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If the gauge pressure is doubled, the absolute pressure will A. be halved. B. be doubled. C. be unchanged. D. be increased, but not necessarily doubled. E. be decreased, but not necessarily halved. SSM

Short Answer

Expert verified
D. The absolute pressure will be increased, but not necessarily doubled.

Step by step solution

01

Understanding the relationship between Gauge Pressure and Absolute Pressure

Gauge pressure is the pressure measured relative to the ambient atmospheric pressure. When we mention 'pressure' in everyday conversation, it's usually gauge pressure we're referring to. On the other hand, Absolute Pressure is the sum of the atmospheric pressure and the gauge pressure. Mathematics form: Absolute Pressure = Atmospheric Pressure + Gauge Pressure
02

Change in Gauge Pressure

If we double the gauge pressure, it doesn't mean that the absolute pressure will also be doubled. The absolute pressure is the sum of gauge pressure and atmospheric pressure, so even if the gauge pressure is doubled, it will not double the absolute pressure, it will simply increase it. This is because the atmospheric pressure component remains unchanged.
03

Final Conclusion

Therefore, if the gauge pressure is doubled, the absolute pressure will not be halved, doubled, or remain unchanged. It will not necessarily be halved either. The most appropriate answer would be that it will be increased, but not necessarily doubled. Hence, Option D is the correct answer. Absolute Pressure = Atmospheric Pressure + 2 X Gauge Pressure

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Gauge Pressure
Gauge pressure is the pressure we typically discuss in everyday life. It measures how much the pressure inside a system (like a tire or a boiler) exceeds the surrounding atmospheric pressure. This is important because atmospheric pressure itself is always present and can significantly affect measurements if not accounted for. Think of gauge pressure as a way to focus only on the extra pressure applied beyond the air that constantly surrounds us.

To understand better:
  • Gauge Pressure = Measured Pressure - Atmospheric Pressure
  • When a tire says it holds a pressure of 30 psi, that's usually its gauge pressure, meaning it’s 30 psi above atmospheric pressure.
So, any changes in gauge pressure directly affect how systems operate or perform. It's especially useful in contexts where we're focused on the additional pressure applied rather than the total pressure including the atmosphere.
Absolute Pressure
Absolute pressure gives us a complete picture by considering the atmospheric pressure along with the gauge pressure. It is crucial when precise measurements are required, such as scientific experiments or calculations in fields like aerodynamics. Absolute pressure measures total pressure exerted above a perfect vacuum, which is a scenario of zero atmospheric pressure.

Here's how it works:
  • Absolute Pressure = Atmospheric Pressure + Gauge Pressure
  • It is expressed in units like psi or pascals, accounting for all pressure components.
By taking into account the atmospheric pressure, absolute pressure calculations ensure that changes in environmental conditions, such as altitude or weather, are factored into analyses. This way, even if the surrounding pressure changes, absolute pressure helps maintain consistency in the measurement of force applied in various scenarios.
Atmospheric Pressure
Atmospheric pressure is the weight of the earth’s atmosphere pushing down on everything at the surface. It can vary due to changes in weather, altitude, and even temperature. When we talk about pressure at sea level, we often reference atmospheric pressure as being approximately 14.7 psi or 101.3 kPa.

Some key points:
  • Atmospheric pressure decreases with altitude; for example, it’s lower on a mountain than at sea level.
  • Even minute changes in atmospheric pressure are essential for weather forecasting and understanding environmental conditions.
In practical use, atmospheric pressure is the baseline from which gauge pressure is measured. While it influences both gauge and absolute pressure, it itself remains constant for a given location and time under specific conditions. Understanding this component is vital, as failing to account for it can lead to inaccuracies in pressure-related calculations.

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Most popular questions from this chapter

In July of 1995 , a spillway gate broke at the Folsom Dam in California. During the uncontrolled release, the flow rate through the gate peaked at \(40,000 \mathrm{ft}^{3} / \mathrm{s}\) and about \(1.35\) billion gallons of water were lost (nearly \(40 \%\) of the reservoir). Estimate the time that the gate was open.

Astronomy Evidence from the Mars rover Discovery suggests that oceans as deep as \(0.50 \mathrm{~km}\) once may have existed on Mars. The acceleration due to gravity on Mars is \(0.379 \mathrm{~g}\) and the current atmospheric pressure is \(650 \mathrm{~N} / \mathrm{m}^{2}\). (a) If there were any organisms in the Martian ocean in the distant past, what pressure (absolute and gauge) would they have experienced at the bottom, assuming the surface pressure was the same as today? Assume that the salinity of Martian oceans was the same as oceans on Earth. (b) If the bottom-dwelling organisms in part (a) were brought from Mars to Earth, how deep could they go in our ocean without exceeding the maximum pressure they experienced on Mars?

How fast is the water leaving the nozzle of a hose with a volume flow rate of \(0.45 \mathrm{~m}^{3} / \mathrm{s}\) ? Assume there are no leaks and the nozzle has a circular opening with diameter of \(7.5 \mathrm{~mm}\).

What force must the surface of a basketball withstand if it is inflated to a pressure of \(8.5\) psi? Assume the ball has a diameter of \(23 \mathrm{~cm}\).

Two wooden boxes of equal mass but different density are held beneath the surface of a large container of water. Box A has smaller average density than box B. When the boxes are released, they accelerate upward to the surface. Which box has the greater acceleration? A. Box A B. Box B C. They are the same. D. We need to know the actual densities of the boxes in order to answer the question. E. It depends on the contents of the boxes. SSM

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