Matematica Detras Cambios De Agua En Su Pecera

Math behind water changes — when the myths should die Eugene Dulov, Ph.D. in Applied Math
Faculty of Science and Technology University of Applied and Ambiental Sciences U.D.C.A Bogotá, Colombia
Looking through the article “Aquarium Science: Time for a Change: A Mathematical Investigation of Water Changes” by David E. Boruchowitz I was impressed, since my personal experience as hobbyist and mathteacher, proved to me that a lot of persons tend to ignore your reasonable advices about filtration, water changes, overstocking and overfeeding. So the attempt to show them that math behind health of their swimming pets is clear and manageable, impressed me. But that article completely avoided analytical math expressions, thus generating a lot of doubts and even leading to several wrongconclusions. In reality you shouldn’t be a math freak to follow our simple derivations – we want go further the school and college math. First of all, we don’t need exact numbers and volumes, since such quantity as concentration or it multipliers represent pollution level. Here usually is a number of waste particles (in millions), is a talk volume. At the same time, the name total dissolved

solids(TDS) of the tank do not represent all kinds of waste substances dissolved in water, so even the proud owner of an advanced TDS-meter will obtain only partial information about concentration. Numerous biological and toxicological studies showed that living beings are affected by concentration of toxic components and time of exposure. In other words, your fish will suffer mostly from accumulatedquantities, except the presence of such substances like , which is highly toxic and can be accumulated inside fine gravel-send mixtures without appropriate cleaning. Speaking about “regular” venoms, the most typical example is nitrogenammonia intoxication of fishes during long transportation. You may buy such fish looking initially quite healthy in your local pet-store, but seeing it dead in a couple ofmonth without any clearly visible symptoms. The same goes for your fish tank. Since all living things inside it produce or transform waste components, we can start building our formula assuming that variable represents

concentration at the beginning of the period right after water change. Over a certain constant period of time (hours, daily, weekly) concentration increases by pollutioncoefficient overall concentration at the end of the period is + . Before going any further, we have to explain that quantities and usually are defined as a and

relation between the number of particles (in millions) divided by the volume (actual volume of water, gallons or liters) of the fish tank. This also means that our model is relevant only for closed filtration systems (not run-through) wherethe amount of water evaporated between water changes (manly for open or partially covered tanks) is very small and can be neglected. So, if you want to reduce them, then you have to take into account three factors:    Reduce number of inhabitants producing waste; Careful feeding (do not overfeed) and food selection (the lowest possible content of ashes, phosphorus especially); Bigger tank or, atleast replenishing water in case of strong evaporation.

But if you want to count the concentration of toxic matters only, there exist another factors which can reduce the value of the coefficient :    Better filtration (mechanical, biological and chemical); Abundant living plants; Special chemical addends like ammonia lockers/breakers which can absorb or decompose dangerous components. Inany case, regular water changes still are the best way to control the health of your tank habitants. Since usually we talk about water changes in terms of percents (like 10% daily, 40% weekly), the most important parameter
= 1− ℎ 100% = 1−
% %

%

represents the quantity in of the “old” water kept inside your tank. Dimensionless parameter is a real number between 0 and 1:
= 0.9 or =1−...