Question

Blood pressure is usually reported in millimeters of mercury (mmHg) or the height of a column of mercury producing the same pressure value. Typical values for an adult human are \(130 / 80\); the first value is the systolic pressure, during the contraction of the ventricles of the heart, and the second is the diastolic pressure, during the contraction of the auricles of the heart. The head of an adult male giraffe is \(6.0 \mathrm{~m}\) above the ground; the giraffe's heart is \(2.0 \mathrm{~m}\) above the ground. What is the minimum systolic pressure (in \(\mathrm{mmHg}\) ) required at the heart to drive blood to the head (neglect the additional pressure required to overcome the effects of viscosity)? The density of giraffe blood is \(1.00 \mathrm{~g} / \mathrm{cm}^{3},\) and that of mercury is \(13.6 \mathrm{~g} / \mathrm{cm}^{3}\)

Short answer

The minimum systolic pressure required at a giraffe's heart to drive blood to its head is approximately 294.3 mmHg.

Step-by-step solution

Identifying the known values and the required variable

We know the following: - Density of giraffe blood: \(\rho = 1.00 \frac{g}{cm^3} = 1000 \frac{kg}{m^3}\) (to convert to SI units) - Density of mercury: \(13.6 \frac{g}{cm^3} = 13,600 \frac{kg}{m^3}\) - Height difference between the head and the heart: \(h = 6.0 m - 2.0 m = 4.0 m\) - Acceleration due to gravity: \(g = 9.81 \frac{m}{s^2}\) We need to find the minimum systolic pressure required at the giraffe's heart in mmHg.

Calculate the pressure difference in Pascals (Pa)

Using the hydrostatic pressure formula, we can calculate the pressure difference: \(P_2 - P_1 = \rho g h\) Substituting the known values: \(P_2 - P_1 = 1000 \frac{kg}{m^3} \times 9.81 \frac{m}{s^2} \times 4.0 m\) \(P_2 - P_1 = 39240 \,\text{Pa}\)

Convert the pressure difference to mmHg

To convert the pressure difference from Pascals to mmHg, we will use the density of mercury. 1 atm = 101325 Pa 1 atm = 760 mmHg (by definition) To convert the pressure difference to atm, we can use the following formula: Pressure difference in atm = \(\frac{Pressure \, difference \, in \, Pa}{1 \, atm \, in \, Pa}\) Pressure difference in atm = \(\frac{39240 \, Pa}{101325 \, Pa}\) = \(0.3873 \, atm\) Now, to convert the pressure difference to mmHg, use the following formula: Pressure difference in mmHg = Pressure difference in atm × 760 mmHg/atm Pressure difference in mmHg = 0.3873 atm × 760 mmHg/atm = 294.3 mmHg The minimum systolic pressure required at the giraffe's heart to drive blood to its head is approximately 294.3 mmHg.

Key concepts

Understanding Hydrostatic Pressure

Hydrostatic pressure is a fundamental concept in the physics of fluids, playing a crucial role in understanding how pressure varies with depth in a fluid. It is the pressure exerted by a fluid at equilibrium at a given point within the fluid, due to the force of gravity. The formula for hydrostatic pressure is given as:
\[ P = \rho gh \]
where

• \(P\) represents the hydrostatic pressure,
• \(\rho\) is the density of the fluid,
• \(g\) is the acceleration due to gravity, and
• \(h\) is the height of the fluid column above the point in question.

This concept explains how pressure increases with depth in a fluid, such as water or blood, because the weight of the fluid above increases. For instance, in the case of a giraffe, the hydrostatic pressure at its heart is greater than at its head due to the height difference, and this must be overcome to transport blood to the brain.

Systolic Pressure Calculation in Giraffes

Systolic pressure calculation involves finding the peak pressure in the arteries during the contraction of the heart muscles. It is fundamental in understanding the cardiovascular health of an organism, including the giraffe with its unique challenges due to the long neck. Calculation of the minimum systolic pressure at the giraffe's heart includes consideration of the required pressure to raise blood from the heart to the head. Starting with the hydrostatic pressure concept, we substitute the known values such as the blood density, gravity, and the height of the giraffe's neck to find the pressure in Pascals (Pa). This pressure is then converted to the more familiar units of mmHg, which is a measure of blood pressure. This conversion uses the relationship between atmospheric pressure (in Pa and in mmHg) to achieve a value that reflects the giraffe's physiological requirements for ensuring blood reaches the brain.

The Giraffe Cardiovascular System

The giraffe cardiovascular system is an extraordinary example of natural adaptation, featuring structural and functional adaptations to manage the requirements of their tall stature. Giraffes have a high average blood pressure compared to other mammals, a necessity to ensure blood reaches their brains 6 meters above the heart. In addition to a powerful heart, giraffes also have a complex network of blood vessels with specially adapted valves to prevent blood from backflowing due to gravity when the head is lowered. Furthermore, their blood vessel walls are incredibly thick to withstand the high pressure needed to pump blood to great heights. Understanding the cardiovascular system of giraffes not only illustrates the principles of hydrostatic pressure and the physiological aspects of systolic pressure but also demonstrates the incredible ways in which living organisms adapt to their environments.