Final answer:
Using the hydrostatic pressure equation, we determine the change in pressure due to the height difference when standing. Converting Pascal to mm Hg and subtracting from the initial pressure, the new blood pressure in the brain when standing is lower than the normal range, potentially causing symptoms of orthostatic hypotension.
Step-by-step explanation:
When understanding orthostatic hypotension, we must consider how blood pressure is affected by posture changes. The scenario given involves calculating the blood pressure in the brain when an individual stands up, assuming an initial pressure of 120 mm Hg when lying down. To find the blood pressure when standing, we can use the hydrostatic pressure equation, which accounts for the height difference between the heart and head.
The hydrostatic pressure difference (ΔP) is determined by the equation ΔP = ρgh, where ρ is the density of blood, g is the acceleration due to gravity (9.8 m/s²), and h is the height difference between the two points. In this case, ρ = 1100 kg/m³, and h = 0.4 m (40 cm). Plugging in the values:
- ΔP = (1100 kg/m³)(9.8 m/s²0.4 m)
- ΔP = 4312 Pa
Since 1 mm Hg is approximately equal to 133.32 Pa, we can convert the pressure difference from Pascals to mm Hg:
- ΔP = 4312 Pa / 133.32 (Pa/mm Hg) ≈ 32.36 mm Hg
Since the pressure in the brain will be lower when standing up due to gravity, we subtract this difference from the initial blood pressure:
- New blood pressure in the brain = 120 mm Hg - 32.36 mm Hg
- New blood pressure in the brain = 87.64 mm Hg
This value is lower than 90 mm Hg, which is considered low and can result in symptoms of postural hypotension, which include fainting or lightheadedness.