Question

Blood pressure is conventionally measured in the dimensions of millimeters in a column of mercury, and the readings are expressed as two numbers, for example, 120 and 80. The first number is called the systolic value, and it is the maximum pressure developed as the heart contracts. The second number (called the diastolic reading) is the pressure when the heart is at rest. In the units of kPa and psi, what is the difference in pressure between the given systolic and diastolic readings? The density of mercury is 13.54 Mg/m3.

Answer 1

- the difference in pressure between the given systolic and diastolic readings in KPa is 5.313 KPa

- the difference in pressure between the given systolic and diastolic readings in psi is 0.77 psi

Step-by-step explanation:

Given the data in the question;

blood pressure reading = 120 and 80 { systolic and diastolic }

To determine the difference in pressure between the two readings, we use the equation as follows;

change in pressure ΔP = p × g × h

where p is mercury density, g is acceleration due to gravity and h is difference of height in mercury column.

Frist,

difference of height in mercury column h = 120 - 80 = 40 mm = 0.04 m

given that; The density of mercury is 13.54 Mg/m³ = 13.54 × 10³ kg/m³

Not that Mg is Megagrams not Milligrams }

we know that g = 9.81 m/s²

so we substitute into our equation;

change in pressure ΔP = (13.54 × 10³) × 9.81 × 0.04

ΔP = 5313.096 kg/m-s² ≈ 5313.096 N/m²

ΔP = 5.313 KPa

Therefore, the difference in pressure between the given systolic and diastolic readings in KPa is 5.313 KPa.

In psi,

ΔP = 5.313 KPa

ΔP = 5313 Pa

ΔP = 5313 pa × ( 1.45 × 10⁻⁴ psi / 1 Pa )

ΔP = 0.770385 psi ≈ 0.77 psi

Therefore, the difference in pressure between the given systolic and diastolic readings in psi is 0.77 psi