Blood pressure is measured when the blood is pumping (systolic) and when the heart is resting (diastolic). When pressure readings are given, the systolic is given first, and healthy blood pressure is around 120 over 80 mm Hg. Recall the density of mercury is 13.6 * 103 kg/m3.

(a) Suppose you have a blood pressure reading of 120 over 83 mm. What is your systolic pressure, in newtons per meter squared? (b) Suppose you have a blood pressure reading of 120 over 83 mm Hg. What is your diastolic pressure, in newtons per meter squared?

a) P = 15993.6 N/m²

b) P' = 11062.24 N/m²

Explanation:

Given:

Density of the mercury, ρ = 13.6 * 10³ kg/m³

The blood pressure reading is given as 120 over 83 mm

a) Now,

The pressure (P) due to a fluid is given as:

P = ρgh

where, g is the acceleration due to the gravity

h is the pressure head

The systolic pressure head from the blood pressure reading is, h = 120 mm = 0.12 m

substituting the value in the formula for pressure,

we get

P = 13.6 * 10³ * 9.8 * 0.12

or

P = 15993.6 N/m²

b) The systolic pressure head from the blood pressure reading is, h' = 83 mm = 0.083 m

substituting the value in the formula for pressure,

we get

P' = 13.6 * 10³ * 9.8 * 0.083

or

P' = 11062.24 N/m²