An intravenous drip must just enter a vein where the blood pressure is 18 mm Hg above atmospheric. The fluid has a density of 1.00 x 10^3 kg/m^3, 1.0 mm Hg is 133 Pa, and g is 9.80 m/s^2. How high above the entry point must the bag hang?

1. For the fluid to enter, the pressure it creates at the needle must match the vein's gauge pressure of 18 mm Hg. 2. Convert to SI first: (18 mm Hg)(133 Pa per mm Hg) = 2400 Pa to two figures. 3. A hanging column of fluid produces gauge pressure = h rho g, so h = gauge pressure divided by rho g. 4. Denominator = (1.00 x 10^3 kg/m^3)(9.80 m/s^2) = 9.80 x 10^3 kg/(m^2 s^2). 5. h = (2400 N/m^2) / (9.80 x 10^3 kg/(m^2 s^2)) = 0.24 m. 6. The value 0.018 m is the trap for treating the 18 mm Hg reading as 18 mm of fluid without converting the units. 7. The values 2.4 m and 1.8 m each slip a power of ten in the conversion or the division. _Source: OpenStax College Physics (CC BY 4.0), Ch 11 "Fluid Statics", section 11.6 Gauge Pressure, Absolute Pressure, and Pressure Measurement_