the absolute pressure of a gas is 42.5 psia and the atmospheric pressure is 840 mbar absolute. Find the gauge pressure in psi, in kilopascals, and in millibars
This text is generated by AI trained by Professor Kirby on his lectures, videos, notes, message board responses, and textbook
PK Bot’s answer:
Gauge pressure is defined as the difference between the absolute pressure and the atmospheric (reference) pressure. In equation form,
p_{\text{gauge}} = p_{\text{abs}} - p_{\text{atm}}.
Here, the given values are
• p_{\text{abs}} = 42.5\text{ psia}
• p_{\text{atm}} = 840\text{ mbar (absolute)}
Because the units differ, we first convert p_{\text{atm}} to psi. The conversion factor is
1\,\text{psi} = 68.9476\,\text{mbar}.
Thus,
p_{\text{atm}}\text{ in psi} = \frac{840\text{ mbar}}{68.9476\,\text{mbar/psi}} \approx 12.18\text{ psi}.
Now, the gauge pressure in psi is
p_{\text{gauge}} \approx 42.5\text{ psia} - 12.18\text{ psi} \approx 30.32\text{ psi}.
To express this gauge pressure in kilopascals, note that
1\text{ psi} = 6.89476\text{ kPa}.
Therefore,
p_{\text{gauge}} \approx 30.32\text{ psi} \times 6.89476\frac{\text{kPa}}{\text{psi}} \approx 209\text{ kPa}.
Finally, to express the gauge pressure in millibars, use the conversion
1\text{ psi} = 68.9476\text{ mbar}.
Thus,
p_{\text{gauge}} \approx 30.32\text{ psi} \times 68.9476\frac{\text{ mbar}}{\text{psi}} \approx 2090\text{ mbar}.
In summary:
\begin{aligned}
p_{\text{gauge}} &\approx 30.3\text{ psi},\\[1mm]
p_{\text{gauge}} &\approx 209\text{ kPa},\\[1mm]
p_{\text{gauge}} &\approx 2090\text{ mbar}.
\end{aligned}
To formulate this response, I reviewed the 2025 edition of Professor Kirby’s textbook (Vol 1 | Vol 2), and I have ranked their significance below. If they are marked as relevant, I encourage you to explore them:
Textbook sections:
- Chapter 3.3: Hydrostatic Distributions in Pipes and Columns (HIGHLY RELEVANT)
- Chapter 3 Fundamentals: Pressure (HIGHLY RELEVANT)
- Chapter 3 How Stuff Works: How manometers measure pressure differences (RELEVANT)
- Chapter 4 Engineering Models: Hydrostatic Equation (RELEVANT)
- Chapter 3 How Stuff Works: How barometers measure absolute pressures (RELEVANT)
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