# See, how hard I am trying to become a (Full) Professor of Mechanical Engineering in SPPU?

Currently, I am not only cashless but also jobless. That’s why, I try harder.

I am trying very hard to be a (Full) Professor of Mechanical Engineering, especially at the Savitribai Phule Pune University (or SPPU for short).

That’s right.

And that’s why, I have decided to adopt an official position whereby I abandon all my other research and study interests, especially those related to the mechanics of the quanta. Instead, I have officially decided to remain interested only in the official problems from the Mechanical Engineering discipline proper—not only for my studies, but also for my research interests.

… If only I were to have my first degree in Mechanical Engineering, instead of in Metallurgy! (It was some 37.5–33.5 years ago, with my decision to choose Metallurgy being from some 36.5 years ago.) … If only I were to choose Mechanical right back then, this problem wouldn’t have arisen today. …

Tch! …

…But, well, thinking of my first degree, its circumstances—where I got it from (COEP, the engineering college with the highest cut-off merit in the entire Maharashtra state), in what class (First Class with Distinction, the highest class possible), and, most crucially, for spending all my time at what place (The Boat Club)… You know, looking back some 3.5 decades later of all those circumstances—the circumstances of how I chose Metallurgy, back then, as I was sitting at the Boat Club… Hmmm… Boat Club. … Boat Club! Boat Club!!

It gives me some ideas.

So, to better support my current endeavors of becoming an Officially Approved Full Professor of Mechanical Engineering in SPPU, may be, I should solve some Mechanical Engineering problems related to boats. Preferably, those involving not just fluid mechanics, but also mechanisms and machine design—and vibrations! [Oh yes. I must not forget them! Vibrations are, Officially, a Mechanical Engineering topic. In fact even Acoustics. …]

Thinking along such lines, I then thought of one problem, and sort of solved it too. Though I am not going to share my answer with you, I certainly want to share the problem itself with you. (Don’t ask me for answers until I get the job as an Officially Approved Full Professor in Mechanical Engineering at SPPU.)

OK, so here we go.

The Problem Description:

Consider a boat floating on a stand-still lake. The boat has a very simple shape; it is in the shape of a rectangular parallelpiped (i.e., like a shoe-box, though not quite exactly like a punt).

In the plan (i.e. the top view), the boat looks like this:

As shown in the figure, at the centers of the front- and back-sides of the boat, there are two circular cylindrical cavities of identical dimensions, both being fitted with reciprocating pistons. These pistons are being driven by two completely independent mechanisms. The power-trains and the prime-movers are not shown in the diagram; in this analysis, both may be taken to be mass-less and perfectly rigid. However, the boat is assumed to have some mass.

We will try to solve for the simplest possible case: perfectly rigid boat walls (with some mass), perfectly rigid but mass-less pistons, complete absence of friction between the pistons and the cylinder walls, etc.

Assume also that both the boat and the lake water are initially stand-still, and that there are no other influences affecting the motions (such as winds or water currents).

Now, let’s put the pistons in oscillatory motions. In general, the frequencies of their oscillations are not equal. Let the frequency for the left- and right-side pistons be $f_L$ and $f_R$ Hz, respectively.

Problem 1:

Build a suitable Mechanical Engineering model, and predict how the boat would move, in each of the following three scenarios:

• $f_L = f_R$
• $f_L > f_R$
• $f_L < f_R$

In each case, determine (i) whether the boat as a whole (i.e. its center of mass or CM) would at all undergo any motion at all or not, (ii) if yes, whether the motion of the CM would have an element of oscillations to it or not, and finally, (iii) whether the boat (i.e. its CM) would undergo a net displacement over a large number of pistons oscillations or not (i.e., the question asks whether the so-called “time-averaged” net displacement occurs in any one direction or not), and if yes, in which direction.

You may make other minor assumptions. For instance, in each of the above 3 cases, you may assume that at time $t = 0$, both the pistons are at their innermost positions, with each piston beginning its motion by pushing outwards. Also check out the effect of assuming, some other, suitable, values for the initial phases.

Though not at all necessary, if it will help you, you may perhaps consider the case where the higher frequency is an integer multiple of the lower frequency, e.g., in the second of the three cases, assume $f_L = n f_R$, where $n \in \mathcal{N}$. However, note that eventually, you are expected to solve the problem in the general case, the one in which the ratio of the frequencies may be any real number. The cases of practical interest may be where the ratio ranges from 0.0 to a real number up to, say, 2.67 or 3.14 (or, may be, 5.25).

Notice that nowhere thus far have we said that the oscillatory motion of the pistons would be SHM (i.e. simple harmonic). You may begin with an SHM, but as a further problem below illustrates, the piston motion may neither be simple-harmonic, nor even symmetrical in the to- and fro-directions.

On the fluid mechanics side: In your analysis, assume that the length of the boat is much, much greater than the stroke-lengths of the pistons. Essentially, we want to ensure that the water waves produced at one end do not significantly affect the local dynamics at the other end.

You may assume a highly simplified model for the fluid—the problem is not supposed to have a crucial bearing on what kind of a fluid you assume. I mean to say, we are not looking for so detailed a model that you would have to perform a CFD analysis. (That task, we will leave to the Naval Architecture engineers.) However, do make sure to note how your model behaves for an inviscid flow vs. for a viscous flow.

So, in short, the problem is to determine the nature of the motion of the boat, if there is any—i.e., to determine if its CM undergoes a net displacement in the time-averaged sense or not, and if yes, in which direction it occurs.

Problem 2:

Assume a relatively smaller stroke-length for one of the pistons, and repeat the problem.

Problem 3:

Assume that one of the frequencies is zero, which is as good as saying that the boat is fitted with only one cylinder-and-piston. Repeat the analysis.

Problem 4:

Continue to assume that one of the frequencies is zero. Now, also assume that the outward stroke of the moving piston happens faster than its inward stroke. Determine the nature of the motion, if any, for the CM of the boat.

Problem 5 (Optional):

Assuming that the prime mover outputs a uniform circular (or rotary) motion, design a suitable mechanism which will help implement the idea of having non-SHM motions—e.g., different stroke-times in the outward and inward directions. Conduct an informal (or a more formal, calculus-based) displacement-, velocity- and acceleration-analysis, if you wish.

Give it a thought whether this entire idea of transforming a circular motion to a nonuniform reciprocating motion can be done away with, thereby saving on energy—in real life, there is friction—using certain ideas from electrical engineering and electronics.

Ooops!

No, no, no! No!! Throw out that horrendous idea! I mean the very last one!!

We want to remain concerned only with the Mechanical Engineering Problems proper. That is the Official position I have adopted, remember?

That’s right. What I described above was, really, really, really only a Mechanical Engineering Problem.

It really, really, really has nothing to do with anything else such as electrical engineering or quantum physics.

[And if even Prof. Thanu Padmanabhan (IUCAA) does not know quantum physics (he told me so once, right in person), why should I be concerned with it, anyway?]

Anyway, so, Officially speaking, I made up this problem only because I want to become an Officially Approved Full Professor of Mechanical Engineering at SPPU.

If you are interested in some other Mechanical Engineering problems, especially on the fluids-thermal side, check out my recent posts on the Eco-Cooler, and see if you can take further the analysis given in them.

I myself had made a much more advanced engineering analysis right at that time, but I am not going to give it—or its results—until some time after I land and join the kind of job I am looking for—a Full Professor’s. (And I hope that you do have the sense to see that this is not a “prestige issue” on my part.)

The post having a preliminary (quantitative) fluids-thermal analysis is here [^], though the qualitative analysis of the problem begins with an earlier post, here [^].

[Guess the problem, as given, is enough for the time being. I may even come back and add one or two variations on the problem! But no guarantees.]

Update right on 2016.12.02: OK, here are a couple of minor variations. What happens if, when a piston comes to a rest at the extreme stroke, it continues staying idle for a while, before resuming its towards-the-center motion? What if the piston motion is such that the point of zero displacement does not occur exactly at the middle of its overall stroke-length?

I may post some further variations on the problem, or suggest alternative analogous problems, in future.

Currently, I am not just cashless but also jobless. That’s why, I try harder.

More, may be later. As to the Song I Like section, I don’t have anything playing at the back of my mind right away, so let me see if something strikes me by the time I come back tomorrow to give a final editing touch to this post. In that case, I will add this section; else, I will not!

[After the update right on 2016.12.02: I am done with this post now, and if there are any errors, I will let them stay. If you find the post confusing somewhere, please do drop me a line, though. Best, and take care.]

[E&OE]

# Analyzing the Eco-Cooler, part 1

OK, that was ample time for you to have hit your fluid mech/heat transfer/thermo books, and to have it verified whether the 5 deg. C drop was believable or not… You must have made your notes, too, no?…  So, in this post, let’s cross-check our notes.

On my part, I will first present the simplest (and the most approximate) model, and also give you a simple Python script to play with, to see what kind of predictions this model makes. Then, we will go on considering more and more complicated but still approximate “engineering” models that hopefully become more and more realistic. We will cross-check their predictions too. We may eventually find that a full-fledged CFD analysis is called for. However, I will save that—I mean doing a full-fledged CFD analysis—for another day. (I in fact plan to write a paper on this problem, using CFD. (…Some day…).)

The reason we follow this method—from the simplest and crudest models to the more complicated and better ones—is because for problems related to fluid mechanics, it is this method which works best!

I mean to say, the full-fledged Navier-Stokes equations are too complicated to solve for, even when they are applied to the simplest of practically encountered geometries—e.g., the flow of air through the Eco-Cooler bottle. Since the NS equations cannot be solved exactly, the traditional engineering models (which are based on analytical or semi-analytical solutions) fall short, and then, a CFD analysis is called for.

But the fact of the matter also is, even CFD itself is only an approximate technique. CFD solutions sometimes even happen to carry more numerical artifacts than real physics. We therefore cannot approach CFD blindly. We ourselves have to have some good idea in the first place of what the desired solution should look like. We should have this idea right before we even think of setting up a CFD model/simulation. The traditional engineering models provide precisely these insights.

Yes, that’s right.

The traditional engineering models actually are more approximate than CFD. Yet, since they are also simpler than CFD, and since they explicitly carry conceptual connections with the major fluid mechanical phenomena in a more direct manner, they also make it easier to gain insights about both the nature of the problem, and the nature of the expected solution. No similar insights can be had by directly using CFD, for several reasons. The CFD theory itself is too complicated, and the CFD practice involves too many different analysis options. In the jungle of all those parameters, iterations, and convergence requirements, CFD happens to loose the directness of the conceptual connections with the basic analytical theory—with the fluid dynamical phenomena.

That’s why we first deal with the simplest engineering models, even though they are known to be approximate—and therefore, they are easily capable of giving us wrong results. But this way, we can build insights. Building insights is an art, and the process progresses slowly.

As I said, we will follow an iterative scheme of model building. In each phase or iteration of the model building activity, we will actually be applying the same set of principles: the conservation of mass, momentum, and energy. However, in going from a model-building phase to the next, we will aim to incorporate an increasing level of complexity or sophistication—and accuracy, hopefully.

Actually, in the fluid dynamics theory, all the three conservation equations come coupled to each other. You cannot solve for conservation of only the mass, or the momentum, or the energy, by neglecting any of the other two. However, for this particular problem (of the Eco-Cooler), for various reasons (which you will come to appreciate slowly), it so turns out that we can get away considering the mass, momentum and energy equations in a decoupled manner, and in the order stated: first mass, then momentum, and then energy. (It’s no accident that text-books spell out these three principles in this order. Many fluids-related phenomena with which we are well familiar through our direct experience of the world are such that for solving problems involving these phenomena, this order happens to be the best one to follow.)

So, with that big introduction, let’s now get going calculating—even though we will not shut up even while performing those calculations.

Model-Building Phase I: The Simplest Possible Model:

Geometry:

Consider the plastic-bottles used in the Eco-Cooler; they all lie horizontally. Consider one of these bottles. A tube has been obtained by cutting off the base of the bottle. Let the base-plane be identified by the subscript 1 and the neck-plane by 2. See the figure below:

Air flows from the base-plane (1) to the neck-plane (2).

Conservation of mass:

The simplest possible expression for mass conservation, applied to the bottle geometry, would be the continuity equation, given below:
$A_1 U_1 = A_2 U_2$
where $A_1$ and $A_2$ are cross-sectional areas of the bottle, and $U_1$ and $U_2$ are wind velocities, at the base and the neck, respectively. Rearranging for $U_2$, we get:
$U_2 = \dfrac{A_1}{A_2} U_1$             …(1)

We can use this simple an equation for mass conservation only if the flow is incompressible. To determine if our flow is incompressible or not, we have to calculate the Mach number for the flow. To do that, we have to first know the expected wind velocities.

Referring to the Wiki article on the Beaufort scale [^], we may make an assumption that the inlet speed can go up to about 60 kmph. Actually, the wind-speeds covered by the Beaufort scale go much higher (in excess of 118 kmph). However, practically speaking, the only times such high wind-speeds (gales etc.) occur in India is when rains also accompany them. The rains bring down the ambient temperature anyway, thereby obviating the need for any form of a cooler. Thus, we have to consider only the lower range of speeds.

Assuming the speed of sound in air to be about 340 m/s, we find that the Mach number (for the range of the winds we consider) goes up to about 0.65. Now, for $\text{Ma} < 0.33$, the flow is sub-sonic, and can be regarded as incompressible. For $0.33 < \text{Ma} < 1.0$, the flow is trans-sonic, meaning, the changes in pressures do not adjust “instantaneously” everywhere in the flow, and so, it is increasingly not possible to even idealize the flow as incompressible.

Therefore, in the interest of simplicity, for our first solution cut, we choose to consider only the wind-speeds up to 100 m/s, i.e. 28 kmph, so that the incompressibility assumption can be justified. Making this assumption about the highest possible wind-speed, we are then free to use the simplest form of mass conservation equation given above as Eq. (1).

For a typical one liter bottle, the base diameter is 7.5 cm, and the neck diameter is 2 cm (both referring to IDs i.e. inner diameters). (I measured them myself!) So, the area ratio $\frac{A_1}{A_2}$ turns out to be about 14.

Thus, the wind accelerates inside the bottle; the outlet velocity is about 14 times the inlet velocity!

This looks like a remarkable bit of acceleration to happen over just some 20 cm of length. (The bottle is cut somewhere in the middle.) More on it, later.

Conservation of momentum:

The simplest possible equation to use for momentum conservation is the steady-state Bernoulli’s equation:
$\dfrac{P_1}{\rho} + \dfrac{U_1^2}{2} = \dfrac{P_2}{\rho} + \dfrac{U_2^2}{2}$        …(2)
where we have ignored the potential head term ($gz$) because the tube is horizontal as well as symmetrical about its central horizontal axis (and because the air is so thin that its weight can be easily neglected here).

Carefully note the assumptions behind Eq (2). It holds only for a steady-state and laminar flow, and only after neglecting viscosity.

Since we are in a hurry, we will assume them all, and proceed!

Rearranging Eq (2) for $P_2$, we obtain:
$P_2 = P_1 + \dfrac{\rho}{2} \left( U_1^2 - U_2^2 \right)$

Conservation of energy:

We basically need the equation of energy conservation only in order to calculate the temperature at the neck ($T_2$), from a knowledge of: (i) the temperature at the base, $T_1$, and (ii) the pressures $P_1$ and $P_2$.

In the last line, I said “from.” This usage implies that there already is an assumption I made, viz., that the energy equation can be decoupled from the momentum equation. How reasonable is this assumption? It seems pretty OK. Think: can air flowing through a 7.5 cm or a 2.0 cm diameter tube at under 100 m/s get heated up to a significant fraction of 5 deg. C, over a length of just a foot or less? Not likely. Can heating up the neck region cause the air flow to come a halt, say because it helps build up a sufficient amount of pressure? Not even remotely likely. So, we may get away by decoupling the two.

The simplest equation to compute $T_2$ from the other three quantities would be: the ideal gas law, given as:
$\dfrac{P_1 V_1}{T_1} = \dfrac{P_2 V_2}{T_2}$.

We have already found that the flow can be considered incompressible (at least up to 28 kmph of wind-speeds). Hence, the volume of each fluid part remains constant, i.e., $V_1 = V_2$. (Note, in this equation, we have to consider the volume of a fluid element or a part, not the volume for a unit axial length at a given cross-section of the bottle.) For constant volume, the ideal gas law reduces to:
$\dfrac{P_1}{T_1} = \dfrac{P_2}{T_2}$,
from which we can conclude:
$T_2 = P_2 \dfrac{T_1}{P_1}$.

But we have to know whether the assumption of the ideal gas itself can be used in our problem—for the real air—or not. For doing that, we have to know the critical pressure and temperature of air. Cengel (“Thermodynamics: An Engineering Approach,” 8th SI units edition) lists them (Appendix A1) as 132.5 K, and 3.77 MPa. Using these values, the reduced temperature and the reduced pressure of air turn out to be $T_{1_R} = (30 + 273.15)/132.5 \approx 2.29$, and $P_{1_R} = (101.32\times10^3)/(3.77\times 10^6) \approx 0.027$. Further, the expected drops in the pressure and temperature would be just small fractions of the inlet values. Hence, the reduced quantities for the outlet also would not differ significantly from those for the inlet. Referring to the chart and the remarks on p. 139 in Cengel, it seems like we can get away using the ideal gas law.

Note, we are using the ideal gas law not as an approximation to the energy equation, but in place of it, simply because looking at the variables, we noticed that $T_2$ had to be determined from the other three variables, and this set of variables reminded us of the ideal gas law! Then, referring to the reduced pressure and temperature, the ideal gas approximation seemed to be OK. In short, we have not directly considered the energy conservation principle at all. We may subsequently have an occasion to revisit this issue.

Assumed data:

Now, let us make assumptions about the data to be used for our calculations.

Suppose that the ambient temperature is 30 deg C, and the Eco-Cooler is kept at the mean sea level (MSL), say by the sea-side (rather than somewhere on a slope going down into the Death Valley [^]). Now, seated at a sea-side, the evaporative cooler isn’t going to be feasible because of humidity, and that’s the reason why we are at all considering using the Eco-Cooler. Alright. So to wrap up this point, we have to use data values at the MSL.

Suppose that we can use the ambient MSL atmospheric pressure for the inlet of the bottle; it would then mean that $P_1 = 101330$ Pa. (Note, this is an assumption; like with many other assumptions, we may have occasion to revisit it later on.) The air density at MSL and at 30 deg. C may be taken to be $\rho = 1.169$ kg/m^3. (Minor changes to this value turn out to have minimal impact on the predictions, so it’s OK to use, even if we might have made a mistake in looking it up hurriedly.)

For wind-speeds, let’s assume that the speed at the inlet (i.e., at the base of the bottle, which is exposed to the outside) is the same as the ambient wind-speed. (Again, this is an assumption; we may have the occasion to revisit it later on.)

Since the wind-speeds vary, and since the pressure drop (and hence the temperature drop) obviously depends on the inlet wind-speed, we will have to repeat our calculations for each wind-speed, again and again.

Referring again to the Wiki article for the Beaufort scale [^], to have representative wind-speed values, we choose to take the averages of the lower and upper wind speeds which together define the range for each wind-grade on the Beaufort scale. Thus, our $U_1$ could be one of: 0.5, 3.0, 8.5, 15.5, 24.0, 33.5, 44.0, all in kmph.

We are now ready to do our calculations. To recap: First, we calculate $U_2$ from $U_1$ using the continuity (mass conservation) equation and the known area ratio (which is about 14). Then we substitute the data in the re-arranged Bernoulli’s equation (which brings in its own assumptions) and obtain $P_2$, the pressure at the outlet (i.e. the neck of the bottle). From the ideal gas law (being used in place of the energy equation proper), we then calculate $T_2$.

Python script:

We use a Python script only because the calculations for $T_2$ have to be repeated again and again for different wind-speeds. Anyway, here is the Python script:

'''
This Python script calculates the expected
outlet temperature for a bottle in the Eco-Cooler.
See the relevant blog posts by Ajit R. Jadhav.
All units are in SI.
'''

d1 = 7.5 # ID at the inlet (i.e. at the base), in cm
d2 = 2.0 # ID at the outlet (i.e. at the neck), in cm
AR = (d1*d1)/(d2*d2) # Area ratio for the bottle

T1 = 30.0 # Ambient temp., in deg. C
T1 = T1 + 273.15 # Conversion from deg. C to K
rho = 1.169 # Density of air, in kg/m^3
P1 = 101330 # Ambient pressure, in Pa

# The Beaufort Scale wind speeds in kmph, and their text descriptions
bsa = [0.5, 3.0, 8.5, 15.5, 24.0, 33.5, 44.0]
bsta = ["Calm","Light air", "Light breeze", "Gentle breeze", "Moderate breeze", "Fresh breeze", "Strong breeze"]

# Calculate the expected temperatures for various wind-speeds
for i in range(7):
s1 = bsa[i] # wind-speed, in kmph
sText = bsta[i] # wind-speed description

U1 = s1 / 3.6 # conversion from kmph to m/s
U2 = U1*AR

# Calculate P2 using Bernoulli's equation
P2 = P1 + rho*(U1*U1 - U2*U2)/2.0

# Calculate T2 using the ideal gas law
T2 = T1*P2/P1
TC = T2 - 273.15 # conversion from K to deg. C
print( "%20s %6.1f %6.2lf %10.0f %6.1f" % (sText, s1, U1, P2, TC) )



The program written using Python is so simple, that you can very easily modify it, say to report any additional calculations that were made along the way.

Output data:

Here is the output data I get. The columns are: wind description in words, wind speed in kmph, wind speed in m/s, outlet pressure, and outlet temperature:

    Wind Description        U_1        P2, Pa   T2, deg. C
kmph  m/s
Calm    0.5   0.14     101328   30.0
Light air    3.0   0.83     101250   29.8
Light breeze    8.5   2.36     100689   28.1
Gentle breeze   15.5   4.31      99198   23.6
Moderate breeze   24.0   6.67      96219   14.7
Fresh breeze   33.5   9.31      91372    0.2
Strong breeze   44.0  12.22      84151  -21.4



Interpretation of results:

Our model predicts that when the breeze is strong (but less strong than when the tube is held near the window of a car that is traveling on an expressway), we should get ice formation at the neck of the bottle—in fact, it should be a super-cooled ice!

From your knowledge of what happens on the Indian sea-side, do you expect a mere half-foot tube of variable diameter, to begin to have ice-formation at its neck?

Obviously, the model we dreamt up has gone wrong somewhere. …

… But precisely where? … We have made so many assumptions…. Which of these assumptions are likely to have impacted our analysis the most? In what all places should we bring in the corrections to our model?

I have already given a lot of explicit notes—not just hints—while writing down the analysis above. So, go through the entire post once again, now pausing especially at the assumptions, and think how we may go on to improve our model.

I will return to the business of improving our model, in my next post.

And as always, sure drop me a line if you think I am going wrong somewhere.

… For instance, also give it a thought as to whether my analysis scheme, based on fluid mechanics, itself is wrong or what. … Here, you may want to refer to the comments on the blog post I had linked to last time [^], esp. the comments made there by Arnaut Jaspers and others. (Jaspers’ and others’ comments appear somewhere in the middle of all the comments, so you have to ask the Web page to load more comments some 3–4 times; the exact URL where the comments in question begin is this: [^]).

Alright, enjoy!

Ummm… Since I have given you Python scripts to play with, guess the usual section on a song I like has become redundant. So, let me mention the “other” song (re. my last post) when I finish this series of posts—which will take one, or at the most two more posts).

[I may come back and cross-check the latex entries in this post, grammar, etc., later on today itself, when I may perhaps edit this post just a bit, but not much. Done on 2016.10.02 itself.]

[E&OE]

# A few remarks on the Eco-Cooler

While generally browsing ISHRAE[^]’s Web site after a long while today, I ran into this coverage of the so-called Eco-Cooler [^] in their News Section.

… My earlier coverage of another creative usage of the used plastic bottles was here: [^] (see the “farm ponds” section in that post).

Anyway, coming back to the Eco-Cooler, a simple Google search on the inventor’s name (“Ashis Paul”) will give you quite a few links, e.g. here [^] and here [^]. A sketchy story as to how Paul ended up inventing the cooler is mentioned here [^].

The idea is so simple that you just have to wonder why no one else thought of it before!

Apart from the cultural reasons (people in this part of the world arguably don’t always try to tackle their life’s problems creatively; they arguably just sit idle and whine and complain) the other reason, I think, is that to a learned engineer (and I will call myself that), it would be difficult to think that the cooling effect obtained this way could be significant—the claim is a drop of up to 5 degrees Celcius (i.e. 9 degrees Fahrenheit) in the room temperature!

… I don’t know why, but somehow, at least on the face of it, a claim of this big a temperature drop does seem unbelievable, at least initially.

Anyway, here are a few things you could pursue, especially if you are a student of mechanical engineering:

• First, name (or hit your text books and find out) the principle that explains the cooling effect.
• Then, assume suitable values for the air flow, and using the appropriate thermodynamic/psychrometric charts and property tables, determine whether the inventor’s claim is acceptable. (I have not done this cross-check myself before writing this post; I just assumed that someone at ISHRAE must have done it!)
• Now check out the DIY YouTube videos on this invention. If interested, think of building an Eco-Cooler and measuring its performance yourself. (And if you do that, and if you are from Pune or a nearby place, then do drop me a line. I would love to come over and check it out myself.) Alternatively, think of doing a “simple” CFD analysis and compute the estimated temperature drop. [… And to think how people keep asking me where I get all my student-project ideas from!]

Next are a few notings (assuming that the cooling effect is indeed big enough) to help you put it all in the right context, and then also some pointers as to how you could try and modify (and even optimize) the existing design.

• Bamboo Curtains: First, try to put it in some context: People in India often use bamboo “chaTai”s or mats [^] as window covers/curtains. (Also the khus curtains.) Some of these “chaTai”s do carry regularly spaced holes. Do such mats (or even Venetian blinds) give rise to any cooling effect? Can they? Why or why not?
• Flow Pattern: Using ink blobs or other tracers in a flow of water, visualize the geometry of the flow going into a hole, and ask yourself: Is a bottle surface at all necessary? Why? When?
• Shape and Size: Would you get a better effect if you modify the dimensions of the bottles used in the Eco-Cooler? Is the size of the water bottle optimal? How about the shape?
• Mounting: What if you mount the bottles on the board not at the neck but at the base? Would it be more stable? Would it be more convenient because nothing goes protruding outside the room? Many questions below assume mouting on the base, such that the bottles come protruding inside the room. Let me call it the Internally Protrduding Design (IPD for short), as compared to the Externally Protruding Design (EPD, which is shown in the original photographs and videos).
• Materials: How about changing the material? What if you use clay for the tube?
• Evaporative Cooling: Assume IPD. Would keeping the clay tubes wet help enhance the cooling? You could keep them wet via a simple system of water from an overhead tank running over or percolating through the thickness of the clay tubes. For this purpose, arrange the base circles in a hexagonal lattice arrangement (rather than the simple square lattice they show in the original sketches and videos). In any case, compare the cooling obtained using the dry Eco-Cooler vs. that using the desert cooler. Then, compare it with the wet Eco-Cooler. To do that, first find out the natural cooling limitations of the desert cooler. (Something like this was a unit test question I had asked my ME (Heat Power) students last year.) Where would the wet Eco-Cooler be more effective—in the humid coastal areas (e.g. in Mumbai), or in the dry-and-hot areas (like in the plains or Delhi)?
• Cooling Achieved: Estimate the size of the biggest room that may be effectively cooled using EPD. Repeat for IPD. Also find out (by CFD analysis or by experiment) the locations where the cooling would be effective enough to bring (at least a bit of) comfort to a human being.
• Forced Circulation: What if you use forced air circulation with IPD? Would it lead to any better cooling? Don’t guess! Bring out your charts, tables and calculators once again, assume suitable values for fans, and provide a quantitative estimate. Then, also figure out if a forced air circulation could be economical enough.
• Enhanced Natural Circulation: (Assume both designs in turn.) Think if you could possibly enhance the natural air circulation by using some simple cardboard flaps erected on the outside of the room. (Do a quick-and-simple CFD analysis if you wish.)
• Radiation: How much of the temperature drop can be attributed to the obvious reduction in the radiative heating alone?
• Internal Reflection: Is the total internal reflection an important factor here? Would using clay tubes (of varying cross section) reduce the glare due to total internal reflection?
• Noise Generation: Does the arrangement emit sound (as in a patch of bamboo trees)?
• Aesthetics: Assume IPD: Think of how the cooler design may be used creatively for aesthetic enhancements of the room interiors in a middle-class apartment or bungalow. (The cooler doesn’t have to be used only in the slums!) Could ready-made panels of standard sizes be made in clay or alternative materials (e.g. cheap ceramics) just as cost-effectively? Would painting the bottles help?
• Reverberations: Assume IPD: Refer to technical acoustics. Can you reduce the sound reverberations if you use such shapes near walls? Could plastic bottles be at all effective in this respect? How about the clay tubes? Would the existence of the holes modify the sound-dampening effect due to the protruding tubes? Would they introduce unwanted modulations? Estimate the range of sound-frequencies (or of musical tones) that stand to get impacted (for the better or for the worse) due to the presence of the Eco-Cooler.

Enjoy…

A Song I Like:

(Hindi) “too laalee hai savere waalee, gagan rang de tu mere man kaa…”
Music: Sapan-Jagmohan
Singers: Kishore Kumar, Asha Bhosale
Lyrics: Indivar Naqsh Lyallpuri [^]

[BTW, this song reminds me of another song which has a similar tune. (I don’t know music well enough to make out “raaga”s. In fact, I often cannot even make out tones! I can only compare the tones in a hand-waving sort of a manner, that’s all! … It’s just that sometimes I happen to notice some similarities.) See if you can guess it—the other song. I will tell you the answer in my next post.]

[I have a habit of coming back and modifying my post a bit even after publication. But guess, at least for this post, there really isn’t anything left to add or modify.  Actually, I did modify! [sigh!] I clarified the two designs and even added the names for them. I even changed the title a bit!!…  Anyway, bye for now, and take care…]

[E&OE]

# Conservation of angular momentum isn’t [very] fundamental!

What are the conservation principles (in physics)?

In the first course on engineering mechanics (i.e. the mechanics of rigid bodies) we are taught that there are these three conservation principles: Conservation of: (i) energy, (ii) momentum, and (iii) angular momentum. [I am talking about engineering programs. That means, we live entirely in a Euclidean, non-relativistic, world.]

Then we learn mechanics of fluids, and the conservation of (iv) mass too gets added. That makes it four.

Then we come to computational fluid dynamics (CFD), and we begin to deal with only three equations: conservation of (i) mass, (ii) momentum, and (iii) energy. What happens to the conservation of the angular momentum? Why does the course on CFD drop it? For simplicity of analysis?

Ask that question to postgraduate engineers, even those who have done a specialization in CFD, and chances are, a significant number of them won’t be able to answer that question in a very clear manner.

Some of them may attempt this line of reasoning: That’s because in deriving the fluids equations (whether for a Newtonian fluid or a non-Newtonian one), the stress tensor is already assumed to be symmetrical: the shear stresses acting on the adjacent faces are taken to be equal and opposite (e.g. $\sigma_{xy} = \sigma_{yx}$). The assumed equality can come about only after assuming conservation of the angular momentum, and thus, the principle is already embedded in the momentum equations, as they are stated in CFD.

If so, ask them: How about a finite rotating body—say a gyroscope? (Assume rigidity for convenience, if you wish.) Chances are, a great majority of them will immediately agree that in this case, however, we have to apply the angular momentum principle separately.

Why is there this difference between the fluids and the finite rotating bodies? After all, both are continua, as in contrast to point-particles.

Most of them would fall silent at this point. [If not, know that you are talking with someone who knows his mechanics well!]

Actually, it so turns out that in continua, the angular momentum is an emergent/derivative property—not the most fundamental one. In continua, it’s OK to assume conservation of just the linear momentum alone. If it is satisfied, the conservation of angular momentum will get satisfied automatically. Yes, even in case of a spinning wheel.

Don’t believe me?

Let me direct you to Chad Orzel; check out here [^]. Orzel writes:

[The spinning wheel] “is a classical system, so all of its dynamics need to be contained within Newton’s Laws. Which means it ought to be possible to look at how angular momentum comes out of the ordinary linear momentum and forces of the components making up the wheel. Of course, it’s kind of hard to see how this works, but that’s what we have computers for.” [Emphasis in italics is mine.]

He proceeds to put together a simple demo in Python. Then, he also expands on it further, here [^].

Cool. If you think you have understood Orzel’s argument well, answer this [admittedly deceptive] question: How about point particles? Do we need a separate conservation principle for the angular momentum, in addition to that for the linear momentum at least in their case? How about the earth and the moon system, granted that both can be idealized as point particles (the way Newton did)?

Think about it.

A Song I Like:

(Hindi) “baandhee re kaahe preet, piyaa ke sang”
Singer: Sulakshana Pandit
Music: Kalyanji-Anandji
Lyrics: M. G. Hashmat

[E&OE]

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