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The Colebrook equation for determination of hydraulic resistances is implicit in fluid flow friction factor and hence it has to be approximately solved using iterative procedure or using some of the approximate explicit formulas developed by many authors. The purpose of this paper is to compare different Lambert W based solutions of the Colebrook equation and to make comparisons among them and identify some constraints in applicability of certain solutions.

Alternate mathematically equivalents to the implicit Colebrook equation in explicit form with no approximation involved actually exist.

These alternate equations were developed using Lambert W‐function. The paper compares various implementations of the Lambert W methodology and shows that some of these are less able than others to yield solutions using modern computer hardware. This is because the functions require the evaluation of terms with numerical values outside the ranges that can be expressed on most computers.

Some of existed transformations cannot be applied for high values of relative roughness of inner pipe surface and the Reynolds number. This limitation applied only for computer computations. Other presented transformations do not sufferer of this limitation.

Presented procedures can be easily implemented in a computer code. Recommended solution can be used in all cases that can occur in engineering practice.

The paper shows some possible practical procedures for solution of the transformed Colebrook equation. Accuracy analysis and comparisons of presented formulas are also performed and recommendation for use is shown.

Considering the entrepreneurship nature and the high number of small and medium enterprises (SMEs) in the Latin American region, this study seeks to empirically test the relationship between organizational culture (OC), transformational leadership (TF) and organizational performance (OP) to support their long-term survival.

Under a post-positivism paradigm, quantitative approach and correlational scope, this research analyzed the interrelationship between OC, TF and OP across Peruvian SMEs. Confirmatory factor analysis (CFA) and structural equation modeling (SEM) were used to test the hypotheses based on the responses of 276 SMEs’ top executives from the commerce, services, manufacturing, construction and agriculture industries.

OC fully mediates the relationship between TL and OP. Although TF solely does not drive OP, the mediating effect of OC is crucial for SMEs’ long-term survival, especially considering their contribution to employment, poverty reduction and GDP in developing countries. Entrepreneurial transformational leaders inspire their followers to achieve goals, strive to develop individual skills, transmit confidence and leave aside their own interests to focus on the common goal of growing their entrepreneurship competitively.

The three variables under analysis have been applied to large companies and SMEs. However, this research enriches previous findings, highlighting the necessity for an adequate OC derived from an entrepreneur with TL, contributing to the survival of SMEs, whose results are critical for developing countries’ economies.

Considerando la naturaleza emprendedora y el elevado número de pequeñas y medianas empresas (PYMES) en Latinoamérica, este artículo busca probar empíricamente la relación entre cultura organizacional (OC), liderazgo transformacional (TF) y desempeño organizacional (OP), con el fin de contribuir a su sobrevivencia en el largo plazo.

Bajo el paradigma post-positivista, con un enfoque cuantitativo y un alcance correlacional, esta investigación analiza la interrelación entre las variables OC, el TF y el OP en PYMES peruanas. Para ello se utilizó análisis factorial confirmatorio (CFA) y modelo de ecuaciones estructurales (SEM) considerando las respuestas de 276 altos ejecutivos de PYMES provenientes de las industrias de comercio, servicios, manufactura, construcción y agricultura.

La cultura organizacional media completamente la relación entre el liderazgo transformacional y el desempeño organizacional. Aunque el liderazgo transformacional por sí solo no influye en el desempeño organizacional, el efecto mediador del TF es clave para la supervivencia a largo plazo de las PYMES, especialmente si se tiene en cuenta su contribución al empleo, su impacto en la reducción de la pobreza y el PBI, en los países en desarrollo. Los emprendedores con liderazgo transformacional inspiran a sus seguidores para alcanzar objetivos, se esfuerzan por desarrollar las habilidades de cada individuo, transmiten confianza y dejan de lado sus intereses personales para centrarse en el objetivo común del crecimiento de su emprendimiento con competitividad.

Las tres variables en estudio han sido aplicadas en empresas grandes y PYMES. Sin embargo, esta investigación enriquece los hallazgos previos, destacando la necesidad de contar con una adecuada cultura organizacional derivada de un emprendedor con liderazgo transformacional, contribuyendo con la supervivencia de las PYMEs, cuyos resultados son críticos para la economía de los países en desarrollo.