Hydromechanical nature of bulk materials movement in vertical pipe of round and square cross-sections

Hydromechanical nature of bulk materials movement in vertical pipe of round and square cross-sections | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Hydromechanical nature of bulk materials movement in vertical pipe of round and square cross-sections Nail Sadykov, Konstantin Bartosh, Egor Zhuravlev, Maksim Zakharov, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7740936/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 11 You are reading this latest preprint version Abstract The traditional gravitational flow of bulk materials has been researched in the vertical pipe of round and square cross-sections on the basis of the viscous fluid model. We assume that the medium viscosity ratio is proportional to the pressure in a given point. Such dependence of viscosity results in the fact that the mass flow rate per unit time does not depend on the height of the column of bulk material. When in steady motion, the dependence of pressure on a vertical coordinate and the distribution of a medium velocity’s vertical component in the cross-sections of pipes has been obtained theoretically. It is shown, that there is a pressure limit some distance away from the free surface of bulk materials. The results obtained via theoretical predictions coincide with ones obtained experimentally. The results for the gravitational flow of bulk materials in pipes are generalized to the movement of such materials along an inclined plane. bulk materials stress tensors viscosity gravitational flow hydrodynamics of bulk materials Navier-Stokes equation Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 26 Oct, 2025 Reviews received at journal 26 Oct, 2025 Reviews received at journal 20 Oct, 2025 Reviewers agreed at journal 19 Oct, 2025 Reviews received at journal 14 Oct, 2025 Reviewers agreed at journal 10 Oct, 2025 Reviewers agreed at journal 06 Oct, 2025 Reviewers invited by journal 05 Oct, 2025 Editor assigned by journal 04 Oct, 2025 Submission checks completed at journal 04 Oct, 2025 First submitted to journal 29 Sep, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7740936","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":529893747,"identity":"4533d95e-e70a-445b-9b7e-7d63451175ce","order_by":0,"name":"Nail 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