Predicting the possible flow that can be delivered through an IV catheter is of interest to clinicians and can help to guide catheter selection. The Hagen-Poiseuille formula

describes flow in specific circumstances through a circular cross-sectional tube when that flow is laminar and is often used to understand the various factors that can influence flow rate through an IV catheter.^{1} The alternative to laminar flow is turbulent flow, which is less easy to describe mathematically and does not have the same relationship between flow rates and fluid type or tube geometry. In the real world, predicting flow through a tube is especially difficult since laminar and turbulent flow can occur within the same tube. Reynolds number (*R*e) indicates the likelihood of turbulent flow occurring, being more likely at higher numbers. A transition of 2000–2300 is commonly used as the point above which turbulence is very likely^{1}; however, this is only the case for fully developed laminar flow in a long, straight, circular, cross-section tube. Flow through an IV cannula should ideally be laminar in the clinically useful range.^{2} However, previous work suggests that turbulent flow occurs in some clinical situations.^{3}

Each cannula manufactured is required to have its maximum flow rate quoted on the packaging as measured by a standard test, BS EN ISO 10555–5:1997.^{4} This test uses flow through a perfectly straight cannula into an open receptical and does not simulate the clinical use of cannulae where fluid flows into blood flowing within a vessel (Fig. 1). However, published flow rates may be useful for predicting flow in clinical situations. A clinician must be able to select the correct cannula for each clinical situation, especially if peripheral veins are scarce and central veins are best avoided. They should also be able to predict the effect of various maneuvers on the flow rate to optimize flow for each situation. The goal of this study was to compare manufacturers’ quoted flows to flows obtained through cannulae under simulated clinical conditions. Furthermore, we wanted to determine if flow is laminar or turbulent at clinically useful flow rates and identify some empirical predictors of flow.

## METHODS

### Description of the Model

Figure 2 illustrates the clinical model we used to measure flow through a cannula. The “venous reservoir” is a large bell jar (Simax borosilicate glass, 10 L capacity; Sklárny Kavalier, Co. Czech Republic). This was connected via a nonreturn valve (Cardiff anti reflux valve; Vygon, Uxbridge, UK) and three-way tap (Becton Dickinson Connecta, Helsingborg, Sweden) to a “vein” consisting of 50 cm of 6.5 mm internal diameter (ID) red rubber tubing (Fisherbrand–Fisher Scientific, UK) held horizontally. Fluid is passed through this “vein” to represent blood. The fluid flow rate from the “venous reservoir” varied between 20–30 mL/min at a fixed pressure of 10 cm H_{2}O. The test cannula was inserted halfway along this vein using the standard technique at approximately 20 degrees above the horizontal, and test fluid flowed through the cannula into the flowing “blood.” The fluid was administered from a single, emptied and washed, 1000 mL Freeflex bag (Fresenius Kabi, Warrington, UK) that had contained Hartmann’s solution, refilled with a measured volume of the desired fluid through a double chamber IV administration set (Universal Hospital Supplies, Enfield, UK). This was connected via a three-way tap to a length of tubing and the cannula under test.

### Standard Conditions

All fluids and equipment were maintained at room temperature and pressure. Before each measurement, the Systemic Filling Pressure was checked and set to 10 cm H_{2}O by altering the volume of deionized water in the venous reservoir. After attaching the IV tubing to the cannula, the cannula filling pressure was measured using the manometer and set by altering the height of the bag. Three examples of each of 14–20 standard wire gauge (SWG) Versatus-W cannulae (Terumo UK, Knowsley, Merseyside, UK) were inserted in turn into the vein using the standard technique. Flow was measured as the difference in volume of the bag before and after fluid infusion divided by the duration of the infusion. Flow through both vein and cannula was started simultaneously and continued until approximately 100 mL had flowed out or 30 s had passed, whichever was longer. Two experiments were performed.

### Experiment 1

The cannula filling pressure was set to 100 cm H_{2}O. Deionized water, Hartmann’s solution and Gelofusine (B Braun Medical, Sheffield, UK) were used in turn.

### Experiment 2

Using the same model with deionized water as infusion fluid, we varied the cannula filling pressure by varying the height of the fluid bag and measured flow through the same cannulae. The filling pressures tested were 10, 20, 30, 40, 50, 60, 70, 80, 90, and 100 cm H_{2}O.

### Analysis

SPSS v14 (SPSS, Chicago, IL) was used for data analysis. A repeated measures analysis of variance with a Scheffé correction for *post hoc* analysis was used to test whether the effect of fluid type on flow rate was significant. A *P* value <0.05 was taken to indicate significant effect.

SPSS v14 (SPSS, Chicago, IL) was also used to calculate best fit constants for curves of the form 𝑄̇ = *a* × *P*_{b} and 𝑄̇ = *c* = *ID*_{d}. The relationship between flow (𝑄̇) and pressure (*P*) is linear during fully developed laminar flow; therefore, the constant *b* should be 1 and, during fully developed turbulent flow, the constant *c* should be 0.5. During laminar flow, the relationship between flow and ID is quartic, i.e., the constant *d* should be 4, whereas in turbulent flow the relationship is not constant. Theoretical flow rates if flow were laminar were calculated from the manufacturer’s given dimensions for length (*l*) and radius (*r*) and the viscosity of water (η) of 1.002 cP;

Poiseuille’s Law was used:

where δ*P* was taken to be the pressure at the proximal end of the cannula, assuming the distal end to have no pressure.

*R*e was calculated

where ρ was taken as 1000 kg/m^{3}, and the fluid velocity,

## RESULTS

The characteristics of the cannulae used are shown in Table 1. Five sizes of cannula were used, 3 of each giving 15 cannulae in total. For Experiment 1, 135 measurements were made by measuring flow through each cannula in triplicate for each of the three fluid types. The mean flow (mL/min) in Experiment 1 increases progressively as the cannula size increases. Our measurements show the same pattern of change in flow with cannula size as the quoted flow by the manufacturers. The highest mean flow measured using deionized water in a 14-gauge cannula was 209 mL/min (Table 2) and that for quoted flow is 290 mL/min (Table 1).

### Use of Quoted Flows

Table 2 shows the ratio between the measured and quoted flow for each fluid and cannula size. The ratios vary within each type of fluid and between fluid types, but all measures were consistently less than the manufacturer’s quoted flow rates. Using repeated measures analysis of variance on the data from Experiment 1, there is an overall significant effect of fluid type on flow (*P* < 0.0001). A *post hoc* analysis confirmed that there are significant differences between all possible pairs of fluid in Experiment 1 (Gelofusine and Hartmanns, Gelofusine and deionized water, Hartmanns and deionized water) (*P* < 0.0001). Mean flow (mL/min) was greatest with Hartmanns than with deionized water, Gelofusine having the lowest mean flow.

Flow at the manufacturer’s quoted rate is not laminar: The best curve fit is 𝑄̇ = 113.3 [1.41] × *ID*^{2.21 [0.05]} (mean [standard error]).

### Laminar or Turbulent Flow

The calculated best curve fit of flow against pressure for each size of cannula is shown in Table 3. The constant b in Table 3 is <1 (nonlinear relationship between flow (𝑄̇) and pressure [P]) for all cannulae tested and more than 0.5 (flow not fully turbulent). Table 4 shows the best curve fit of flow against diameter for each pressure. It clearly shows that the relationship between our measured flow and the ID is not quartic, it is double for the flows at the 10 different pressures tested.

In Experiment 2, using the same cannulae, flow through each cannula was measured in triplicate at 10 different infusion pressures, yielding 450 measurements. Flow through each cannula for varying pressures in Experiment 2 is shown in Figure 3 and Table 5. The data show a flow pattern consistent with the Hagen-Poiseuille formula. As the pressure head increases from 10 to 100 cm H_{2}O, the flow of deionized water increases with increasing cannula size.

## DISCUSSION

The results of our study indicate that, under our simulated clinical conditions, the actual flows which can be delivered through IV cannulae are consistently less than those published by the manufacturer. Furthermore, the factors that influence flow through the cannulae do not follow the relationships predicted by Poisseulle’s law. In particular, although radius is the single most important factor affecting flow, the fourth power rule cannot be used. This is because flow is not just laminar; it is most likely a mixture of both laminar and turbulent flow.

This study is based upon a laboratory model which is intended to be more clinically relevant than the model used by the manufacturers to determine published flow rates. There are, however, a number of limitations to the model relevant to true clinical conditions. The model vein does not have all the characteristics of a real vein. In particular, the distal end is open, therefore the back pressure on the cannula cannot vary, as in a real vein. Experienced clinicians are well aware of the effect of position of the catheter in a vein, which can reduce flow to zero in some cases. The model blood is also not real, and therefore will not demonstrate the same flow characteristics as real blood. In particular, the tendency of cells to flow in the middle of the vein and plasma around the outside cannot be replicated. This effect decreases the apparent viscosity of blood at high flows.

The results of our study indicate that flow through a cannula is not a consistent ratio of the quoted maximum flow. This severely limits the application of the standard quoted values to clinical practice. It is not possible to predict from these values what the flow will be, even if the type of fluid and feeding pressure are also known. Flow at the manufacturer’s quoted rate is turbulent. Flow through the cannulae is always turbulent within the measured range of flows. Poiseuille’s law is therefore not useful in trying to predict the flow in any given situation, or the effect of changes made to the system by the clinician. One cannot predict that doubling the infusion pressure will double the resulting flow. In fact, the pressure must be quadrupled to double the flow. Trainees are often encouraged to insert large bore cannulae with the adage that doubling the radius gives 16 times the flow. In fact, the relationship here is nearer to a quadratic than quartic. Nevertheless, the radius of the cannula is still the most significant factor influencing flow.

*R*e is often below 2000 even though flow was likely to be turbulent in our experiments. The common understanding is that the type of flow is determined by *R*e. However, two points are relevant here: first, that *R*e only is related to the probability of turbulence occurring, and second, that there are many other determinants that must also be considered. Many investigators have evaluated the infusion flow rate with different sizes of conduction tubes and IV catheters.^{5–7} Philip and Philip,^{8} in their work on flow in the IV infusion system, proposed a binomial model, P = *R*_{L}F + *R*_{T}*F*^{2}, to define the relationship between the flow rate (*F*) and driving pressure (P) in a pressurized IV infusion system without including the gravity head. *R*_{L} and *R*_{T} are the coefficients of laminar and turbulent flow, respectively; the sum of both values for the components utilized in an infusion system will influence the dynamics. Our findings are consistent with the fact that turbulent flow occurs in IV systems even at a very low *R*e. We agree with Philip and Philip^{8} that there is a combination of laminar and turbulent flows within the fluid administration system, and pressure losses from both types of flow characteristics due to the attached IV tubing need to be considered when evaluating the performance of cannulae.^{9} Poiseuille described flow of a Newtonian fluid through a straight, circular cross-section cylinder. In a clinical setting, meeting these conditions is impossible. Even if these conditions could be met, we believe laminar flow would still not occur. After a discontinuity in a tube that creates eddies, a length of at least 20 times the diameter is required for the eddies to diminish and laminar flow to return. There is an insurmountable discontinuity in clinical systems where the giving set joins the cannula and the diameter of tubing necessarily decreases dramatically. Interestingly, the ratio between length and diameter of these cannulae varies from 29 to 42, suggesting that approximately the distal half of the cannula could have laminar flow if all other conditions were met.

The lowest measured flow is 11.62 mL/min, which is approximately 600 mL/h. This is not an unusual flow rate during anesthesia, but is toward the upper limit of what is commonly used. The results of this study clearly show the discrepancy between quoted values and factors influencing flow rate. Although we have not measured flow below this rate, turbulence is likely to continue for the reasons given above.

We have not found an easy way to predict the maximum flow possible through an IV cannula in a clinical situation. However, neither the International Organization for Standardization standard test nor Poiseuille’s law are useful. There are many determinants of flow in a clinical situation that clinicians must be aware of. The binomial equation proposed by Philip and Philip highlights a number of factors influencing fluid flow through an IV administration system. The determinants of flow characteristics expressed in Reynolds and Hagen-Poiseuille’s equations do not reflect the whole picture when cannula performance in a clinical situation is being evaluated. The influence of the properties (viscosity and density) and the type of fluid are well recognized and accounted for by both formulae.

The properties of an IV fluid administration set (including properties of their components), and the IV cannulae (smoothness/roughness of the interior of the cannula) play a significant role in the fluid flow dynamics in the clinical setting and would have played a role in the mixed flow pattern that our findings suggest. The friction factor that determines turbulent flow is dependent on the *R*e and the roughness of the internal surface of the cannula. The relative surface roughness is given by the formula: mean height of bumps perpendicular to the surface (microscopic view) divided by the ID of the cannula.^{10} How the nature of the interior of the cannulae investigated influences the fluid dynamics clinically should be revisited in future studies.

While the effect of radius is less than commonly believed, it is still important. However, clinicians should be aware of the limitations of increasing radius and use other strategies to increase flow when needed. These could include use of pressure, choice of fluid to be infused, and using multiple cannulae in parallel.

## ACKNOWLEDGMENTS

We would like to thank Chris Juniper, Technician in the Academic Department of Anesthetics and Intensive Care Medicine (Cardiff University) for his help with the schematic drawing of our model.