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School
The University of Tennessee, Knoxville *
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Course
221
Subject
Aerospace Engineering
Date
Jan 9, 2024
Type
docx
Pages
4
Uploaded by BarristerGoat3890
Exploration 1:
Density
Pipe diameter (m)
Flow speed (m/s)
Pressure (kPa)
Flow rate Q=vAm3/s
Case 1
Water
2m
1.6 m/s
127.9 kPa
5000
Case 2
water
3m
0.7 m/s
128 kPa
5000
Case 3
water
4m
0.4 m/s
127.2 kPa
5000
Case 4
gasoline
3m
0.7 m/s
120.2 kPa
5000
honey
3m
0.7m/s
136.2 kPa
5000
Insert your table into your log. Answer the following question.
Do your measurements yield the same volume flow rate for all cases?
Yes
For a given flow rate, how does the flow speed change as the pipe diameter changes?
The speed is faster when the pipe is smaller. When it is larger the speed is slower.
For a given flow rate, how does the pressure at the bottom of the pipe change as the pipe diameter changes?
The pressure at the bottom gets greater if the pipe is bigger and smaller if the pipe is also smaller.
For a given flow rates and pipe diameter, how does the pressure change as the fluid density changes?
The higher the density the higher the pressure.
Describe the profile of the flow. Is it the same for all cases?
The flow is not all the same for all four cases. When the honey is in the pipe it is slow and moves
slowly like it is thick and heavy. The pipe size affects this too. The fluid with lower density like gasoline moved at the same speed but with much lower pressure in the pipe.
Density
Pipe diameter
(m)
Flow speed (m/s)
Pressure (kPa)
Flow rate Q=vAm3/s
Location 1
Water
4m
0.4m/s
139.0kPa
5000
Location 2
Water
2m
1.6m/s
129.1kPa
5000
Insert your table into your log. Answer the following question.
At which location do you measure the higher pressure? What is the pressure difference in kPa?
The higher pressure was in the first location at the bottom of the widest part of the pipe. There is a 10kPa difference.
What is the speed of the liquid in the middle of the pipe in m/s?
1.1 m/s
Describe the profile of the flow. Compare it to the profile without friction.
The speed is 0.6 m/s, pressure is 130.7, and flow rate is 3313.8 L/s.
Comment on the effects of friction (viscosity).
Without friction the speed is the same throughout the middle top and bottom of the pipe. With friction the middle of the pipe is the fastest while the bottom and top are slowest. The pressure is also different when you take away friction. Without it is 130, and with it is 129.
Exploration 2:
Keeping everything else the same, does the flow speed of the water depend upon the height of water level in the tank?
Yes, it does.
Justify your answer by giving the numbers for the flow speed for two different water levels.
At 9 meters it is 14 m/s. At 5 meters it is 11 m/s.
Keeping everything else the same, does the speed of the flow of the water depend upon the height of the tank?
No, it does not.
Justify your answer by giving the numbers for the flow speed for two different tank heights.
At 20 meters tall and 7 meters in the tank, the speed was 13.7 m/s. At 28 meters tall and 7 meters
in the tank, it was also about 13.5 m/s. It may be off by decimal due to human error.
Does the speed of the flow depend upon the fluid density?
No, it does not
Justify your answer by describing how you checked this?
I measured the speed of all three Fluid densities: Honey, gasoline, and water. All three, when full,
had the speed of 14 m/s when coming out of the tank.
What happens to the stream of fluid after it leaves the tank?
To shoots out horizontally and slowly gets less and less far as the tanks fullness goes down.
How far (horizontally) will a stream of water travel if it exits the water tower at 14 m/s, 10 m above the ground?
19.77 meters. Exercise:
Is increasing blood pressure 5 - 10 times higher a viable option? What percentage increase in blood pressure is reasonable? Explain!
I don’t think that it is viable because increasing blood pressure would ultimately decrease the ability to flow. Around 5% increase would probably be reasonable.
Is decreasing the length of your blood vessels a viable option? Explain!
Decreasing the lengths is defiantly not a viable option because without the length they are now the heart would have to pump a lot more blood to the short veins so they could send more blood out quicker.
The arterioles (small arteries) are surrounded by circular muscles.
To increase the blood flow rate by a factor of 5, what percentage increase in the radius of a blood
vessel is needed? (This is called vasodilatation.)
You would need to do an increase of roughly 50 %.
Arteries in the human body can be constricted when plaque builds up on the inside walls. How does this affect the blood flow rate through this artery? Is it possible for the body to keep the flow rate constant? Explain!
This would affect the blood flow because the pressure is decreasing meaning the flow is increasing.
No, it is not possible for the body to keep the flow rate constant. When plaque buildup on the arteries it makes the opening for blood smaller so the flow rate would be higher than in the areas with no plaque.
Record your explanations in your log.
Experiment:
Insert your data table and your plot of position versus time (with trendline) into your log.
Calculate the viscosity η of the shampoo using your measured velocity in units of poise = g/(cm-
s). Use the densities in units of g/cm
3
, the speed in units of cm/s, the radius of the sphere in units of cm and g = 981 cm/s
2
.
(1 Pa-s = 1 kg/(m s) = 10 g/(cm-s) = 10 poise)
Calculate the Reynolds number R = 2ρ
fluid
r
sphere
v/η. It is a dimensionless number.
Check that the Reynolds number is less than 1, so that we are in the regime where Stokes' law is valid.
The table below lists typical viscosities of some viscous fluids at room temperature. Does your value for the viscosity of the shampoo seem reasonable? Discuss.
Viscosity (pa-s)
Honey
2-10
molasse
5-10
ketchup
50-100
Chocolate syrup
10-25
I do think that my viscosity would be considered reasonable. I did however barely have a number
lower than one for the Reynolds number so I may have made some mistakes in calculations.
Predict the terminal velocity of a sphere made of the same material but with diameter of 3/8 inch in the same fluid.
I think this hypothetical would have a greater terminal velocity because the diameter is also greater.
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