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Chapter 13: Problem 25

Blood pressure on the moon. A resident of a lunar colony needs to have her blood pressure checked in one of her legs. Assume that we express the systemic blood pressure as we do on earth and that the density of blood does not change. Suppose also that normal blood pressure on the moon is still \(\frac{120}{80}\) (which may not actually be true). If the lunar colonizer has her blood pressure taken at a point on her ankle that is \(1.3 \mathrm{~m}\) below her heart, what will be her systemic blood-pressure reading, expressed in the standard way, if she has normal blood pressure? The acceleration due to gravity on the moon is \(1.67 \mathrm{~m} / \mathrm{s}^{2}\).

Short Answer

Expert verified
The blood pressure at the ankle is approximately \(137/97\) mmHg.

Step by step solution

01

Understand the Blood Pressure Components

Blood pressure is expressed as systolic over diastolic. It's measured in mmHg (millimeters of mercury). The normal benchmark is 120/80 mmHg on Earth.
02

Calculate the Pressure Change Due to Height

The change in blood pressure due to a height difference can be calculated using the formula: \[ \Delta P = \rho \cdot g \cdot h \]where \(\rho\) is the density of blood (approximately 1050 kg/m鲁), \(g\) is the acceleration due to gravity (1.67 m/s虏 on the Moon), and \(h\) is the height difference (1.3 m).
03

Calculate the Pressure Difference

Substitute the values into the formula: \[ \Delta P = 1050 \, \text{kg/m}^3 \cdot 1.67 \, \text{m/s}^2 \cdot 1.3 \, \text{m} \approx 2280.15 \, \text{Pa} \]Convert this pressure from pascals to mmHg using the conversion factor 1 mmHg = 133.322 Pa:\[ \Delta P \approx \frac{2280.15}{133.322} \approx 17.1 \, \text{mmHg} \]
04

Adjust the Blood Pressure Reading

The additional pressure due to the height is added to the normal systolic and diastolic readings, which are both measured relative to the heart level. Therefore, the systolic pressure at the ankle is:\[ 120 + 17.1 \approx 137.1 \, \text{mmHg} \] and the diastolic pressure is:\[ 80 + 17.1 \approx 97.1 \, \text{mmHg} \].
05

Provide the Final Blood Pressure Reading

The blood pressure at the ankle of the lunar colonizer is approximately \( \frac{137}{97} \) mmHg.

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Key Concepts

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

Systemic Blood Pressure
Systemic blood pressure is a way of expressing the force exerted by circulating blood on the walls of blood vessels throughout the body. It is normally recorded as two numbers, given in millimeters of mercury (mmHg), to represent systolic and diastolic pressures.
Systolic pressure is the higher figure, signifying the pressure in arteries when the heart beats. Diastolic pressure, being the lower figure, shows the pressure when the heart rests between beats.
  • Standard systemic blood pressure on Earth is considered to be around 120/80 mmHg.
  • This measure is crucial as it helps assess an individual's cardiovascular health.
Maintaining systemic blood pressure is vital for adequate blood circulation and ensuring the organs receive sufficient oxygen and nutrients.
Acceleration due to Gravity on the Moon
The acceleration due to gravity on the Moon is significantly less than on Earth, and understanding this helps us comprehend how different physical processes work on the lunar surface.
On Earth, the gravitational acceleration is about 9.81 m/s虏. In contrast, the Moon's gravity is only 1.67 m/s虏.
This is crucial because any object, including blood in vertebrates, experiences an altered gravitational force.
  • The change in gravity affects how fluids, like blood, distribute and flow.
  • Considering moon gravity is essential when evaluating systemic blood pressure effects, especially in specific body positions.
  • Lower gravity means changes in pressure due to height differences are less impactful than on Earth.
Density of Blood
Blood density plays an important role in computing changes in pressure when blood moves in the gravitational field.
In general, blood density is roughly 1050 kg/m鲁, a nearly constant value that relates the mass and volume of blood.
  • This density significantly influences how pressure changes with height differences in the body.
  • In pressure calculations, blood density is a consistent factor whether on Earth or the Moon.
  • Density remains unchanged in altered gravitational conditions but essential to calculate blood pressure effects accurately.
Thus, understanding blood density helps us calculate changes in systemic blood pressure more precisely.
Pressure Difference Calculation
Calculating the pressure difference due to height in a less intense gravitational field (like on the Moon) requires integrating various factors.
The formula used is \[\Delta P = \rho \cdot g \cdot h\]where \( \Delta P \) is the pressure difference, \( \rho \) is the blood density, \( g \) is the moon's gravity, and \( h \) is the height difference.
  • The computed pressure difference needs converting from Pascals to millimeters of mercury (mmHg) for ease of interpretation (1 mmHg = 133.322 Pa).
  • In our lunar blood pressure scenario, the calculated \( \Delta P \) is added to systemic pressure values (systolic and diastolic) to reflect readings at different body parts below the heart level.
  • Resulting numbers illustrate increased pressures at lower extremities when standing, vital for systemic blood pressure readings.
Understanding these computations enables accurate assessment of blood pressure changes in non-Earth environments.

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Most popular questions from this chapter

Landing on Venus. One of the great difficulties in landing on Venus is dealing with the crushing pressure of the atmosphere, which is 92 times the earth's atmospheric pressure. (a) If you are designing a lander for Venus in the shape of a hemisphere \(2.5 \mathrm{~m}\) in diameter, how many newtons of inward force must it be prepared to withstand due to the Venusian atmosphere? (Don't forget about the bottom!) (b) How much force would the lander have to withstand on the earth?

(a) Calculate the buoyant force of air (density \(1.20 \mathrm{~kg} / \mathrm{m}^{3}\) ) on a spherical party balloon that has a radius of \(15.0 \mathrm{~cm} .\) (b) If the rubber of the balloon itself has a mass of \(2.00 \mathrm{~g}\) and the balloon is filled with helium (density \(0.166 \mathrm{~kg} / \mathrm{m}^{3}\) ), calculate the net upward force (the "lift") that acts on it in air.

A \(975-\mathrm{kg}\) car has its tires each inflated to "32.0 pounds." (a) What are the absolute and gauge pressures in these tires in \(1 \mathrm{~b} /\) in. \(^{2}, \mathrm{~Pa},\) and atm? (b) If the tires were perfectly round, could the tire pressure exert any force on the pavement? (Assume that the tire walls are flexible so that the pressure exerted by the tire on the pavement equals the air pressure inside the tire.) (c) If you examine a car's tires, it is obvious that there is some flattening at the bottom. What is the total contact area for all four tires of the flattened part of the tires at the pavement?

An ore sample weighs \(17.50 \mathrm{~N}\) in air. When the sample is suspended by a light cord and totally immersed in water, the tension in the cord is \(11.20 \mathrm{~N}\). Find the total volume and the density of the sample.

Find the gauge pressure in pascals inside a soap bubble \(7.00 \mathrm{~cm}\) in diameter. The surface tension of this soap is \(0.0250 \mathrm{~N} / \mathrm{m}\).
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