Water bottle lab report, written by Sean Mabey. Jordon von helf did minor editing and
added the engineering calculations and the pump mistake sections. Our other team members
were Isaac and Devon
Abstract
Our model for the lab project was based upon the idea that forced convection of water
over the frozen water bottle would cool the unfrozen water bottle the most efficiently. We
experimented with different set ups and insulation ideas and found a suitable set up that would
work for our purpose.
Introduction
This experiment was done to show the basics of thermo conductivity between two object
using methods of either conduction (a solid object touching another solid object), convection (a
fluid flowing over a solid object), or a combination of the two. Each group was given 2 water
bottles (one frozen one at room temperature) and was to cool the room temp water bottle using
the frozen water bottle. The team that cooled the room temperature water bottle to the lowest
temperature won. Teams could not spend more than $15.00 on supplies and could only use a 9
volt battery as a power source. Also, a large effort was focused on the predicted calculations for
the final temperature of the unfrozen water bottle. Extra credit was also given for those who
figured out the convective heat transfer coefficient for the heat transfer variable in the equation
for our own real world applications. To do this, it took a great time of research, collaboration,
and algebra.
In the experiment we had to think about multiple levels of heat transfer from various
resources of heat. To be able to calculate the final temperature we would have to take into
account all the variables and be able to apply them into the equations. This experiment taught us
the complexity of heat transfer in real world applications and the importance of being able to do
those calculations.
Procedure
To be able to predict the results of the project we started with the equations for
conduction and convection. We took the values that we could find by looking up or by finding
experimentally or mechanically and tried to orient the equations to be able to solve for the
unknowns in the equation. All experimental temperatures were found using a temperature gun.
When we started to compare values between conduction and convection by putting in
hypothetical values the conclusion was made to use convection to transfer heat from the two
water bottles.
q= hA(Tsurface – Tfluid)
We decided to use this equation for the initial design hypothesis. We hypothesized that
we could use the equation to find the heat transfer between the pre-cooled water to the room
temperature water bottle. Because the temperature of frozen water does not change until all the
water has thawed and turned into a liquid state, the temperature will remain constant. So if we
were able to run water around the frozen water bottle and recycle the water over the frozen water
bottle repeatedly, we would reach a constant temperature close to that of the frozen water bottle.
For our initial calculations we hypothesized that the temperature would be about 35 F. This
temperature should remain fairly constant while running over the unfrozen water bottle. Because
the calculation of the heat transfer of the frozen water bottle to the water wasn’t as important we
decided to leave that calculation for later.
From the equation we wanted a design that produced a larger surface area or area of contact, a
heavily insulated container to reduce heat transfer from outer sources, a strong pump that ran on
a 9 volt battery, and a way to recycle the already lower temperature water over the frozen water
bottle. Our design was as follows:
We decided to insulate the entire system with styrofoam and put the pump at the bottom
because the pump had to be gravity fed. Also, the pump was not submersible, so we had to make
the funnel water proof. Because the pump did generate some heat it was decided that the pump
should be away from the water catch basin as to not transfer too much heat to the cooled water.
During the design process a few problems were encountered. Some adhesives or glues
did not adhere well to the styrofoam and took hours to cure. Also, the ability of the glues that we
ended up using did not seal well. So, the system did leak water. In the project, we used gorilla
glue, henrys roofing cealer, liquid nails, and duct tape to hold the insulated box together.
Because of a lack of time, we were not able to fabricate an entire cealed system but finished only
the part that covered the water bottles.
Engineering calculations
1. To calculate the final temperature of the room temperature water bottle, I first needed a
convection coefficient. I decided to find my own convection coefficient for extra credit instead
of just loosely estimating one from the engineering textbook. After some digging on the internet,
I found the equation Nu=convective heat transfer coefficient/conductive heat transfer
coefficient= h*L/kf, where h=convective heat transfer coefficient, kf=thermal conductivity of the
fluid, and L=characteristic length. I couldn’t find any useful information on the characteristic
length, so I assumed it was roughly equal to the length of the two water bottles (0.4064 meters).
2. Next, I used Nu=(3.66+0.0668(D/L)*Re*Pr)/ (1+0.04[(D/L)*Re*Pr]^2/3 to find Nu so that I
could substitute it back into the first equation and solve for the convection coefficient.
Re=p*V*d/u and Pr=Cp*u/k, where p=density, V=fluid velocity, u= viscosity, D=characteristic
length, Cp=heat capacity, u=viscosity, k=thermal conductivity. I found the viscosity and heat
capacity values for water on the internet. And the engineering textbook had the thermal
conductivity value of water.
To find the fluid velocity, I knew our pump was rated at 7 liter per minute and that the diameter
of the tube pumping the water was 0.01 meters in diameter. I then converted liters to cubic
meters and minutes to seconds. I then divided the volumetric flow rate by the cross sectional
area of the tube to get the velocity of the water. From my calculations, the velocity of water in
our system=1.485 meters per second.
3. After plugging all the numbers back into the second equation, I found my Nu value and put
that into the first equation. Next, I multiplied my Nu value by the thermal conductivity of the
fluid and divided it by the characteristic length. This gave me the convective heat transfer
coefficient of 40.36897 W/(m^2*K). This number probably isn’t that accurate since I assumed
constant fluid velocity and I had to fudge with the characteristic lengths. The constant fluid
velocity wasn’t too bad of an assumption but the characteristic length is where I ran into some
problems. I first assumed D to equal the diameter of the fluid running over the water bottles and
L to be equal to the system’s length. However, this gave me an answer off by at least 5 orders of
magnitude! So, I had to assume that the characteristic lengths D and L after being divided by
each other in both the top and bottom of the equation would equal 1. This is a bad assumption
since they can’t directly cancel because the D/L in the denominator is being raised to the 2/3 and
being added to 1 and the D/L in the numerator is being added to 3.66. But, it was the only
assumption I could make that could give me a meaningful answer, so I had to go with it.
4. With my convective coefficient found, I had all the variables I needed to find the final
temperature of the water flowing over the frozen water bottle after one hour. q=hA(deltaT).
Where h=convective coefficient (40.37), A=surface area of the frozen water bottle (0.04307
m^2), and deltaT= 20 C since the frozen water bottle=0 C and the room temperature water = 20
C. Plugging everything in, I found my q, which is the heat transfer rate, to equal 34.77 J/s or
125,186.19 J/hour. Multiplying q by one hour, I had my E value for the equation E=mc(T~finalT~initial). I knew we would use 1 liter of water and that the density of water was 1000 kg/m^3
which means 1 liter of water has a mass of 1 kg. The specific heat of water = 4180 J/kg*K.
T~initial= 20 C. Solving for T~final, I got 9.95 C. Next I added the cold temperature of the
running water (9.95 C) to the initial temperature of the running water (20 C) and divided by two
to get the average temperature of the running water, which equals 14.97 C.
5. I repeated step four with the equation q=hA(Ts-Tf) for the water running over the room
temperature water bottle. I used the same h value, same A value, the average temperature of the
water, and the temperature of the room temperature water bottle to find my q. q=8.74 J/s or
31456.63 J/hour. Multiplying by an hour, I found my E value for the equation E=mc(Tf-Ti). My
mass was the same, my specific heat was the same and my detla T was Tf-20C. Rearranging and
solving for Tf, I got 12.47 degrees Celsius.
I assumed the resistance of the plastic between the frozen water and the running water wouldn’t
matter since the plastic would also be about 0 C. But, I didn’t account for the thermal resistance
of the plastic between the room temperature water bottle and the running water. Also, I didn’t
calculate the heat losses and gains to the surrounding environment. But, I guessed that the final
temperature of the room temperature water bottle was going to be lower than the calculated
12.47 if the motor ran for the whole hour. But, the motor only lasted a few minutes so our final
temperature was actually higher than my calculated temperature of 12.47 C. The final
temperature was 14.5 C. So, I was off by 2 degrees Celsius. It would be interesting to see how
close I would have been had the motor lasted the whole hour. But, I am still proud of my result;
even though it is off by quiet a bit.
The pump mistake:
The pump we ordered is designed to run off of 9 volts, so we figured it would work fine with the
battery. However, it drained the battery in two or three minutes. Although the website doesn’t
list its current draw, a reviewer measured it to be 0.84 amps at 6 volts. Using these to solve
V=IR for resistance, R=6/0.84=7.14 ohms. So, for 9 volts the current would be roughly 9/7.14=
1.26 amps. Since the battery is rated in the milliamp range, its energy was quickly drained. I
should have paid more attention to this detail before purchasing the pump, but I thought it was
designed to run off a 9 volt battery, the amperage wasn’t listened in the product details, and I
purchased it before studying the chapter on electricity in the engineering textbook. Due to this
oversight, we placed fourth out of the six groups of students. Had our motor lasted the hour, I
believe our water bottle would have been the first or second coldest, but I am at least pleased that
we didn’t get last place like we did in the wind turbine labs.
Results
The result of our project was that after 2 minutes our room temperature water bottle was
cooled by at least 6 degrees celsius. This temperature was read after the system sat with no
pump on for 58 minutes. So, the actual temperature reading of the bottle was probably lower than
that of the measured amount after 2 minutes. But even though the pump only lasted 2 minutes we
still saw a substantial temperature difference.degrees.
Conclusion
The experiment was a success in that we were able to see a substantial temperature
difference even though their were major backdraws and scientific error. We can see how the
system was effected in two short minutes and how the number could improve with more time.
Some experimental error: If the pump ran for a longer duration of the time, our results may have
yeilded a temperature below 10C. This was a very educational lab assignment. It showed us how
hard it is to accuractly model real world problems with mathematic equations. It was also a good
assignment for applying what we learned in class without being given specific directions; we
were able to design or project any way we wanted. This freedom forced us to use our creativity,
ingenuity, and resourcefulness