{"id":{"repo_id":"city-london","oai_identifier":"oai:openaccess.city.ac.uk:8329"},"canonical_url":"https://search.dev.ndltd.org/etd/city-london/oai:openaccess.city.ac.uk:8329","repository":{"repo_id":"city-london","name":"City University of London","base_url":"https://openaccess.city.ac.uk/cgi/oai2"},"display":{"title":"Scour under air entrained jets below dams and flip buckets","abstract":"The most popular and accurate form of expression used over the last 50 years for estimating scour under falling jets is: D=Kqx Hy/dz There is, however, disagreement between Authors concerning which values should be used for K, x, y and z. It was. surmised by the writer that plunge pool air entrainment could also be a relevant parameter and apparatus was built to examine this assumption. Two dimensional testing without air indicated scour to be independent of head drop (H) and directly proportional to flow (q), such that x=1.0 and y=0.0. The introduction of air, to give air/water ratios that a falling jet would entrain naturally, produced values for x of about 0.6 to 0.7 and y of about 0.03 to 0.2. The latter are very close to normally assumed values and it is concluded that such values have been produced by the aeration on previous Authors' models. As aeration is not a simple function of q and H, not allowing for it was bound to produce variable results. Results from the testing indicated that scour depth varied with aeration to maintain a characteristic force on the particles of bed material. The expression obtained for two dimensional scour was: 8.4 q (1 + /a ) 0.5 h 0.15 /d 0.10 It was also reasoned that the expression would have to be modified to allow for the lateral development of plunge pools in the three dimensional case such that (approximately): D=K qo-5 (l +A)0.25 h 0.15 /do* 10 An analysis of data from previous hydraulic model tests of various dams produced the expression: D=1.438 q 0.6 (1 +/a ) 0.25 h 0.15 /d 0.10 with a coefficient of variation of results of 26.8%. This expression was used to analyse a body of scour data from prototype dams and also gave good results. It is concluded that it represents a new form of expression for calculating scour under jets which seems to be applicable to models and prototypes. In the case of the former it is at least as accurate as any previous expressions. It is concluded that any future plunge pool scour formulae should incorporate an allowance for air entrainment if they are not to be essentially flawed one last conclusion from this study is that air entrainments on prototypes may not be significantly different to those encountered on reasonably sized models, given that there may be an upper limit on & of around 2 to 3 and that such figures can easily be approached on models.","abstract_html":"The most popular and accurate form of expression used over the last 50 years for estimating scour under falling jets is: D=Kqx Hy/dz There is, however, disagreement between Authors concerning which values should be used for K, x, y and z. It was. surmised by the writer that plunge pool air entrainment could also be a relevant parameter and apparatus was built to examine this assumption. Two dimensional testing without air indicated scour to be independent of head drop (H) and directly proportional to flow (q), such that x=1.0 and y=0.0. The introduction of air, to give air/water ratios that a falling jet would entrain naturally, produced values for x of about 0.6 to 0.7 and y of about 0.03 to 0.2. The latter are very close to normally assumed values and it is concluded that such values have been produced by the aeration on previous Authors' models. As aeration is not a simple function of q and H, not allowing for it was bound to produce variable results. Results from the testing indicated that scour depth varied with aeration to maintain a characteristic force on the particles of bed material. The expression obtained for two dimensional scour was: 8.4 q (1 + /a ) 0.5 h 0.15 /d 0.10 It was also reasoned that the expression would have to be modified to allow for the lateral development of plunge pools in the three dimensional case such that (approximately): D=K qo-5 (l +A)0.25 h 0.15 /do* 10 An analysis of data from previous hydraulic model tests of various dams produced the expression: D=1.438 q 0.6 (1 +/a ) 0.25 h 0.15 /d 0.10 with a coefficient of variation of results of 26.8%. This expression was used to analyse a body of scour data from prototype dams and also gave good results. It is concluded that it represents a new form of expression for calculating scour under jets which seems to be applicable to models and prototypes. In the case of the former it is at least as accurate as any previous expressions. It is concluded that any future plunge pool scour formulae should incorporate an allowance for air entrainment if they are not to be essentially flawed one last conclusion from this study is that air entrainments on prototypes may not be significantly different to those encountered on reasonably sized models, given that there may be an upper limit on & of around 2 to 3 and that such figures can easily be approached on models.","abstract_has_math":false,"creators":["Mason, P.J."],"institution":"City University London","degree_name":"phd","degree_level":"doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1987,"date_issued":"1987-04","date_published":"1987-04","updated_at":"2026-07-24T01:39:11Z","subjects":["TA Engineering (General). Civil engineering (General)"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Mason, P.J."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["1987-04"]},{"key":"dc:date.issued","label":"Date","values":["1987-04"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Department of Engineering","Civil Engineering"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["City University London"]},{"key":"dc:relation.isreferencedby","label":"Dc Relation Isreferencedby","values":["https://openaccess.city.ac.uk/id/eprint/8329/"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["phd"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["TA Engineering (General). Civil engineering (General)"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://openaccess.city.ac.uk/id/eprint/8329/1/Scour_under_air_entrained_jets_below_dams_and_flip_buckets.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The most popular and accurate form of expression used over the last 50 years for estimating scour under falling jets is: D=Kqx Hy/dz There is, however, disagreement between Authors concerning which values should be used for K, x, y and z. It was. surmised by the writer that plunge pool air entrainment could also be a relevant parameter and apparatus was built to examine this assumption. Two dimensional testing without air indicated scour to be independent of head drop (H) and directly proportional to flow (q), such that x=1.0 and y=0.0. The introduction of air, to give air/water ratios that a falling jet would entrain naturally, produced values for x of about 0.6 to 0.7 and y of about 0.03 to 0.2. The latter are very close to normally assumed values and it is concluded that such values have been produced by the aeration on previous Authors' models. As aeration is not a simple function of q and H, not allowing for it was bound to produce variable results. Results from the testing indicated that scour depth varied with aeration to maintain a characteristic force on the particles of bed material. The expression obtained for two dimensional scour was: 8.4 q (1 + /a ) 0.5 h 0.15 /d 0.10 It was also reasoned that the expression would have to be modified to allow for the lateral development of plunge pools in the three dimensional case such that (approximately): D=K qo-5 (l +A)0.25 h 0.15 /do* 10 An analysis of data from previous hydraulic model tests of various dams produced the expression: D=1.438 q 0.6 (1 +/a ) 0.25 h 0.15 /d 0.10 with a coefficient of variation of results of 26.8%. This expression was used to analyse a body of scour data from prototype dams and also gave good results. It is concluded that it represents a new form of expression for calculating scour under jets which seems to be applicable to models and prototypes. In the case of the former it is at least as accurate as any previous expressions. It is concluded that any future plunge pool scour formulae should incorporate an allowance for air entrainment if they are not to be essentially flawed one last conclusion from this study is that air entrainments on prototypes may not be significantly different to those encountered on reasonably sized models, given that there may be an upper limit on & of around 2 to 3 and that such figures can easily be approached on models."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Scour under air entrained jets below dams and flip buckets"]}]}],"canonical_facts":{"dc:creator":["Mason, P.J."],"dc:date":["1987-04"],"dc:date.issued":["1987-04"],"dc:description.abstract":["The most popular and accurate form of expression used over the last 50 years for estimating scour under falling jets is: D=Kqx Hy/dz There is, however, disagreement between Authors concerning which values should be used for K, x, y and z. It was. surmised by the writer that plunge pool air entrainment could also be a relevant parameter and apparatus was built to examine this assumption. Two dimensional testing without air indicated scour to be independent of head drop (H) and directly proportional to flow (q), such that x=1.0 and y=0.0. The introduction of air, to give air/water ratios that a falling jet would entrain naturally, produced values for x of about 0.6 to 0.7 and y of about 0.03 to 0.2. The latter are very close to normally assumed values and it is concluded that such values have been produced by the aeration on previous Authors' models. As aeration is not a simple function of q and H, not allowing for it was bound to produce variable results. Results from the testing indicated that scour depth varied with aeration to maintain a characteristic force on the particles of bed material. The expression obtained for two dimensional scour was: 8.4 q (1 + /a ) 0.5 h 0.15 /d 0.10 It was also reasoned that the expression would have to be modified to allow for the lateral development of plunge pools in the three dimensional case such that (approximately): D=K qo-5 (l +A)0.25 h 0.15 /do* 10 An analysis of data from previous hydraulic model tests of various dams produced the expression: D=1.438 q 0.6 (1 +/a ) 0.25 h 0.15 /d 0.10 with a coefficient of variation of results of 26.8%. This expression was used to analyse a body of scour data from prototype dams and also gave good results. It is concluded that it represents a new form of expression for calculating scour under jets which seems to be applicable to models and prototypes. In the case of the former it is at least as accurate as any previous expressions. It is concluded that any future plunge pool scour formulae should incorporate an allowance for air entrainment if they are not to be essentially flawed one last conclusion from this study is that air entrainments on prototypes may not be significantly different to those encountered on reasonably sized models, given that there may be an upper limit on & of around 2 to 3 and that such figures can easily be approached on models."],"dc:format":["application/pdf"],"dc:identifier.uri":["https://openaccess.city.ac.uk/id/eprint/8329/1/Scour_under_air_entrained_jets_below_dams_and_flip_buckets.pdf"],"dc:publisher.department":["Department of Engineering","Civil Engineering"],"dc:publisher.institution":["City University London"],"dc:relation.isreferencedby":["https://openaccess.city.ac.uk/id/eprint/8329/"],"dc:subject":["TA Engineering (General). Civil engineering (General)"],"dc:title":["Scour under air entrained jets below dams and flip buckets"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["doctoral"],"dc:type.qualificationname":["phd"]},"updated_at":"2026-07-24T01:39:11Z"}