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When the gauge pressure is doubled, what happens to the absolute pressure?
- a)It increases by a factor less than 2.
- b)It stays the same.
- c)It is halved.
- d)It doubles.
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
When the gauge pressure is doubled, what happens to the absolute press...
Understanding Gauge and Absolute Pressure
In fluid mechanics, it's important to differentiate between gauge pressure and absolute pressure.
- Gauge Pressure: This is the pressure measured relative to atmospheric pressure. It can be positive or negative, depending on whether the pressure inside the system is greater or less than atmospheric pressure.
- Absolute Pressure: This is the total pressure measured relative to a perfect vacuum. It is always positive and is calculated as:
Absolute Pressure = Gauge Pressure + Atmospheric Pressure
Impact of Doubling Gauge Pressure
When the gauge pressure is doubled, let's analyze what happens to the absolute pressure:
- Initial Condition:
- Let the initial gauge pressure be P_g.
- The initial absolute pressure (P_a) can be represented as:
P_a = P_g + P_atm
(where P_atm is the atmospheric pressure)
- New Condition:
- When the gauge pressure is doubled, the new gauge pressure becomes 2P_g.
- The new absolute pressure (P_a_new) is:
P_a_new = 2P_g + P_atm
- Comparison:
- The change in absolute pressure is:
P_a_new - P_a = (2P_g + P_atm) - (P_g + P_atm)
= 2P_g - P_g
= P_g
From this, we see that the new absolute pressure is equal to the original absolute pressure plus the original gauge pressure.
Conclusion
When the gauge pressure is doubled, the absolute pressure does not simply double; it increases by a factor less than 2 relative to the original absolute pressure. Thus, the correct answer is option 'A': It increases by a factor less than 2.
In fluid mechanics, it's important to differentiate between gauge pressure and absolute pressure.
- Gauge Pressure: This is the pressure measured relative to atmospheric pressure. It can be positive or negative, depending on whether the pressure inside the system is greater or less than atmospheric pressure.
- Absolute Pressure: This is the total pressure measured relative to a perfect vacuum. It is always positive and is calculated as:
Absolute Pressure = Gauge Pressure + Atmospheric Pressure
Impact of Doubling Gauge Pressure
When the gauge pressure is doubled, let's analyze what happens to the absolute pressure:
- Initial Condition:
- Let the initial gauge pressure be P_g.
- The initial absolute pressure (P_a) can be represented as:
P_a = P_g + P_atm
(where P_atm is the atmospheric pressure)
- New Condition:
- When the gauge pressure is doubled, the new gauge pressure becomes 2P_g.
- The new absolute pressure (P_a_new) is:
P_a_new = 2P_g + P_atm
- Comparison:
- The change in absolute pressure is:
P_a_new - P_a = (2P_g + P_atm) - (P_g + P_atm)
= 2P_g - P_g
= P_g
From this, we see that the new absolute pressure is equal to the original absolute pressure plus the original gauge pressure.
Conclusion
When the gauge pressure is doubled, the absolute pressure does not simply double; it increases by a factor less than 2 relative to the original absolute pressure. Thus, the correct answer is option 'A': It increases by a factor less than 2.
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Community Answer
When the gauge pressure is doubled, what happens to the absolute press...
- Absolute pressure is equal to atmospheric pressure plus gauge pressure.
- Atmospheric pressure is 101,300 Pa, while a typical gauge pressure for a tire is 30 psi or 207 Pa.
- Since atmospheric pressure is relatively large compared to most gauge pressures, doubling the gauge pressure would not end up doubling the absolute pressure.
- To use the tire example, if the gauge is 414 Pa, then absolute pressure would be 101,314 Pa. Absolute pressure increase by a factor less than 2.
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