel or breathing tube increases breathe more comfortably on the surface. It is recommended FiCO2 (CO2/carbon dioxide fraction in inhaled gas) the snorkel be made a mandatory safety accessory. The best due to its dead space, which could result in hypercapnia multipurpose snorkel (19-21 mm) has no top appendages [2,3]. Although reducing the tube diameter reduces dead and no water release valve. space, it also increases flow resistance which in turn ________________________________________________________________________ increases the work of breathing. This may result in a KEYWORDS laminar; turbulent; spirometry; airways; modeling hypercapnic effect reducing the advantage of the Copyright © 2021 Undersea & Hyperbaric Medical Society, Inc. 81 UHM 2021, VOL. 48 NO. 1 – FLOW RESISTANCE AND COST OF SNORKEL BREATHING smaller dead space. In this study hypercapnia is ad- However, often the respiratory minute volume (RMV) dressed only in passing, the focus being on resistance, is so high that the airflow in the snorkel is turbulent. ventilatory capacity and breathing expenditure. With MVV, the flow in the snorkel is always fully tur- This study aims to quantify the snorkel’s flow resis- bulent (Resnorkel > 15.000). For turbulent flow the resis- tance and its effect on respiratory cost for a large range of tance of the tube is (rewritten from eq. 14 of ref. [4]): respiratory minute volumes (RMV). This resistance and 5/2 -7/4 -19/4 1/4 3/4 3/4 -1 (2b) Rtube = 2 π LD η V’ ρ (Pa∙s∙L ) extra breathing cost were calculated using a physical model for laminar and for turbulent flow. The calcula- The basic difference between these equations is that tions used both hypothetical low and intermediate flows, the latter is flow-dependent (~V’0.75). as well as actual flows which were obtained from maximal voluntary ventilation (MVV) of volunteers mea- Flow resistance of a snorkel sured by spirometry. A snorkel can be divided into several sections, all with When a snorkel has a substantial resistance compared measurable axial lengths, diameters and curvatures. to that of the airways one would expect a substantial The resistance of the straight part (Rst) can be calcu- reduction in MVV. It is assumed that in an MVV exper- lated using (eq. 2a) for laminar flow and with (eq. 2b) iment with snorkel (WiSn) and without snorkel (NoSn) for turbulence. The bends result in extra resistance that the total cost of breathing is the same. Then, using the can be, expressed by the Hütte correction coefficient calculated snorkel resistance and an estimated airways ζi with i the bend number. When calculating the resis- resistance, the decrease in MVV WiSn – as opposed tance of each bend, Rst was used as the reference. The to NoSn – can be predicted. This prediction is tested resistance of a snorkel, Rsnorkel is the sum of the resis- by comparison with the actual decrease obtained by tance of the straight part and the n bends: dry spirometric measurements of the subject’s MVVs. n Resistances can also be measured directly in a physical (3) Rsnorkel = Rst + Rst ∙ Σ(1+ζi)(Li /Lst) experimental setup. However, this was not considered to i=1 be beneficial in terms of accuracy (see Discussion). where Li is the axial length of the i-th bend. It is Since no similar study has been previously conducted assumed that the flow is continuous. it is difficult to speculate over the contribution of a The one snorkel used in all the physiological experi- snorkel to resistance and cost of breathing. ments by all subjects was of classic J-type design, made of rubber without appendages at the top and without a MATERIAL AND METHODS water release valve. The tip-to-tip length was 36 cm with Theory of flow resistance and cost of breathing a total axial length of L= 42.3 cm, an inner diameter of Laminar and turbulent flow 20.5 mm and a volume of 136 mL. It comprised a To calculate the resistance of a tube, the flow-depen- straight section Lst of 23.8 cm, followed by three bends: dent Reynolds number Re should first be calculated: a gentle bend (22.5°; L1 13 cm; ζ1 = 0.045), a sharp bend -1 -1 -1 (1) Re = 4V’ρπ D η (60°; L2 = 2.5 cm; ζ2 = 0.21) and finally the rubber mouthpiece (80° bend, L = 2 cm; ζ3 = 0.7). To be able where V’=flow (m3∙s-1); D=inner tube diameter (m); 3 to generalize our findings we also examined a similar ρ=gas specific mass at 28°C (the estimated average J-type snorkel and two J-types with a water purge of inhaled and exhaled gas) at 1 bar (dry air), being 1.17 valve, all with different dimensions. kg∙m-3; η=dynamic viscosity (18.9 x 10-6 Pa∙s-1 at 28°C). Laminar flow happens at Re < 2300 (with our snorkel Extra cost of breathing at a stationary flow this corresponds to < 16 L∙min-1). The flow-dependent mechanical work W, of the flow Flow is fully turbulent at Re > 2900 (flow > 24 L∙min-1). through a tube is: In between is the transition zone. 2 For laminar flow of a fluid through a straight tube (4) W = V’ Rtube with length L (m) and a smooth surface Poiseuille’s where Rtube is Rsnorkel, the airways resistance Raw (see be- law applies, yielding the flow resistance: low) or Raw + Rsnorkel. (Note: metabolic W is about 4.5 4 -1 (2a) Rtube = 128ηL/(πD) (Pa∙s∙L ) times higher.) For laminar flow the mechanical cost 82 Schellart NAM UHM 2021, VOL. 48 NO. 1 – FLOW RESISTANCE AND COST OF SNORKEL BREATHING UHM 2021, VOL. 48 NO. 1 – FLOW RESISTANCE AND COST OF SNORKEL BREATHING depends strongly on the flow (~V’2) and even more so A short questionnaire (Quest1) was presented to dive for turbulent flow (~V’2, 75; eq. 2b substituted in eq. 4). physicians asking them to estimate the relative differ- In this calculation it is assumed for the sake of simpli- ence in breathing resistance between the conditions city that flows during inhalation and exhalation are WiSn and NoSn for a theoretical swimmer who is equal. However, the flow under the MMV12 protocol is swimming moderately fast (turbulent flow in snorkel).