A gravity infusion and a ward circuit: pressure and current
A nurse sets up a gravity infusion for a patient in a ward. The bag contains 500 mL, to run over 4 hours. The giving set delivers 20 drops per mL. The fluid level in the bag is 1.2 m above the cannula entry point. The fluid density is 1000 kg/m³ and g = 9.8 m/s².
On the same ward, six identical 220 V infusion pumps each draw 0.5 A. They share one socket circuit, protected by a 10 A circuit breaker, with a 1500 W heater.
1. Calculate the drip rate in drops per minute. If the nurse instead sets 60 drops per minute, when will the bag empty?
Read the worked answer
Required rate.
- 500 mL over 4 h = 500 ÷ 240 min = 2.08 mL/min
- drops = 2.08 × 20 = 41.7 ≈ 42 drops/min
Counting drops over a full minute gives 42; over 15 seconds it would be about 10.5, which is too short a sample to round reliably - a short count is a common source of a 20% error.
If set at 60 drops/min.
- 60 ÷ 20 = 3 mL/min
- 500 ÷ 3 = 166.7 min ≈ 2 h 47 min
The bag runs out about 1 h 13 min early, i.e. roughly 30% faster than prescribed. For a fluid with potassium, glucose or a drug, that is a clinically meaningful rate error, not just a timing nuisance; for a plain maintenance fluid it still matters because the patient loses the intended cover for the last hour of the shift.
2. Calculate the hydrostatic pressure at the cannula in kPa and in mmHg. Compare it with venous pressure and explain what a 40 cm reduction in stand height does.
Read the worked answer
Pressure. P = ρgh = 1000 × 9.8 × 1.2 = 11 760 Pa ≈ 11.8 kPa.
Converting: 1 kPa ≈ 7.5 mmHg, so 11.8 × 7.5 ≈ 88 mmHg.
Comparison with venous pressure. Peripheral venous pressure is roughly 5–10 mmHg (about 0.7–1.3 kPa). At 88 mmHg the driving pressure is around ten times venous pressure, which is why flow is brisk and why the bag needs only a modest height. The pressure also has to overcome the resistance of the cannula and tubing, which is why the real flow is lower than the pressure alone would suggest.
Effect of lowering the stand by 40 cm. ΔP = 1000 × 9.8 × 0.40 = 3.9 kPa ≈ 30 mmHg. The pressure falls to about 7.9 kPa (59 mmHg). Because the driving pressure is compared with a venous pressure of only ~10 mmHg, height changes are not marginal: at about 0.30 m the pressure is ~22 mmHg and flow becomes sluggish; below roughly 0.10 m it is ~7 mmHg, close to venous pressure, so flow may stop altogether - and if the line is open to the vein, blood can back up into the tubing. Judgement point: never "speed up" a gravity infusion by raising the stand without checking the prescription and the vein.
3. For the ward circuit, calculate the total current drawn and decide whether the arrangement is acceptable on the 10 A breaker. What would you recommend?
Read the worked answer
Current per pump. 0.5 A each at 220 V, so power per pump = 220 × 0.5 = 110 W.
Total.
- pumps: 6 × 0.5 = 3.0 A
- heater: 1500 ÷ 220 = 6.82 A
- total = 9.82 A against a 10 A breaker
The arithmetic says the breaker is not exceeded - but the margin is only 0.18 A, under 2%.
Why that is not acceptable.
- Breakers are not precision devices; they are rated for a continuous load of about 80% of nominal (≈ 8 A here). At 9.8 A the circuit runs above that for hours, so nuisance tripping is likely and cable heating is a real risk.
- The figure is nominal. A pump drawing a transient inrush at start-up, or a heater cycling on, can momentarily exceed the total.
- Any additional device plugged into the same ring would push it over, and the trip would take out all six pumps at once - a patient-safety event, not just an inconvenience.
Recommendation. Move the heater to a separate circuit (it is the single largest load, 69% of the total), keep the pumps on the protected circuit at about 3 A, and confirm the circuit is supplied through an RCD so that a leakage fault trips on current imbalance rather than waiting for an overload.