Research Article
Application of Statistical Thermodynamics to Modelling Fluid Discharge Through a Circular Orifice System
Issue:
Volume 10, Issue 1, February 2025
Pages:
1-11
Received:
29 November 2024
Accepted:
7 January 2025
Published:
24 January 2025
DOI:
10.11648/j.ajmie.20251001.11
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Abstract: This study presents the application of statistical thermodynamics in modeling orifice discharge function. Micro-based variables such as the velocity of fluid flow at the midpoint of the reservoir elevated to the mid-height of the orifice and the head loss due to sudden expansion that was neglected in the classical discharge model were considered in the modeling operation. Bernoulli’s equation was used to determine the velocity model at the exit point of the orifice. Some classical thermodynamic models were used to compute certain parameters like: the flow pressure of fluid (water) (Pf), pressure drop (Pd), exit temperature, polytropic work (W), heat absorption/rejection (Q), and flow energy (E). The grand canonical ensemble which applies to open systems was used to establish a relationship between the flow discharge and energy variables according to the micro-based behavior of fluid flow through the orifice that generates the observable macro-flow behavior of a fluid. The discharge values obtained using the experimental (Qe), classical (Q(c,)) and statistically derived orifice discharge (Qs) models were compared and accessed statistically using the indices of: mean bias error (MBE), mean percentage error (MPE), root mean square error (RMSE), Nash-Sutcliffe equation (NSE), and coefficient of correlation (R). The results of the study showed that the new model that was derived using a statistical thermodynamics approach outperformed the classical orifice model as its MBE value of 5.032E-05, MPE of 5.62, RMSE of 5.24E-05, NSE of 0.873 and R of 0.999 were all better than that of the classical model having an MBE value of -1.0042E-04, MPE of -11.30 (underestimation), RMSE of 5.814E-05, and R of 0.999. In addition, the values of Pf, T2, W, Q, and E increased as the flow head increased. The polytropic work, W was negative, indicating that the system did some work. The positive values of Q and E showed that the system absorbed energy from its environment during the fluid flow operation. Furthermore, all the orifice discharge functions (Qs, Q(c) and Qe) had a direct linear relationship with flow energy, E which therefore satisfied the grand canonical ensemble model for the open system’s thermodynamic micro-variable description. Hence, the new orifice discharge model is recommended for the industry's volumetric flow rate measurement of Newtonian fluids.
Abstract: This study presents the application of statistical thermodynamics in modeling orifice discharge function. Micro-based variables such as the velocity of fluid flow at the midpoint of the reservoir elevated to the mid-height of the orifice and the head loss due to sudden expansion that was neglected in the classical discharge model were considered in...
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,
Chinonso Hubert Achebe
