Absolute Pressure and Gauge Pressure

Whenever you have a regular health checkup at your doctor's office, they will likely measure your blood pressure. In that case, a medical tool called the sphygmomanometer is inflated around your arm to temporarily stop the blood flow in an artery.

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What is the mathematical expression for absolute pressure \(P\) if the gauge pressure is hydrostatic pressure? Here, \(P_0\) is atmospheric pressure, \(\rho\) is the mass density of the fluid, \(g\) is the gravitational acceleration, and \(h\) is the height of the fluid column.

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Blood pressure is an absolute pressure.

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Two tanks of water are filled to the same height. The cross-sectional area of tank \(A\) is two times larger than the area of tank \(B\). What is the relation between the pressure on the bottom of these two tanks? 

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What is the difference between gauge pressure and absolute pressure? 

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Which of the following is not an example of a pressure measurement? 

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Gauge pressure can be calculated by subtracting the atmospheric pressure from the absolute pressure.

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What is the hydrostatic pressure?

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When is gauge pressure a negative value? 

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A tank full of methane has a depth of \(2.0\,\mathrm{m}\). What is the gauge pressure exerted on the bottom of this tank, if the density of methane is \(0.68 \, \frac{\mathrm{kg}}{\mathrm{m}^3}\)? Use \(10\,\frac{\mathrm{m}}{\mathrm{s}^2}\) for the acceleration due to gravity. 

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Atmospheric pressure is the same everywhere on Earth. 

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Which of the following situations would require the use of absolute pressure?

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What is the mathematical expression for absolute pressure \(P\) if the gauge pressure is hydrostatic pressure? Here, \(P_0\) is atmospheric pressure, \(\rho\) is the mass density of the fluid, \(g\) is the gravitational acceleration, and \(h\) is the height of the fluid column.

Show Answer
  • + Add tag
  • Immunology
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  • Mo

Blood pressure is an absolute pressure.

Show Answer
  • + Add tag
  • Immunology
  • Cell Biology
  • Mo

Two tanks of water are filled to the same height. The cross-sectional area of tank \(A\) is two times larger than the area of tank \(B\). What is the relation between the pressure on the bottom of these two tanks? 

Show Answer
  • + Add tag
  • Immunology
  • Cell Biology
  • Mo

What is the difference between gauge pressure and absolute pressure? 

Show Answer
  • + Add tag
  • Immunology
  • Cell Biology
  • Mo

Which of the following is not an example of a pressure measurement? 

Show Answer
  • + Add tag
  • Immunology
  • Cell Biology
  • Mo

Gauge pressure can be calculated by subtracting the atmospheric pressure from the absolute pressure.

Show Answer
  • + Add tag
  • Immunology
  • Cell Biology
  • Mo

What is the hydrostatic pressure?

Show Answer
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  • Immunology
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  • Mo

When is gauge pressure a negative value? 

Show Answer
  • + Add tag
  • Immunology
  • Cell Biology
  • Mo

A tank full of methane has a depth of \(2.0\,\mathrm{m}\). What is the gauge pressure exerted on the bottom of this tank, if the density of methane is \(0.68 \, \frac{\mathrm{kg}}{\mathrm{m}^3}\)? Use \(10\,\frac{\mathrm{m}}{\mathrm{s}^2}\) for the acceleration due to gravity. 

Show Answer
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  • Immunology
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  • Mo

Atmospheric pressure is the same everywhere on Earth. 

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Which of the following situations would require the use of absolute pressure?

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    Absolute Pressure and Gauge Pressure A patient getting their blood pressure measured by using a sphygmomanometer StudySmarterFig. 1 - Blood pressure measurements are made using a sphygmomanometer, which ignores the air pressure around it. It's an example of gauge pressure.

    As the pressure from the cuff is slowly released, the artery expands and blood rushes back into the arm. This allows the medical professional to quantify the force exerted by the blood flow against the artery walls, as the heart pumps the blood through the body. This procedure takes no longer than a couple of minutes, yet requires a thorough understanding of fluid mechanics, types of pressure, and their measurements. In this article, we'll focus on gauge pressure (e.g., blood pressure) and absolute pressure, their differences, and applications!

    Definition of Gauge Pressure and Absolute Pressure

    Earth's atmosphere is filled with air which constantly exerts a pressure on all objects and surfaces, as it experiences the gravitational pull toward the planet's surface. This pressure is known as atmospheric pressure.

    Atmospheric pressure is the pressure exerted on all surfaces by the air in the Earth's atmosphere.

    Sometimes it's also referred to as the barometric or air pressure and has been assigned a special unit of the standard atmosphere (\(\mathrm{atm}\)), where \(1 \, \mathrm{atm}\) describes the average atmospheric pressure at sea level at \(15\,^\circ \mathrm{C}\).

    Pressure can be expressed in various units. In SI units, \(1 \, \mathrm{atm}\) is equal to \(101\,325 \, \mathrm{Pa}\) (commonly rounded to \(10^5\,\mathrm{Pa}\)). However, it is also the same as \(760 \, \mathrm{mmHg}\) and \(1.013\, \mathrm{bar}\).

    Although we tend to assume atmospheric pressure to be a constant value, it differs across the planet's surface with altitude and temperature. These fluctuations are very minor near the Earth's surface, where most of the measurements we deal with occur, hence the valid assumption for a constant atmospheric pressure value. However, if the calculations deal with sensitive weather patterns or the pressure measured at the top of a mountain or deep in the ocean, the atmospheric pressure value should be adjusted accordingly.

    So, we can use the fact that atmospheric pressure is a constant value at sea level to define two types of pressure: one that accounts for this additional atmospheric pressure (absolute pressure), and one that ignores it (gauge pressure).

    Gauge pressure is the pressure of a fluid relative to the atmospheric pressure.

    Absolute pressure is the pressure of a fluid relative to the zero pressure experienced in a vacuum.

    In other words, atmospheric pressure is set as the reference point for the gauge pressure. If the absolute pressure is greater than atmospheric pressure, the gauge pressure will have a positive value. On the other hand, if the absolute pressure is smaller than atmospheric pressure, the gauge pressure will be negative.

    The absolute pressure is the total pressure exerted by a fluid and includes the atmospheric pressure in its measurements.

    Now that we have established the basic definitions for different kinds of pressure measurements, let's identify the key differences between gauge pressure and absolute pressure.

    Difference between Gauge Pressure and Absolute Pressure

    Returning to the blood pressure example from earlier, the sphygmomanometer used by the doctor will have a scale ranging from \(0 \, \mathrm{mmHg}\) to around \(300 \, \mathrm{mmHg}\). Considering that humans experience atmospheric pressure, shouldn't the scale go up to a minimum of \(1060 \, \mathrm{mmHg}\), as before taking any measurements on a patient, the sphygmomanometer will already display a value of roughly \(760 \, \mathrm{mmHg}\)?

    Atmospheric pressure is always present on Earth and is experienced by the sphygmomanometer and the blood flowing through the patient, so keeping a record of this constant measurement doesn't make sense. The interesting value is the blood pressure compared to its surroundings because that value is what the arteries will feel as a net force per unit of artery area. So we are interested in the blood's gauge pressure. Thus, for convenience purposes, it's common to adapt these kinds of instruments to read zero at the atmospheric pressure, which means utilizing the gauge pressure.

    On the other hand, if we have a completely sealed system where the atmospheric pressure has an effect on the events occurring, we use absolute pressure. It's commonly used in laboratory settings as well as manufacturing, where even the slightest fluctuation in the setup can alter the results. A great example is vacuum-packaged food, where the longevity of the food depends on the quality of the vacuum seal, or the lack of any pressure, including atmospheric pressure.

    Absolute Pressure and Gauge Pressure Vacuum sealed fish StudySmarterFig. 2 - When food is placed into a vacuum packing chamber, an absolute pressure gauge is used to measure the pressure drop way below the atmospheric pressure.

    Relationship between Absolute Pressure and Gauge Pressure

    Just based on the definitions of both values, it's clear that absolute pressure and gauge pressure are closely related. A visual reference for connecting the two pressures is visible in Figure 3.

    Absolute Pressure and Gauge Pressure Measurements of various pressures displayed as arrows, where the value from zero pressure to the measurement is the absolute pressure, while it's made up of two separate arrows of the atmospheric pressure and the gauge pressure StudySmarterFig. 3 - The final measurement of pressure in a system can be made relative to zero (absolute pressure) or to the atmospheric pressure (gauge pressure).

    We can then use this diagram to come up with a mathematical expression connecting the two types of pressures.

    Formula Describing Absolute and Gauge Pressure

    Based on the explanation provided above, the simple version of the relationship between absolute and gauge pressure is

    $$P=P_0+P_\mathrm{G}, $$

    where \(P\) is the absolute pressure, \(P_0\) is the atmospheric pressure, and \(P_\mathrm{G}\) is the gauge pressure. Considering \(P_0\) is a constant value, we only need to elaborate on the gauge pressure, so let's explain it in more detail.

    Gauge Pressure

    Pressure in a fluid occurs as the upper layers press their weight onto the lower layers. So let's imagine a closed container filled with a liquid, meaning we can ignore the atmospheric pressure. The pressure \(P\) exerted on the bottom of this container by a vertical, rectangular column of liquid can be expressed mathematically as

    $$ P=\frac{F}{A}, $$

    where \(F\) is the force the fluid exerts and \(A\) is the area over which the fluid exerts this force. The force in this case is simply the force of gravity acting on the liquid of mass \(m\) with the gravitational acceleration \(g\). Mass can be re-expressed in terms of liquid density \(\rho\) and volume \(V\) as

    $$ m=\rho V,$$

    where volume is that of the rectangular column, meaning it's equal to the surface area \(A\) multiplied by the column's height \(h\). Now we simply insert all of these values into the pressure equation,

    $$ P=\frac{mg}{A}=\frac{\rho gV}{A}= \frac{\rho g \bcancel{A}h}{\bcancel{A}}, $$

    to obtain the expression for hydrostatic pressure:

    $$ P_\text{fluid}=\rho h g. $$

    Hydrostatic pressure is the pressure exerted by a static fluid as a result of the force of gravity acting on it.

    This means that a fluid that isn't moving will exert a pressure that only depends on the density of the fluid and its depth.

    Absolute Pressure

    We can use the hydrostatic pressure equation to complete the absolute pressure formula mentioned earlier to obtain

    $$P=P_0+\rho gh. $$

    This equation simply tells us that the total pressure exerted on the bottom of a column of fluid that is at sea level is the hydrostatic pressure (which is the gauge pressure) plus the atmospheric pressure. This is logical because both fluid (hydrostatic pressure) and air (atmospheric pressure) exert a force on the bottom of the column of fluid.

    Example of Absolute and Gauge Pressure

    Let's look at an example problem applying the absolute and gauge pressure formula!

    A cube-shaped container is filled to the top with \(500\,\mathrm{L}\) of water. What are the gauge and absolute pressure exerted by the water on the bottom of this container?

    Solution

    The equation used to calculate the absolute pressure is

    $$P=P_0+\rho gh.$$

    In SI units, the volume of the water

    $$ 500 \,\mathrm{L}= 500 \,\bcancel{\mathrm{L}} \times \frac{1 \mathrm{m^3}}{1000\,\bcancel{\mathrm{L}}}=0.500\, \mathrm{m^3}$$

    represents the volume \(V_\text{cube}\) of the cubed container with a side length of \(a\). We can use this value to find the depth of the fluid \(h\):

    \begin{align} V_\text{cube}&= a^3, \\ a&=\sqrt[3]{V_\text{cube}},\\ a&=\sqrt[3]{0.500 \, \mathrm{m^3}}, \\ a&=h=0.794 \, \mathrm{m}. \end{align}

    We know that the acceleration due to gravity is \(g=9.8\,\frac{\mathrm{m}}{\mathrm{s^2}}\) and that the water density is \(\rho=1000\,\frac{\mathrm{kg}}{\mathrm{m^3}}\), so we can calculate the gauge pressure:

    \begin{align}P_\mathrm{G}&=\rho gh\\&=\left(1000\,\frac{\mathrm{kg}}{\mathrm{m^3}}\right)\left(9.8\,\frac{\mathrm{m}}{\mathrm{s^2}}\right)(0.794 \, \mathrm{m})\\ &=7.7\times 10^3 \, \frac{\mathrm{kg}}{\mathrm{m} \, \mathrm{s}^2} \\ &=7.7\times10^3\, \mathrm{Pa}. \end{align}

    Now, we can find the absolute pressure \(P\) by simply adding together the gauge pressure \(P_\text{G}\) we just calculated and the atmospheric pressure (\(P_0=1.013\times 10^5\,\mathrm{Pa}\)) to obtain

    $$P=P_0+P_\mathrm{G}= (7.74\times10^3\, \mathrm{Pa}) + (1.013\times 10^5 \,\mathrm{Pa}) = 1.090\times10^5 \, \mathrm{Pa}.$$

    Absolute Pressure and Gauge Pressure - Key takeaways

    • Atmospheric pressure is the force exerted on all surfaces by the air in the Earth's atmosphere.
    • Gauge pressure is the pressure of a fluid relative to the atmospheric pressure.
    • Absolute pressure is the pressure of a fluid relative to the zero pressure experienced in a vacuum.
    • Gauge pressure is used when atmospheric pressure doesn't affect the system, for instance, measuring blood pressure.
    • Absolute pressure is used to take measurements in systems that are affected by atmospheric pressure, such as laboratory experiments and vacuum-sealed food.
    • Mathematically, absolute pressure can be found using \(P=P_0+P_\text{G}\).
    • Hydrostatic pressure is the pressure exerted by a static fluid as a result of the force of gravity acting on it.
    • When the gauge pressure is hydrostatic pressure, the absolute pressure is \(P=P_0+\rho gh\).



    References

    1. Fig. 1 - Blood pressure monitoring (https://commons.wikimedia.org/wiki/File:Blood_pressure_monitoring.jpg) by rawpixel.com is licensed by Public Domain.
    2. Fig. 2 - Fish Preserved in Vacuum Pack Plastic (https://www.pexels.com/photo/fish-preserved-in-vacuum-pack-plastic-8254505/) by Алекке Блажин (https://www.pexels.com/@28799211/) is licensed by Public Domain.
    3. Fig. 3 - Absolute pressure and gauge pressure diagram, StudySmarter Originals.
    Frequently Asked Questions about Absolute Pressure and Gauge Pressure

    What are the types of pressure?

    The three types of pressure are gauge pressure, absolute pressure, and differential pressure.

    Is blood pressure absolute or gauge?

    Blood pressure is gauge pressure.

    What is the formula for gauge pressure?

    The formula for gauge pressure is Pgauge=ρgh=P-P0.

    What is gauge and absolute pressure?

    Gauge pressure is the pressure of a fluid relative to the atmospheric pressure, and absolute pressure is the pressure of a fluid relative to the zero pressure experienced in a vacuum.

    What is the difference between gauge pressure and absolute pressure?

    The difference between gauge pressure and absolute pressure is that atmospheric pressure is set as the reference point in gauge pressure, while the vacuum pressure is the reference point in absolute pressure.

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    What is the mathematical expression for absolute pressure \(P\) if the gauge pressure is hydrostatic pressure? Here, \(P_0\) is atmospheric pressure, \(\rho\) is the mass density of the fluid, \(g\) is the gravitational acceleration, and \(h\) is the height of the fluid column.

    Blood pressure is an absolute pressure.

    Two tanks of water are filled to the same height. The cross-sectional area of tank \(A\) is two times larger than the area of tank \(B\). What is the relation between the pressure on the bottom of these two tanks? 

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