Northwest of Iran has plant, animal and environmental varieties because of its geographical location. Therefore, alternate weather may have irreparable outcomes in numerous environmental sectors. In the prevailing research, it was turned into consideration to investigate the droughts that with inside the northwestern vicinity of Iran all through a 30-yr statistical period (1987–2016) that occurred, the usage of the records of fifty-five synoptic, climatology and rain gauge stations was evaluated with inside the positioned area. Using the SPI in a 12-month period, 360 maps had been produced for drought severity and month-to-month droughts. Then, the maps had been transformed into records, and the calculations associated with its descriptive information consisting of the common center, well-known circle and ellipse had been calculated on 4236 cells. The consequences of the month-to-month evaluation of droughts and moist duration intensities all through 360 months confirmed that the chance of susceptible moist durations with inside the important elements and extreme droughts with inside the southern half of the vicinity is better than different situations. More extreme droughts arise on this vicinity.
Stepwise derivation of flow equations of the Herschel–Bulkley (HB) model is not available in the literature. These equations are crucial for mechanical, chemical and petroleum engineering academia and industries where fundamental works on non-Newtonian fluids may be done to reach future models and estimation methods. Therefore, this work focuses on derivation of laminar flow equations and estimation methods of HB fluids through pipes. In this work, first, stepwise derivation of the HB fluid flow parameters consisting of fluid velocity, flow rate, average velocity and relative velocity equations is presented, followed by a straightforward mathematical model for use in numerical solution. Next, stepwise mathematical derivation of the laminar pressure drop equations by Merlo et al. (An innovative model for drilling fluid hydraulics. Paper presented at the SPE Asia Pacific oil and gas conference, Kuala Lumpur, Malaysia, 1995) and Gjerstad and Time (SPE J 20:1–18, 2014) is presented, and finally practical and user-friendly calculation procedures for different estimation methods are presented. The step-by-step derivation procedures presented in this work contribute to effective learning for engineering students and practitioners in addition to providing a clear example derivation guideline for future researchers to reach other more accurate non-Newtonian hydraulics models and estimation methods.
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