Static Fluid Pressure and Fluid Flow

by | Nov 15, 2021 | Physics

Apply the concept of static fluid pressure to real world problems
Investigate concepts of fluid flow

Head to the following website to investigate fluid pressure. Click ‘Run Now!’
http://phet.colorado.edu/en/simulation/fluid-pressure-and-flow

Notes for today:
Use Pascals for your unit of pressure. Remember, [Pa]=[N/m^2 ]
For all of your pressures today, use four significant figures for your answers. For example, if the pressure meter gives you 101.325 kPa you can write that as 101,300 Pa.

Part 1: Atmospheric Pressure

Setup
In the top right hand corner, select the grid option for the simulation.
Using the sliding knob, fill the pool so that there the water is 3 meters deep
Make sure that the acceleration due to gravity is equal to 9.8 m/s2

Click the pressure meter to control it. Drag the pressure meter to ground level and determine the pressure at the ground. Record this value in the space below.

Patm = ______ Pa

This value is the atmospheric pressure; because that is the pressure you feel when one atmosphere is on top of you.

Where do you think the atmospheric pressure is the least?

 Denver, CO (1609 m above sea level)  Ocean City, NJ (0 meters above sea level)
 Death Valley, CA (86 meters below sea level)  Hillsborough, NJ (45 meters above sea level)

Explain your response: ___________________________________________________________

Part II: Gauge pressure, Absolute Pressure, and atms

Now let’s go under water, where the pressure is different. The pressure-meter on the simulation measures absolute pressure, the actual pressure that is occurring. Depending on our situation it may be beneficial to represent the pressure in a different way. Gauge pressure ignores atmospheric pressure and only takes into account the fluid. Atmospheres or atms represent the “number of atmospheres” you are experiencing. Use the simulation and your brain to fill in the table below.

Gauge Pressure  Absolute Pressure   Atmospheres

1.0 meter below the surface

2.0 meters below the surface

3.0 meters below the surface

Part III: Calculating Pressure

To determine the absolute pressure of a static (unmoving) fluid, we can apply the following concept.

P= P_0+ ρgh

Summarize this formula in words. __________________________________________________

For this next part you’ll have to decide what type of person you are. Do you want to jump into a pool full of honey or gasoline?
 Gasoline (ρg = 700 kg/m3)  Honey (ρH = 1420 kg/m3)

Justify your response: ____________________________________________________________

So now that you’ve made your decision, predict the gauge pressure 3.0 meters below the surface of your fluid. Show your work in the space below.

Check your answer by using the simulation.
Part IV: Pressure at different depths

Rank the following points on the diagram above from least pressure to greatest pressure. If any points have the same pressure, give them the same ranking.

_ A B C D E F ___ G

Justify your response: ____________________________________________________________

Part V: Fluid Flow

Setup
Click on the ‘Flow’ Tab

We are now going to talk about fluids moving. Begin by record the current time in the space below.
_ : _
Mess around with the simulation for at least 2 minutes. Experiment with every variable you can until you are familiar with the simulation.

Okay. It better be at least 2 minutes later. We’re going to talk about mass flow rate and volume flow rate, which are two ways to talk about fluids flowing.

Setup
Click on the ‘Reset All’ button

Mass flow rate, Δm/t , is the mass of the fluid passing through a pipe in a given second.
In physics, mass flow rate is measured in kg/s

Volume flow rate, ΔV/t , is the volume of the fluid passing through a pipe in a given second

What unit do you think volume flow rate is measured in?

In the current simulation, the volume flow rate is 5000 L/s, or 5 m3/s. This means that 5 cubic meters of water are passing through the pipe in a second. If the density of this water is 1000 kg/m3, answer the following questions.

What is the volume of water that flows through the pipe in 6 seconds?

What is the mass flow rate of the water?

What is the mass of the water that flows through the pipe in 6 seconds?

Part VI: Continuity

The mass flow rate and the volume flow rate are always the same in a closed pipe. Why do you think that has to be the case? (Try and think about what might happen if the rates were not the same). ____

Setup
Select the ‘Flux meter’ option
Drag the pipe so that you have areas of 12.5 m2, 10.0 m2, 5.0 m2, 2.5 m2, and 1.0 m2

What do you notice about the volume flow rate at different points along the pipe? __________

What do you notice about the speed of the water at different points along the pipe? When is the water the fastest? The slowest? ___________________________________________________________

Use the simulation to fill in the table below.
Area
(m2) Speed
(m/s) Volume Flow Rate
(m3/s)
1.0

2.5

5.0

10.0

12.5

Determine the continuity formula, which relates two points where fluid flows in a closed pipe.

Answer the questions below about water moving through a closed pipe.

Determine the speed at which water would flow through a point in the pipe that has a cross sectional area of 0.25 m2 and a volume flow rate of 5.0 m3/s.

Determine the speed at which water would flow through a point in the pipe that has a cross sectional area of 0.25 m2 and a volume flow rate of 10.0 m3/s.

Determine the speed at which water would flow through a point in the pipe that has a cross sectional area of 1.0 m2 and a volume flow rate of 10.0 m3/s.

Determine the speed at which water would flow through a point in the pipe that has a cross sectional area of 1.0 m2 and a volume flow rate of 20.0 m3/s.

Sample Solution

Sample solution

Dante Alighieri played a critical role in the literature world through his poem Divine Comedy that was written in the 14th century. The poem contains Inferno, Purgatorio, and Paradiso. The Inferno is a description of the nine circles of torment that are found on the earth. It depicts the realms of the people that have gone against the spiritual values and who, instead, have chosen bestial appetite, violence, or fraud and malice. The nine circles of hell are limbo, lust, gluttony, greed and wrath. Others are heresy, violence, fraud, and treachery. The purpose of this paper is to examine the Dante’s Inferno in the perspective of its portrayal of God’s image and the justification of hell. 

In this epic poem, God is portrayed as a super being guilty of multiple weaknesses including being egotistic, unjust, and hypocritical. Dante, in this poem, depicts God as being more human than divine by challenging God’s omnipotence. Additionally, the manner in which Dante describes Hell is in full contradiction to the morals of God as written in the Bible. When god arranges Hell to flatter Himself, He commits egotism, a sin that is common among human beings (Cheney, 2016). The weakness is depicted in Limbo and on the Gate of Hell where, for instance, God sends those who do not worship Him to Hell. This implies that failure to worship Him is a sin.


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God is also depicted as lacking justice in His actions thus removing the godly image. The injustice is portrayed by the manner in which the sodomites and opportunists are treated. The opportunists are subjected to banner chasing in their lives after death followed by being stung by insects and maggots. They are known to having done neither good nor bad during their lifetimes and, therefore, justice could have demanded that they be granted a neutral punishment having lived a neutral life. The sodomites are also punished unfairly by God when Brunetto Lattini is condemned to hell despite being a good leader (Babor, T. F., McGovern, T., & Robaina, K. (2017). While he commited sodomy, God chooses to ignore all the other good deeds that Brunetto did.

Finally, God is also portrayed as being hypocritical in His actions, a sin that further diminishes His godliness and makes Him more human. A case in point is when God condemns the sin of egotism and goes ahead to commit it repeatedly. Proverbs 29:23 states that “arrogance will bring your downfall, but if you are humble, you will be respected.” When Slattery condemns Dante’s human state as being weak, doubtful, and limited, he is proving God’s hypocrisy because He is also human (Verdicchio, 2015). The actions of God in Hell as portrayed by Dante are inconsistent with the Biblical literature. Both Dante and God are prone to making mistakes, something common among human beings thus making God more human.

To wrap it up, Dante portrays God is more human since He commits the same sins that humans commit: egotism, hypocrisy, and injustice. Hell is justified as being a destination for victims of the mistakes committed by God. The Hell is presented as being a totally different place as compared to what is written about it in the Bible. As a result, reading through the text gives an image of God who is prone to the very mistakes common to humans thus ripping Him off His lofty status of divine and, instead, making Him a mere human. Whether or not Dante did it intentionally is subject to debate but one thing is clear in the poem: the misconstrued notion of God is revealed to future generations.

 

References

Babor, T. F., McGovern, T., & Robaina, K. (2017). Dante’s inferno: Seven deadly sins in scientific publishing and how to avoid them. Addiction Science: A Guide for the Perplexed, 267.

Cheney, L. D. G. (2016). Illustrations for Dante’s Inferno: A Comparative Study of Sandro Botticelli, Giovanni Stradano, and Federico Zuccaro. Cultural and Religious Studies, 4(8), 487.

Verdicchio, M. (2015). Irony and Desire in Dante’s” Inferno” 27. Italica, 285-297.

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