Given Pressure
Express Result as: Gauge Pressure: 30 kPa (abs) 100 kPa Absolute Pressure: -12 psig 14.4 psia Show your work:
The Correct Answer and Explanation is:
To solve this, we’ll first clarify the difference between absolute pressure and gauge pressure and then convert each pair accordingly.
Key Concepts:
- Atmospheric Pressure (standard): 101.325 kPa = 14.7 psi
- Absolute Pressure = Gauge Pressure + Atmospheric Pressure
- Gauge Pressure = Absolute Pressure – Atmospheric Pressure
Problem 1: Gauge Pressure = 30 kPa, Find Absolute Pressure
We are given:
- Gauge Pressure = 30 kPa
- Atmospheric Pressure = 101.325 kPa (standard at sea level)
Formula:
Absolute Pressure = Gauge Pressure + Atmospheric Pressure
Absolute Pressure = 30 kPa + 101.325 kPa = 131.325 kPa
Answer:
✔ Absolute Pressure = 131.325 kPa
Problem 2: Absolute Pressure = 100 kPa, Find Gauge Pressure
Given:
- Absolute Pressure = 100 kPa
- Atmospheric Pressure = 101.325 kPa
Formula:
Gauge Pressure = Absolute Pressure – Atmospheric Pressure
Gauge Pressure = 100 kPa – 101.325 kPa = –1.325 kPa
Answer:
✔ Gauge Pressure = –1.325 kPa
This means the pressure is slightly below atmospheric pressure (a vacuum condition).
Problem 3: Gauge Pressure = –12 psig, Find Absolute Pressure
Given:
- Gauge Pressure = –12 psig
- Atmospheric Pressure = 14.7 psi
Formula:
Absolute Pressure = Gauge Pressure + Atmospheric Pressure
Absolute Pressure = –12 psi + 14.7 psi = 2.7 psia
Answer:
✔ Absolute Pressure = 2.7 psia
Problem 4: Absolute Pressure = 14.4 psia, Find Gauge Pressure
Given:
- Absolute Pressure = 14.4 psia
- Atmospheric Pressure = 14.7 psi
Formula:
Gauge Pressure = Absolute Pressure – Atmospheric Pressure
Gauge Pressure = 14.4 psi – 14.7 psi = –0.3 psig
Answer:
✔ Gauge Pressure = –0.3 psig
Explanation
Pressure measurements can be expressed in two main forms: gauge pressure and absolute pressure. Gauge pressure measures the pressure relative to the atmospheric pressure, while absolute pressure measures pressure relative to a perfect vacuum (zero pressure). This distinction is critical in scientific, industrial, and engineering applications.
In everyday scenarios, most pressure gauges display gauge pressure, meaning they show how much pressure is above (positive) or below (negative or vacuum) atmospheric pressure. However, when analyzing thermodynamic systems or calculating gas laws, absolute pressure is used, as it provides a true measure from zero pressure.
To convert between the two, the standard atmospheric pressure (approximately 101.325 kPa or 14.7 psi) must be added or subtracted. For example, a gauge pressure of 30 kPa indicates that the pressure is 30 kPa higher than the atmospheric pressure. Adding the standard atmospheric value gives an absolute pressure of 131.325 kPa.
On the other hand, if an absolute pressure of 100 kPa is reported, it is lower than atmospheric pressure, leading to a negative gauge pressure of –1.325 kPa. This means the system is under a slight vacuum.
In imperial units, a gauge pressure of –12 psig means the pressure is 12 psi below atmospheric. To find the absolute pressure, we add atmospheric pressure (14.7 psi), resulting in 2.7 psia, indicating a vacuum condition.
Understanding these conversions ensures proper equipment operation, safety, and compliance with engineering standards.
