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Chapter 13: Problem 10

Blood pressure. Systemic blood pressure is defined as the ratio of two pressures-systolic and diastolic-both expressed in millimeters of mercury. Normal blood pressure is about \(\frac{120 \mathrm{~mm}}{80 \mathrm{~mm}}\) which is usually stated as \(\frac{120}{80}\). What would normal systemic blood pressure be if, instead of millimeters of mercury, we expressed pressure in each of the following units but continued to use the same ratio format? (a) atmospheres, (b) torr, (c) \(\mathrm{Pa},\) (d) \(\mathrm{N} / \mathrm{m}^{2},\) (e) psi.

Short Answer

Expert verified
BP ratio remains the same, but values change to (a) \( \frac{0.158 \text{ atm}}{0.105 \text{ atm}} \), (b) \( \frac{120 \text{ torr}}{80 \text{ torr}} \), (c) \( \frac{16000.64 \text{ Pa}}{10665.76 \text{ Pa}} \), (d) \( \frac{16000.64 \text{ N/m}^2}{10665.76 \text{ N/m}^2} \), (e) \( \frac{2.32 \text{ psi}}{1.55 \text{ psi}} \).

Step by step solution

01

Understanding the Conversion from mm Hg

The given blood pressure ratio is \( \frac{120 \text{ mm}}{80 \text{ mm}} \). To solve each part, we'll need conversion factors from millimeters of mercury (mm Hg) to the desired units: (a) 1 mm Hg = 0.001316 atmosphere, (b) 1 mm Hg = 1 torr, (c) 1 mm Hg = 133.322 Pa, (d) 1 mm Hg = 133.322 N/m虏 (since 1 Pa = 1 N/m虏), (e) 1 mm Hg = 0.0193368 psi.
02

Converting to Atmospheres

Using the conversion factor for atmospheres, calculate the systolic and diastolic pressures: - Systolic: \( 120 \times 0.001316 = 0.15792 \text{ atm} \)- Diastolic: \( 80 \times 0.001316 = 0.10528 \text{ atm} \).Thus, the blood pressure in atmospheres is \( \frac{0.158 \text{ atm}}{0.105 \text{ atm}} \).
03

Converting to Torr

In torr, the unit is the same as mm Hg, hence the blood pressure does not change: \( \frac{120 \text{ torr}}{80 \text{ torr}} \).
04

Converting to Pascal (Pa)

Using the conversion factor to Pa, calculate the pressures: - Systolic: \( 120 \times 133.322 = 16000.64 \text{ Pa} \)- Diastolic: \( 80 \times 133.322 = 10665.76 \text{ Pa} \).Thus, the blood pressure is \( \frac{16000.64 \text{ Pa}}{10665.76 \text{ Pa}} \).
05

Converting to Newtons per square meter (N/m虏)

Since N/m虏 is equivalent to Pa, the conversion is the same: \( \frac{16000.64 \text{ N/m}^2}{10665.76 \text{ N/m}^2} \).
06

Converting to psi

Using the conversion for psi, calculate the pressures: - Systolic: \( 120 \times 0.0193368 = 2.320416 \text{ psi} \)- Diastolic: \( 80 \times 0.0193368 = 1.546944 \text{ psi} \).Thus, the blood pressure in psi is \( \frac{2.32 \text{ psi}}{1.55 \text{ psi}} \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Systolic Pressure
Systolic pressure refers to the higher pressure of the two measurements used to describe blood pressure. It represents the pressure in the arteries when the heart's ventricles contract, pumping blood out to the rest of the body. This pressure is crucial as it indicates how much pressure your blood is exerting against your artery walls during heartbeats. Normal systolic pressure is usually around 120 mm Hg, which is considered healthy. However, this value can vary depending on individual health conditions and lifestyle. It is used in various conversion calculations, such as converting the pressure from millimeters of mercury (mm Hg) to atmospheres or pascals.
Diastolic Pressure
Diastolic pressure is the lower of the two numbers in a blood pressure reading. It measures the pressure in the arteries when the heart is at rest, specifically between beats when the heart is relaxed and refilling with blood. This measurement is vital because it shows how much pressure your blood is exerting against your artery walls when the heart is not contracting. In a normal reading, diastolic pressure is typically around 80 mm Hg. Monitoring this value can help in assessing the health of your cardiovascular system. Just like systolic pressure, diastolic pressure can also be converted into other units for various scientific and medical purposes.
Pressure Units
Pressure is a physical force exerted over a surface area, and it can be measured in various units depending on the context. In medical settings, blood pressure is commonly measured in millimeters of mercury (mm Hg). However, for scientific calculations or to tailor measurements to different contexts, conversions might be necessary. Some alternative units include:
  • Atmospheres (atm): A unit based on the average atmospheric pressure at sea level.
  • Torr: Numerically equivalent to mm Hg, making it a convenient unit for some scientific calculations.
  • Pascals (Pa) or Newtons per square meter (N/m虏): The SI unit of pressure, defined as one newton per square meter.
  • Pounds per square inch (psi): Commonly used in mechanical and aeronautical applications.
Understanding these units and being able to convert between them is essential for accurately interpreting blood pressure readings in different scientific and clinical disciplines.
Unit Conversion
Unit conversion is the process of converting a measurement from one unit to another, essential in scenarios where different standards are used. In medical sciences, converting blood pressure readings into different units can help in international research comparisons and understanding across diverse systems. For example:
  • To convert from mm Hg to atmospheres: Multiply by 0.001316.
  • Torr conversion: Since 1 mm Hg is equal to 1 torr, no conversion is needed.
  • To convert to Pascals (Pa): Multiply by 133.322.
  • To convert to psi: Multiply by 0.0193368.
These mathematical adjustments ensure that medical professionals and researchers can communicate effectively, regardless of the unit system in their region or the domain they operate in. Accurate conversions allow for precise comparisons and understanding in global medical and scientific communities.

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