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tap.html
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
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<div class="bTitle"><p><u><strong>Reynolds Number of Kitchen Tap</strong></u><p /></div>
<img class="bImg" src="/includes/other/tap/thumbnail.jpg" alt="Thumbnail for tap"></img>
The tap in the kitchen appeared uniform and made me think that it could be laminar flow.
A fluid dynamic engineer thought otherwise so I put it to the test.
<div class="bSub"><p><b>Preface</b><p /></div>
The flow of a fluid can be broadly grouped into two categories: laminar and turbulent. This refers to the relative direction
each particle of the fluid is traveling with respect to one another. If the delta in the angle of travel is small enough, the
flow is said to be laminar. Generally turbulent flow appears messy whilst laminar appears uniform.
The state of the flow can be obtained via calculating the Reynolds Number. If this number is under 2,000 the flow is said to be laminar. If
the number is above 2,000 the flow is said to be turbulent. Technically there is also critical flow between 2,000 and 4,000 but for simplicity I will
leave it out. The Reynolds Number is dependent on characteristics of the flow which will be covered below.
<div class="bSub"><p><b>Variables</b><p /></div>
The equation for the Reynolds Number I am using comes from <i>Transmission Pipeline Calculations and Simulations Manual</i> by E. Shashi Menon.
The equation is:
<img class="bEqu" height="30px" src="/includes/other/tap/img1.png" alt="R = 3160Q/vD"></img>
Where <i>R</i> is the Reynolds Number, <i>Q</i> is the flow rate in gal/min, <i>v</i> is the kinematic viscosity in cSt, and <i>D</i> is the diameter of the pipe in
inches.
<p />
The flow rate can be measured by filling a known volume with the liquid and timing it. The kinematic viscosity can be found using the
<a href="https://www.omnicalculator.com/physics/water-viscosity">Water Viscosity Calculater</a>. From this calculator we see that the viscosity is only dependant on
temperature. Finally the diameter of the pipe can be measured using a ruler.
<div class="bSub"><p><b>The Experiment</b><p /></div>
As seen in the thumbnail, I used a coffee pot to fill with the tap water. The moment I turned on the tap, I started a stopwatch on my phone. Again the moment I turned off
the tap, I stopped the timer. The result was 21.21 seconds.
<img class="bImg" src="/includes/other/tap/img2.png" alt="timer"></img>
I put a thermometer in the liquid and got a result of 39.9 <sup>o</sup>C.
<p />
Note: The image shows a different temperature (continuity error)
<img class="bImg" src="/includes/other/tap/img3.jpg" alt="thermometer"></img>
This was actually the second time because the first time I tried, the water was too cold for the thermometer. Since the thermometer is meant for bodies (~37.5<sup>o</sup>C),
20<sup>o</sup>C was past its lower bounds.
<p />
I then poured the fluid from the coffee pot into a measuring cup to more accurately measure the volume. I filled the large measuring cup up 7 times and the small up just once.
<img class="bImg" src="/includes/other/tap/img4.jpg" alt="large cup"></img>
<img class="bImg" src="/includes/other/tap/img5.jpg" alt="small cup"></img>
This worked out to be 1810 ml.
<p />
Finally I used a ruler to measure the inner diameter of the tap which was 12 mm.
<img class="bImg" src="/includes/other/tap/img6.jpg" alt="bottom of tap"></img>
<div class="bSub"><p><b>The Math</b><p /></div>
Note: I kept all my sig figs but rounded to two decimals for the sake of readability.
<p />
Starting with flow rate, the equation needed gallons per minute. According to Google, the conversion from ml to gals is
1 ml for every 0.00026 gallons. Next seconds to minutes is 60 seconds per minute. I now had 0.48 gallons in 0.35 minutes!
This gives me a flow rate of 1.35 gal/min.
<p />
Next the kinematic viscosity was calculated using the Omni calculator which resulted in 0.66 cSt. The units are called centi-stoke
and are equivalent to 1 mm<sup>2</sup>/s.
<p />
Finally the diameter was converted using 25.4 mm in one inch. This resulted in a diameter of 0.47 in.
<p />
Putting this all together and in the formula:
<img class="bEqu" height="30px" src="/includes/other/tap/img7.png" alt="R = 3160Q/vD filled in"></img>
<img class="bEqu" height="30px" src="/includes/other/tap/img8.png" alt="R = 3160Q/vD"></img>
Not laminar... not even close. I was surprised when I calculated this! It makes me reconsider flows that I use to think where laminar but
in reality probably are not.
<img class="bImg" src="/includes/other/tap/img9.png" alt="spreadsheet"></img>
Using my spreadsheet, the viscosity would have to increase to 4.5 cSt which according to the Omni calculator is not possible. The flowrate
would have to decrease to 0.20 gal/min. It is interesting that the flow would actually need to slow down to get more laminar. I would think that
laminar flow would be the most efficient and thus the highest flow rate but this says otherwise. This results in a time of 145 seconds for the
same volume or 265 ml at the same time. Finally if the pipe was 82 mm the flow would become laminar.
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