This document summarizes the calculation of heptane height in a cylindrical cistern using Bernoulli's theorem and fluid dynamics principles.
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[...] Simplified models : For many practical problems, it is often acceptable to make approximations by using simplified models. Assuming the tank is cylindrical, we can obtain results that are sufficiently accurate for many applications without having to consider more complex shapes. However, it is essential to note that this assumption is not always realistic in all cases. In certain situations, tanks may have more complex shapes for design, space, or other practical considerations. In such cases, more sophisticated mathematical models may be necessary to account for the actual geometry of the tank. [...]
[...] We can thus calculate the height of heptane in the tank. n=0.75*2*1.08=1.62 m Application of Bernoulli's theorem: We consider that there are no losses of charge (no loss of energy). Bernoulli's theorem is an important concept in fluid dynamics that establishes a relationship between the pressure, velocity, and altitude of a fluid in perfect and stationary flow. Here is the expression of the Bernoulli quantity for an incompressible and lossless flow : v²+gz+p/?=constant where : - p is the pressure at the point of study, - ? [...]
[...] Let's calculate the surface area of the hole. The hole is circular with a diameter of d=1.8cm=0.018 m A=?×r² where r is the radius of the circle. r=d/2=0.018 /2=0.009 m Now, we can use this value to calculate the area of the hole : A=?×(0.009 )² A=?×0.000081 A?0.000254 m² Thus, the surface of the circular hole is approximately 0.000254 m² We can now calculate the flow rate: Q=v.A=7,60*0,000254=0.00193m3/s=1.93 L/s Evolution of flow rate over time The flow rate in the reservoir is QR= - dn/dt being the free surface when the liquid height is n. [...]
[...] Evaporation Rate Calculation: ? Once we have calculated the heat fluxes entering and leaving, we can establish a thermal balance for the heptane puddle and use the balance equation to solve for the evaporation rate Unfortunately, without the specific data on the intensity of solar radiation, the exact wind speed, and other meteorological parameters, I am unable to perform the calculations with precision. In the case of a single chemical species, there is no planar geometric interface at the microscopic level between the two media: the molecules in the internal region (the liquid) are linked to their neighbors in a complex geometry. [...]
[...] On the other hand, a molecule that comes into contact can form a bond that makes it part of the liquid. This mechanism is described by the Hertz-Knudsen relation, giving the mass flux per unit area of the interface at the macroscopic level : where p is the pressure, ps the saturated vapor pressure, M the molar mass and ? an efficiency coefficient of the phenomenon depending on the species and temperature T (adhesion coefficient, in English 'sticking coefficient') such that R is the universal gas constant. [...]
