Air Displacement Pressure

In summary: P2 = .75*ρ*(Q/A)^2.In summary, Caleb is struggling to determine the pressure of air displaced by gasoline flowing into a tank. He uses the Bernoulli equation to calculate the pressure at the exit of the tank, and finds that the pressure is around 2psi, which is higher than he expected. He shows his work and concludes that the gas would create less pressure because it has a lower density.
  • #1
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I am struggling with what seemed to be a simple problem and any help would be greatly appreciated.
I have to determine the amount of pressure created when air is displaced buy gasoline flowing into a tank.
The gas enters the tank at 10gpm. The entrance has a diameter of 1.5" and the vent has a diameter of 5/8".
I need to know the pressure of the air at the exit of the tank.
Can this be modeled with the Bernoulli equation?
Using the Bernoulli equation I got an answer of around 2psi but this does not seem quite right.
 
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  • #2
Yes, I would think Bernoulli's would work.

2psi seems high. Can you show your work?
 
  • #3
Here's what I've got.
 

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  • #4
Caleb, you want the entrance pressure to the vent, which is also the tank static pressure, with an vent air volume flow equivalent to that of the gasoline volume flow into the tank.

The simplest Bernoulli's equation for that determination reduces to: P1 = .5*ρ*(Q/A)^2, With ρ in lb/cu ft, Q in cfs, and A in ft^2 for units consistency.

In that equation, P1 is the static pressure in the tank, and .5*ρ*Q/A is the equivalent amount of dynamic flowing energy thru the vent that can be converted from the P1 tank static pressure.
The result will be a tank pressure in psf that when converted to psi is much less than 1 psi.
 
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  • #5
I also attempted to use the fluid momentum equation which gave me approximately .06 psig but I was very unsure about the validity of this principle in this particular situation. I was also able to use water that had a flow rate of 7 gpm and determine the pressure experimentally and it was about .75 psig. I assume this is very similar to the number I would get with the gas except the gas would create less pressure because it has a lower density.
 
  • #6
Using my above equation and units, my result for air is:

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What is air displacement pressure?

Air displacement pressure, also known as air pressure or atmospheric pressure, refers to the force exerted by the weight of air in the Earth's atmosphere on a given area of the Earth's surface. It is caused by the Earth's gravitational pull on the air molecules and can vary with altitude and weather conditions.

How is air displacement pressure measured?

Air displacement pressure is typically measured using a device called a barometer, which measures the weight of mercury in a column of air and converts it into a pressure reading. Other common units of measurement for air displacement pressure include pascals (Pa) and millibars (mb).

What factors can affect air displacement pressure?

Air displacement pressure can be affected by several factors, including altitude, temperature, and weather conditions. As altitude increases, air pressure decreases due to the thinner atmosphere. Higher temperatures can cause the air to expand, resulting in lower air pressure. Weather conditions such as storms and high winds can also temporarily affect air pressure in a given area.

How does air displacement pressure impact our daily lives?

Air displacement pressure plays a crucial role in our daily lives. It helps regulate the Earth's climate and weather patterns, and affects the distribution of oxygen and other gases necessary for life. Changes in air pressure can also impact our bodies, causing changes in blood pressure and affecting our ability to breathe comfortably at higher altitudes.

What are some real-world applications of understanding air displacement pressure?

Understanding air displacement pressure is important in a variety of fields, including aviation, meteorology, and scuba diving. It is also essential in engineering and construction, as changes in air pressure can affect the stability of structures and the performance of machinery. Additionally, knowing about air pressure can help us predict and prepare for extreme weather events such as hurricanes and tornadoes.

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