IV Infusion at 60 mL/h: Which Element Actually Sets the Drip Rate?
A 26-year-old man admitted with dengue haemorrhagic fever at a Kathmandu hospital needs continuous intravenous fluid at 60 mL/h. The infusion bag hangs so that the fluid surface is 1.10 m above the tip of the cannula in his forearm. The cannula is 3.0 cm long with an internal radius of 0.30 mm. The fluid is 0.9% sodium chloride solution, density 1000 kg/m³, viscosity 1.0 × 10⁻³ Pa·s. Venous pressure at the cannula tip is 10 mmHg (1333 Pa). The drip rate observed is much lower than the bag height alone would predict, because a roller clamp on the giving set is partly closed. Later in the day the patient needs the same fluid at three times the present rate. The ward has no larger cannula, but it does have a taller stand that can raise the bag surface to 2.20 m, and a pressure cuff that can be wrapped around the bag and inflated to 300 mmHg.
1. Calculate the pressure difference actually driving flow through the cannula and the Poiseuille flow rate it would permit. Compare this with the prescribed 60 mL/h and state what is really limiting the drip rate.
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Driving pressure. Hydrostatic pressure from the column: ρgh = 1000 × 9.8 × 1.10 = 10 780 Pa. The vein pushes back with 1333 Pa, so the net driving pressure across the cannula is 10 780 − 1333 = 9447 Pa (about 71 mmHg).
Poiseuille flow. r = 3.0 × 10⁻⁴ m, so r⁴ = 8.1 × 10⁻¹⁵ m⁴; L = 0.030 m. Q = πΔP r⁴ / (8ηL) = (3.14 × 9447 × 8.1 × 10⁻¹⁵) / (8 × 1.0 × 10⁻³ × 0.030) Numerator ≈ 2.40 × 10⁻¹⁰; denominator = 2.4 × 10⁻⁴. Q ≈ 1.0 × 10⁻⁶ m³/s = 1.0 mL/s ≈ 3600 mL/h.
Interpretation. The cannula alone would pass about 60 times the prescribed rate. The bottleneck is therefore not the needle but the giving set - tubing bore, drip chamber, in-line filter and, above all, the partly closed roller clamp, which adds a large series resistance. Poiseuille's law is being used correctly only as a check on the needle; using it to predict the actual drip rate would give a dangerously wrong answer, because the clamp resistance is unknown and adjustable. The correct judgement is that flow is clamp-controlled until the clamp is fully open.
2. The patient needs three times the current rate. Compare opening the clamp fully, raising the stand to 2.20 m, and inflating the pressure cuff to 300 mmHg. Which gives the largest gain and which the smallest, and in what order should they be used?
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1. Open the clamp (first). This removes the dominant resistance in the circuit. It costs nothing, is instantly reversible, and can raise flow many-fold. Nothing else should be attempted until the clamp is fully open.
2. Taller stand (smallest gain per unit effort). At 2.20 m: ΔP = (1000 × 9.8 × 2.20) − 1333 = 21 560 − 1333 = 20 227 Pa. Ratio = 20 227 / 9447 = 2.14, not 2.0. The reason is that venous back-pressure is a fixed offset: the driving pressure rises by 9800 Pa, but the relative increase is smaller. A taller stand alone therefore probably cannot triple the rate.
3. Pressure cuff (largest gain). 300 mmHg = 300 × 133.3 ≈ 40 000 Pa added to the bag. New ΔP ≈ 9447 + 40 000 ≈ 49 400 Pa, i.e. about 5.2 times the present flow - comfortably more than the 3× needed. The constraint is no longer physics but safety: the giving set must be rated for pressure infusion, the vein must be checked for infiltration, and air embolism risk rises.
Judgement. Solve the cheap, reversible, actually-limiting problem first (the clamp). Use the cuff only if the set and cannula are rated for it and the limb is being watched; treat the taller stand as a modest adjunct, not a solution.
3. The fluid is changed to 5% dextrose, viscosity 1.5 × 10⁻³ Pa·s, with the clamp left at the same setting. A colleague predicts flow will fall to two-thirds. Is that correct? Explain.
Read the worked answer
Partly - and the naive answer is misleading.
For a single tube, Q ∝ 1/η, so if the cannula were the only resistance the flow would fall to 1.0/1.5 = 0.67, i.e. two-thirds. That is where the colleague's number comes from.
But resistances in series add: R_total = R_cannula + R_clamp. From the first task, the cannula contributes only a small share of the total resistance - that is exactly why the observed drip was far below the 3600 mL/h the needle would allow. If R_clamp ≫ R_cannula, then R_total barely changes when the fluid viscosity rises by 50%, and the actual fall in flow is much smaller than one-third.
What does change is the pressure drop distribution: the extra viscosity means a larger fraction of the available pressure is now dissipated across the needle rather than the clamp, so the pressure at the cannula hub falls. Clinically the flow is still clamp-set; the safe conclusion is that switching to dextrose will reduce flow only slightly at the same clamp setting, and any rate change must be re-measured with a drip counter rather than predicted from the needle dimensions alone.