Gauge pressure at the bottom of a barrel

In summary, the question asks for the pressure at the bottom of a barrel that contains both a layer of oil and water. The correct formula to use is Poil + Pwater = Ptotal, as both substances are present in the barrel. Treating the pressure of the water as a negation of the pressure of the oil would not be correct in this scenario.
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Of Mike and Men
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Homework Statement


A barrel contains a 0.110 m layer of oil and a density of 690 kg/m3 floating on water that is 0.300 m deep. What is the pressure at the bottom of the barrel?

Homework Equations

The Attempt at a Solution



Poil + Pwater = Ptotal

My question is why am I using this formula? I got the correct answer, but initially I wanted to treat the pressure of the water as a negation of the pressure of the oil, causing the barrel to float. So, Poil - Pwater. Is the reason for the addition because I am treating the bottom of the barrel as a point and the pressure acting on it in every direction equally and taking my gauge pressure from that exact point?

Thanks
 
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  • #2
Of Mike and Men said:
My question is why am I using this formula? I got the correct answer, but initially I wanted to treat the pressure of the water as a negation of the pressure of the oil, causing the barrel to float.

My reading of the question is that both the oil and the water are in the barrel.
 
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  • #3
CWatters said:
My reading of the question is that both the oil and the water are in the barrel.
Okay, thank you. I mis-read that. I was assuming the barrel was floating on the water. Paying attention to sentence structure is useful. ?:)
 

FAQ: Gauge pressure at the bottom of a barrel

1. What is gauge pressure at the bottom of a barrel?

Gauge pressure at the bottom of a barrel is the measurement of the force per unit area exerted by the weight of the liquid within the barrel on the bottom of the barrel. It is typically measured in units of pounds per square inch (psi) or pascals (Pa).

2. How is gauge pressure at the bottom of a barrel calculated?

Gauge pressure at the bottom of a barrel can be calculated using the formula P = ρgh, where P is the gauge pressure, ρ is the density of the liquid, g is the acceleration due to gravity, and h is the height of the liquid column. Alternatively, it can also be determined using a pressure gauge.

3. What factors affect gauge pressure at the bottom of a barrel?

The gauge pressure at the bottom of a barrel is affected by the density of the liquid, the height of the liquid column, and the acceleration due to gravity. Additionally, the shape and material of the barrel also play a role in determining the gauge pressure.

4. What is the significance of gauge pressure at the bottom of a barrel?

Gauge pressure at the bottom of a barrel is important for various reasons. It can help determine the stability of the barrel, the amount of force the liquid is exerting on the bottom, and the potential for leaks or ruptures. It is also a crucial factor in determining the flow rate of the liquid out of the barrel.

5. How does gauge pressure at the bottom of a barrel differ from absolute pressure?

Gauge pressure is measured relative to atmospheric pressure, while absolute pressure is measured relative to a perfect vacuum. This means that gauge pressure at the bottom of a barrel will always be a positive value, while absolute pressure can be either positive or negative. Additionally, gauge pressure will change with variations in atmospheric pressure, while absolute pressure will remain constant.

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