The Flow under Gravity of a Swirling Liquid through an Orifice-Plate
An examination has been made of the whirlpool formed when a perfect liquid possessing swirl passes under gravity through a circular sharp-edged hole in the base of a large tank. Relaxation methods were applied to determine the velocity distribution in the liquid and the shapes of the air-core and of...
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| Veröffentlicht in: | Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences Mathematical and physical sciences, 1949-12, Vol.199 (1059), p.443-457 |
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| container_issue | 1059 |
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| container_title | Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences |
| container_volume | 199 |
| creator | Binnie, Alfred Maurice Davidson, John Frank |
| description | An examination has been made of the whirlpool formed when a perfect liquid possessing swirl passes under gravity through a circular sharp-edged hole in the base of a large tank. Relaxation methods were applied to determine the velocity distribution in the liquid and the shapes of the air-core and of the initial part of the emergent jet. In the numerical case considered, the swirl was large; and it was found that, except close to the orifice, the radial and vertical velocities were too small to influence the shape of the air-core within the tank. Below the orifice the liquid was emitted as a conical and rapidly thinning jet. In spite of the contraction at the edge of the hole, the discharge was not greatly different from that determined by Binnie & Hookings’ (ɪ948) approximate method for flow through a trumpet. Experiments with water were made for comparison with the calculations. It was noticed that under certain conditions of low swirl the annular jet assumed a cylindrical vibrating form. The theory of these oscillations, which was confirmed by observation, shows that, unless the air-core occupies a large fraction of the cross-section of the jet, the wavelength is nearly the same as that in a ‘solid’ jet of the same outer diameter. |
| doi_str_mv | 10.1098/rspa.1949.0147 |
| format | Article |
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Relaxation methods were applied to determine the velocity distribution in the liquid and the shapes of the air-core and of the initial part of the emergent jet. In the numerical case considered, the swirl was large; and it was found that, except close to the orifice, the radial and vertical velocities were too small to influence the shape of the air-core within the tank. Below the orifice the liquid was emitted as a conical and rapidly thinning jet. In spite of the contraction at the edge of the hole, the discharge was not greatly different from that determined by Binnie & Hookings’ (ɪ948) approximate method for flow through a trumpet. Experiments with water were made for comparison with the calculations. It was noticed that under certain conditions of low swirl the annular jet assumed a cylindrical vibrating form. 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Series A, Mathematical and physical sciences</title><addtitle>Proc. R. Soc. Lond. A</addtitle><addtitle>Proc. R. Soc. Lond. A</addtitle><description>An examination has been made of the whirlpool formed when a perfect liquid possessing swirl passes under gravity through a circular sharp-edged hole in the base of a large tank. Relaxation methods were applied to determine the velocity distribution in the liquid and the shapes of the air-core and of the initial part of the emergent jet. In the numerical case considered, the swirl was large; and it was found that, except close to the orifice, the radial and vertical velocities were too small to influence the shape of the air-core within the tank. Below the orifice the liquid was emitted as a conical and rapidly thinning jet. In spite of the contraction at the edge of the hole, the discharge was not greatly different from that determined by Binnie & Hookings’ (ɪ948) approximate method for flow through a trumpet. Experiments with water were made for comparison with the calculations. It was noticed that under certain conditions of low swirl the annular jet assumed a cylindrical vibrating form. The theory of these oscillations, which was confirmed by observation, shows that, unless the air-core occupies a large fraction of the cross-section of the jet, the wavelength is nearly the same as that in a ‘solid’ jet of the same outer diameter.</description><subject>Bessel functions</subject><subject>Boundary conditions</subject><subject>Flow velocity</subject><subject>Interfacial tension</subject><subject>Kinetics</subject><subject>Liquids</subject><subject>Mathematical constants</subject><subject>Mathematical tables</subject><subject>Radial velocity</subject><subject>Vibration</subject><issn>1364-5021</issn><issn>0080-4630</issn><issn>1471-2946</issn><issn>2053-9169</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1949</creationdate><recordtype>article</recordtype><recordid>eNp9UcFu1DAUjBBIlMKVAyf_QBa_2E7sE6oKLRWLWrWlV8vr2BsvIQ520nb79XU2qNIKtRfbT29m3rxxln0EvAAs-OcQe7UAQcUCA61eZQfphLwQtHyd3qSkOcMFvM3exbjBGAvGq4Ps63Vj0Enr79DY1Sag06Bu3bBF3iKFru5caF23Rkv3d3Q1Gprgx3WDVIfOg7NOm_yiVYN5n72xqo3mw7_7MPt18u36-Hu-PD89Oz5a5ppW5ZCXYmWrGhtKWA2EA2YVr0HpWq9oYQ0jCrQpWKFAKVZapaBIhs1KYG2TwIocZotZVwcfYzBW9sH9UWErAcspAzllIKcM5JRBIpCZEPw2GfPamWErN34MXSqfZ8WXWJdXF0cgCL8FIVxaIrE4AVwRAC4fXL-TmwBJUkgX42jkDrY_5v-pn-apmzj48LSZ4ISVqZnPTRcHc__UVOG3LCtSMXnDqeQ3jCz5zx-ySHiY8Y1bN-kXjdzbJRV9iGpncGeNUpI4X17kTHa17wbTDXtEace2lX1tySMXqcZs</recordid><startdate>19491207</startdate><enddate>19491207</enddate><creator>Binnie, Alfred Maurice</creator><creator>Davidson, John Frank</creator><general>The Royal Society</general><general>Cambridge University Press</general><scope>BSCLL</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>19491207</creationdate><title>The Flow under Gravity of a Swirling Liquid through an Orifice-Plate</title><author>Binnie, Alfred Maurice ; Davidson, John Frank</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c476t-69bf7d0e435d13810578d1acdcb42fe53a1ce252a1aa56faa12021eb90cf476b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1949</creationdate><topic>Bessel functions</topic><topic>Boundary conditions</topic><topic>Flow velocity</topic><topic>Interfacial tension</topic><topic>Kinetics</topic><topic>Liquids</topic><topic>Mathematical constants</topic><topic>Mathematical tables</topic><topic>Radial velocity</topic><topic>Vibration</topic><toplevel>online_resources</toplevel><creatorcontrib>Binnie, Alfred Maurice</creatorcontrib><creatorcontrib>Davidson, John Frank</creatorcontrib><collection>Istex</collection><collection>CrossRef</collection><jtitle>Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Binnie, Alfred Maurice</au><au>Davidson, John Frank</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Flow under Gravity of a Swirling Liquid through an Orifice-Plate</atitle><jtitle>Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences</jtitle><stitle>Proc. R. Soc. Lond. A</stitle><addtitle>Proc. R. Soc. Lond. A</addtitle><date>1949-12-07</date><risdate>1949</risdate><volume>199</volume><issue>1059</issue><spage>443</spage><epage>457</epage><pages>443-457</pages><issn>1364-5021</issn><issn>0080-4630</issn><eissn>1471-2946</eissn><eissn>2053-9169</eissn><abstract>An examination has been made of the whirlpool formed when a perfect liquid possessing swirl passes under gravity through a circular sharp-edged hole in the base of a large tank. Relaxation methods were applied to determine the velocity distribution in the liquid and the shapes of the air-core and of the initial part of the emergent jet. In the numerical case considered, the swirl was large; and it was found that, except close to the orifice, the radial and vertical velocities were too small to influence the shape of the air-core within the tank. Below the orifice the liquid was emitted as a conical and rapidly thinning jet. In spite of the contraction at the edge of the hole, the discharge was not greatly different from that determined by Binnie & Hookings’ (ɪ948) approximate method for flow through a trumpet. Experiments with water were made for comparison with the calculations. It was noticed that under certain conditions of low swirl the annular jet assumed a cylindrical vibrating form. The theory of these oscillations, which was confirmed by observation, shows that, unless the air-core occupies a large fraction of the cross-section of the jet, the wavelength is nearly the same as that in a ‘solid’ jet of the same outer diameter.</abstract><cop>London</cop><pub>The Royal Society</pub><doi>10.1098/rspa.1949.0147</doi><tpages>15</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1364-5021 |
| ispartof | Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences, 1949-12, Vol.199 (1059), p.443-457 |
| issn | 1364-5021 0080-4630 1471-2946 2053-9169 |
| language | eng |
| recordid | cdi_royalsociety_journals_10_1098_rspa_1949_0147 |
| source | JSTOR Mathematics & Statistics; Jstor Complete Legacy; Alma/SFX Local Collection |
| subjects | Bessel functions Boundary conditions Flow velocity Interfacial tension Kinetics Liquids Mathematical constants Mathematical tables Radial velocity Vibration |
| title | The Flow under Gravity of a Swirling Liquid through an Orifice-Plate |
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