Question

Blood pressure is normally taken on the upper arm at the level of the heart. Suppose, however, that a patient has his arms in a cast, so you cannot take his blood pressure in the usual way. If you have him stand up and take the blood pressure at his calf, which is 88.5 cm below his heart, what would be the magnitude of the difference between this measurement of blood pressure and a normal blood-pressure measurement? The density of blood is 1060 kg/m3. Is the blood pressure measured at the calf larger or smaller than the blood pressure measured at the upper arm?

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Density of blood = = 1060 kg/m³

Distance of calf from the heart = H = 88.5 cm = 0.885 m

Pressure difference between the measurements at the calf and the normal measurement = P

P = gH

P = (1060)(9.81)(0.885)

P = 9202.76 Pa

The blood pressure measured at the calf is larger than the blood pressure measured at the upper arm as the calf is below the upper arm and the pressure in a fluid increases with depth.

Pressure difference between the measurements at the calf and the normal measurement = 9202.76 Pa

The blood pressure measured at the calf is larger than the blood pressure measured at the upper arm.