• Fire Science and Engineering
• /
• v.21 no.4
• /
• pp.32-37
• /
• 2007

An accurate knowledge of the flash point is important in developing appropriate preventive and control measures in industrial fire protection. The lower flash points for the 2-propanol+acetic acid and 2-propanol+-n-propionic acid systems were measured by Cleveland open cup apparatus. The experimental data were compared with the values calculated by the Raoult's law, the Wilson equation and the NRTL(non random two liquids) equation. The calculated values based on the Wilson and NRTL equations were found to be better than those based on the Raoult's law. And the predictive curve of the flash point prediction model, based on NRTL equation described the experimentally-derived data were more effective than the case of the Wilson equation.

• Journal of the Korean Society of Safety
• /
• v.22 no.2 s.80
• /
• pp.47-52
• /
• 2007

The flash points and the fire points for the m-xylene+n-propionic acid and n-butanol+n-pentanol systems were measured by using Tag open-cup apparatus(AS1M D 1310-86). The experimental flash points of two binary systems were compared with the values calculated by the Raoult's law, Van Laar equation and Wilson equation. The calculated values based on the Raoult's law on m-xylene+n-propionic acid system were found to be better than those based on Van Laar and Wilson equations. The calculated values based on Van Laar equation on n-butanol+n-pentanol system were found to be better than those based on the Raoult's law and Wilson equation. The the fire points for the m-xylene+n-propionic acid system were about $7{\sim}8^{\circ}C$ above the flash points. In the case of n-butanol+n-pentanol system, the flash points and the fire points had been found to be identical.

• Fire Science and Engineering
• /
• v.25 no.3
• /
• pp.113-118
• /
• 2011

The flash point is an important indicator of the flammability of a chemical. The minimum flash point behaviour (MFPB) is exhibited when the flash point of a mixture is below the flash points of the individual components. The identification of this behaviour is critical, because a hazardous situation results from taking the lowest component flash point value as the mixture flash point. In this study, the flash points for the n-butanol + n-decane and n-octane + n-propanol systems which exhibit MFPB, were measured by Tag open-cup apparatus. The experimental data were compared with the alues calculated by the Raoult's law, the van Laar equation and the Wilson equation. The calculated values based on the van Laar and Wilson equations were found to be better than those based on the Raoult's law. It was concluded that the van Laar and Wilson equations were more effective than the Raoult' law at describing the activity coefficients for non-ideal solution such as the n-butanol + n-decane and n-octane + n-propanol systems. The predictive curve of the flash point prediction model based on the Wilson equation described the experimentally-derived data more effectively than was the case when the prediction model was based upon the van Laar equation.

• Journal of the Korean Wood Science and Technology
• /
• v.37 no.2
• /
• pp.128-136
• /
• 2009

Curved glued laminated timber (glulam) is rapidly coming into the domestic modern timber frame buildings and predominant in building construction. The radial stress is frequently occurred in curved beams and is a critical design parameter in curved glulam. Three models, Wilson equation, Exact solution and Approximation equation were introduced to determine the radial stress of curved glulam under pure bending condition. It is obvious that radial stress distribution between small radius and large radius was different due to slight change of neutral plane location to center line. If the beam design with extremely small radius, it should be considered to determine the exact location of maximum radial stress. The current standard KSF 3021 was reviewed and would be considered some adjustment determining the optimum radius in curved glulam. Current design principle is that the stress factor is given by the curvature term only in constant depth of the beam, but like tapered or small radius of beams, the stress factor by Wilson equation was underestimated. So current design formula should be considered to improvement for characterizing the radial stress factor under pure bending condition.

• International Journal of Safety
• /
• v.10 no.1
• /
• pp.5-9
• /
• 2011

Two popular activity coefficient models, Wilson and NRTL equations have been used to correlate the published flash point data on the n-propanol + propionic acid and n-butanol + propionic acid systems through the optimization method. The results of these correlation were compared with the results calculated by Raoult's law. The optimization method were found to be better than those based on the Raoult's law. The optimization method based on the Wilson equation described the published data more effectively than was the case when the optimization method was based upon the NRTL equation.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.4
• /
• pp.1157-1169
• /
• 2016

We find the distributional solutions of the Wilson's functional equations $$u{\circ}T+u{\circ}T^{\sigma}-2u{\otimes}v=0,\\u{\circ}T+u{\circ}T^{\sigma}-2v{\otimes}u=0,$$ where $u,v{\in}{\mathcal{D}}^{\prime}({\mathbb{R}}^n)$, the space of Schwartz distributions, T(x, y) = x + y, $T^{\sigma}(x,y)=x+{\sigma}y$, $x,y{\in}{\mathbb{R}}^n$, ${\sigma}$ an involution, and ${\circ}$, ${\otimes}$ are pullback and tensor product of distributions, respectively. As a consequence, we solve the $Erd{\ddot{o}}s$' problem for the Wilson's functional equations in the class of locally integrable functions. We also consider the Ulam-Hyers stability of the classical Wilson's functional equations $$f(x+y)+f(x+{\sigma}y)=2f(x)g(y),\\f(x+y)+f(x+{\sigma}y)=2g(x)f(y)$$ in the class of Lebesgue measurable functions.

• Fire Science and Engineering
• /
• v.17 no.2
• /
• pp.50-55
• /
• 2003

The lower flash points for the binary system, n-butanol+n-decane, were measured by Pensky-Martens closed cup tester. The experimental results showed the minimum in the flash point versus composition curve. The experimental data were compared with the values calculated by the reduced model under an ideal solution assumption and the flash point-prediction models based on the Van Laar and Wilson equations. The predictive curve based upon the reduced model deviated form the experimental data for this system. The experimental results were in good agreement with the predictive curves, which use the Van Laar and Wilson equations to estimate activity coefficients. However, the predictive curve of the flash point prediction model based on the Willson equation described the experimentally-derived data more effectively than that of the flash point prediction model based on the Van Laar equation.

• Communications of the Korean Mathematical Society
• /
• v.35 no.3
• /
• pp.711-722
• /
• 2020

Given a semigroup S generated by its squares equipped with an involutive automorphism 𝝈 and a multiplicative function 𝜇 : S → ℂ such that 𝜇(x𝜎(x)) = 1 for all x ∈ S, we determine the complex-valued solutions of the following functional equations f(xy) + 𝜇(y)f(𝜎(y)x) = 2f(x)g(y), x, y ∈ S and f(xy) + 𝜇(y)f(𝜎(y)x) = 2f(y)g(x), x, y ∈ S.

• Communications of the Korean Mathematical Society
• /
• v.38 no.4
• /
• pp.1063-1074
• /
• 2023

Let S be a semigroup. We determine the complex-valued solutions of the following functional equation f(xy) + 𝜇(y)f(𝜎(y)x) = 2f(x)g(y), x, y ∈ S, where 𝜎 : S → S is an automorphism, and 𝜇 : S → ℂ is a multiplicative function such that 𝜇(x𝜎(x)) = 1 for all x ∈ S.

• Journal of the Korean Institute of Gas
• /
• v.14 no.5
• /
• pp.19-25
• /
• 2010

The flash points for the systems, o-xylene+n-pentanol and m-xylene+n-hexanol, were measured by using Tag open-cup tester(ASTM D1310-86). The experimental data were compared with the values calculated by the Raoult's law and the optimization method using van Laar and Wilson equations. The calculated values based on the optimization method were found to be better than those based on the Raoult's law. The predictive curve of the flash point prediction model based on the van Laar equation described the experimentally-derived data more effectively than was the case when the prediction model was based upon the Wilson equation.