Question

A patient is given an intravenous drip from a bottle of fluid through a needle in the patient's arm. At what height above the arm should the bottle be placed so that the gauge pressure of the fluid entering the vein matches the patient's systolic blood pressure of 145mmHg?

Answer 1

The IV bag should be placed approximately 1.965 meters above the arm to match the gauge pressure of the fluid with the patient’s systolic blood pressure of 145mmHg, after converting the pressure to pascals and using the hydrostatic pressure formula.

Step-by-step explanation:

To calculate at what height the IV bag should be placed above the arm so that the gauge pressure of the fluid entering the vein matches the patient's systolic blood pressure of 145mmHg, we must first convert the pressure into SI units. We know that 1.0 mm Hg is equivalent to 133 Pa. Given that the systolic blood pressure is 145 mm Hg, we first convert this value to pascals: 145 mm Hg × 133 Pa/mm Hg = 19285 Pa.

Now, we use the hydrostatic pressure formula P = h⋅ρ⋅g, where P is the pressure, h is the height of the fluid column, ρ is the density of the fluid, and g is the acceleration due to gravity (approximately 9.81 m/s²). Solving for h, we have h = P / (ρ⋅g).

Assuming the density of the fluid being administered is 1.00 g/ml (or 1000 kg/m³) and substituting the known values, the equation becomes h = 19285 Pa / (1000 kg/m³⋅9.81 m/s²) which simplifies to approximately 1.965 m. Therefore, the IV bag must be placed approximately 1.965 meters above the entry point into the patient's arm.