{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-06T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":51168,"title":"Flow rate in a pipe","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 370px 8px; transform-origin: 370px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFind the flow rate (m^3/s) in a pipe that has a radius of r in cm, velocity of v (m/s) and round the flow rate to 4 decimal places.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = flow_rate(r,v)\r\n\r\nend","test_suite":"%%\r\nr = 10;\r\nv=13.54;\r\ny_correct = 0.4254;\r\nassert(isequal(flow_rate(r,v),y_correct))\r\n\r\n\r\n%%\r\nr = 8.4;\r\nv= 9.66;\r\ny_correct = 0.2141;\r\nassert(isequal(flow_rate(r,v),y_correct))\r\n\r\n\r\n%%\r\nr = 7.3;\r\nv= 5.37;\r\ny_correct = 0.0899;\r\nassert(isequal(flow_rate(r,v),y_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":995198,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":51,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-03-24T07:05:35.000Z","updated_at":"2026-02-10T11:15:13.000Z","published_at":"2021-03-24T07:05:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the flow rate (m^3/s) in a pipe that has a radius of r in cm, velocity of v (m/s) and round the flow rate to 4 decimal places.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2441,"title":"Bernoulli's Equation","description":"Bernoulli's equation states that for an incompressible fluid the following summation is constant across the flow: v^2/2 + g*z + P/rho, where v = fluid velocity, g = gravitational constant, z = elevation, P = pressure, and rho = density (constant throughout the fluid due to incompressible nature). The values of v, z, and P change at points along the flow whereas values for g and rho are assumed constant.\r\n\r\nAssuming all units are congruent, fill in the holes (zero values) in the given matrix of v, z, and P values, in three respective rows for n measured points (3 x n matrix). Use g = 9.81. Rho will be given for each test case. The input matrix will contain one complete set of values to calculate the constant. The completed matrix will not contain any zeros (or very small numbers).\r\n","description_html":"\u003cp\u003eBernoulli's equation states that for an incompressible fluid the following summation is constant across the flow: v^2/2 + g*z + P/rho, where v = fluid velocity, g = gravitational constant, z = elevation, P = pressure, and rho = density (constant throughout the fluid due to incompressible nature). The values of v, z, and P change at points along the flow whereas values for g and rho are assumed constant.\u003c/p\u003e\u003cp\u003eAssuming all units are congruent, fill in the holes (zero values) in the given matrix of v, z, and P values, in three respective rows for n measured points (3 x n matrix). Use g = 9.81. Rho will be given for each test case. The input matrix will contain one complete set of values to calculate the constant. The completed matrix will not contain any zeros (or very small numbers).\u003c/p\u003e","function_template":"function out = Bernoulli_eq(in,rho)\r\n out = in;\r\nend","test_suite":"%%\r\nin = [1 0.6 0.8 1 1; 1 1.1 1.2 1.3 1.4; 10 0 0 0 0];\r\nrho = 1.0;\r\nout = [1 0.6 0.8 1 1; 1 1.1 1.2 1.3 1.4; 10 9.339 8.218 7.057 6.0760];\r\neps = 1e-3;\r\nassert(sum(sum(abs(Bernoulli_eq(in,rho)-out))) \u003c eps)\r\n\r\n%%\r\nin = [1 0.6 0.8 1 1; 0 0 1 0 0; 10 12 10 14 8];\r\nrho = 1.5;\r\nout = [1 0.6 0.8 1 1; 0.9817 0.8784 1 0.7098 1.1176; 10 12 10 14 8];\r\neps = 1e-3;\r\nassert(sum(sum(abs(Bernoulli_eq(in,rho)-out))) \u003c eps)\r\n\r\n%%\r\nin = [0 0 0 1 0; 1 1.1 1.2 1.3 1.4; 10 12 10 14 8];\r\nrho = 0.75;\r\nout = [4.1896 3.2027 3.6917 1 3.8779; 1 1.1 1.2 1.3 1.4; 10 12 10 14 8];\r\neps = 1e-3;\r\nassert(sum(sum(abs(Bernoulli_eq(in,rho)-out))) \u003c eps)\r\n\r\n%%\r\nin = [1 1.6 0.8 1 1 0 0 1 1 1.2; 1 1.6 0 1.3 0 1.9 1.8 1.7 0 1.8; 0 12 5 0 8 7.5 7.7 0 11.1 0];\r\nrho = 0.97;\r\nout = [1 1.6 0.8 1 1 2.4397 2.7390 1 1 1.2; 1 1.6 2.4335 1.3 2.0999 1.9 1.8 1.7 1.7741 1.8; 18.466 12 5 15.6113 8 7.5 7.7 11.805 11.1 10.6401];\r\neps = 1e-3;\r\nassert(sum(sum(abs(Bernoulli_eq(in,rho)-out))) \u003c eps)","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":57,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-07-16T17:48:45.000Z","updated_at":"2026-01-31T12:50:33.000Z","published_at":"2014-07-16T17:48:45.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBernoulli's equation states that for an incompressible fluid the following summation is constant across the flow: v^2/2 + g*z + P/rho, where v = fluid velocity, g = gravitational constant, z = elevation, P = pressure, and rho = density (constant throughout the fluid due to incompressible nature). The values of v, z, and P change at points along the flow whereas values for g and rho are assumed constant.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAssuming all units are congruent, fill in the holes (zero values) in the given matrix of v, z, and P values, in three respective rows for n measured points (3 x n matrix). Use g = 9.81. Rho will be given for each test case. The input matrix will contain one complete set of values to calculate the constant. The completed matrix will not contain any zeros (or very small numbers).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":51168,"title":"Flow rate in a pipe","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 370px 8px; transform-origin: 370px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFind the flow rate (m^3/s) in a pipe that has a radius of r in cm, velocity of v (m/s) and round the flow rate to 4 decimal places.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = flow_rate(r,v)\r\n\r\nend","test_suite":"%%\r\nr = 10;\r\nv=13.54;\r\ny_correct = 0.4254;\r\nassert(isequal(flow_rate(r,v),y_correct))\r\n\r\n\r\n%%\r\nr = 8.4;\r\nv= 9.66;\r\ny_correct = 0.2141;\r\nassert(isequal(flow_rate(r,v),y_correct))\r\n\r\n\r\n%%\r\nr = 7.3;\r\nv= 5.37;\r\ny_correct = 0.0899;\r\nassert(isequal(flow_rate(r,v),y_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":995198,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":51,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-03-24T07:05:35.000Z","updated_at":"2026-02-10T11:15:13.000Z","published_at":"2021-03-24T07:05:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the flow rate (m^3/s) in a pipe that has a radius of r in cm, velocity of v (m/s) and round the flow rate to 4 decimal places.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2441,"title":"Bernoulli's Equation","description":"Bernoulli's equation states that for an incompressible fluid the following summation is constant across the flow: v^2/2 + g*z + P/rho, where v = fluid velocity, g = gravitational constant, z = elevation, P = pressure, and rho = density (constant throughout the fluid due to incompressible nature). The values of v, z, and P change at points along the flow whereas values for g and rho are assumed constant.\r\n\r\nAssuming all units are congruent, fill in the holes (zero values) in the given matrix of v, z, and P values, in three respective rows for n measured points (3 x n matrix). Use g = 9.81. Rho will be given for each test case. The input matrix will contain one complete set of values to calculate the constant. The completed matrix will not contain any zeros (or very small numbers).\r\n","description_html":"\u003cp\u003eBernoulli's equation states that for an incompressible fluid the following summation is constant across the flow: v^2/2 + g*z + P/rho, where v = fluid velocity, g = gravitational constant, z = elevation, P = pressure, and rho = density (constant throughout the fluid due to incompressible nature). The values of v, z, and P change at points along the flow whereas values for g and rho are assumed constant.\u003c/p\u003e\u003cp\u003eAssuming all units are congruent, fill in the holes (zero values) in the given matrix of v, z, and P values, in three respective rows for n measured points (3 x n matrix). Use g = 9.81. Rho will be given for each test case. The input matrix will contain one complete set of values to calculate the constant. The completed matrix will not contain any zeros (or very small numbers).\u003c/p\u003e","function_template":"function out = Bernoulli_eq(in,rho)\r\n out = in;\r\nend","test_suite":"%%\r\nin = [1 0.6 0.8 1 1; 1 1.1 1.2 1.3 1.4; 10 0 0 0 0];\r\nrho = 1.0;\r\nout = [1 0.6 0.8 1 1; 1 1.1 1.2 1.3 1.4; 10 9.339 8.218 7.057 6.0760];\r\neps = 1e-3;\r\nassert(sum(sum(abs(Bernoulli_eq(in,rho)-out))) \u003c eps)\r\n\r\n%%\r\nin = [1 0.6 0.8 1 1; 0 0 1 0 0; 10 12 10 14 8];\r\nrho = 1.5;\r\nout = [1 0.6 0.8 1 1; 0.9817 0.8784 1 0.7098 1.1176; 10 12 10 14 8];\r\neps = 1e-3;\r\nassert(sum(sum(abs(Bernoulli_eq(in,rho)-out))) \u003c eps)\r\n\r\n%%\r\nin = [0 0 0 1 0; 1 1.1 1.2 1.3 1.4; 10 12 10 14 8];\r\nrho = 0.75;\r\nout = [4.1896 3.2027 3.6917 1 3.8779; 1 1.1 1.2 1.3 1.4; 10 12 10 14 8];\r\neps = 1e-3;\r\nassert(sum(sum(abs(Bernoulli_eq(in,rho)-out))) \u003c eps)\r\n\r\n%%\r\nin = [1 1.6 0.8 1 1 0 0 1 1 1.2; 1 1.6 0 1.3 0 1.9 1.8 1.7 0 1.8; 0 12 5 0 8 7.5 7.7 0 11.1 0];\r\nrho = 0.97;\r\nout = [1 1.6 0.8 1 1 2.4397 2.7390 1 1 1.2; 1 1.6 2.4335 1.3 2.0999 1.9 1.8 1.7 1.7741 1.8; 18.466 12 5 15.6113 8 7.5 7.7 11.805 11.1 10.6401];\r\neps = 1e-3;\r\nassert(sum(sum(abs(Bernoulli_eq(in,rho)-out))) \u003c eps)","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":57,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-07-16T17:48:45.000Z","updated_at":"2026-01-31T12:50:33.000Z","published_at":"2014-07-16T17:48:45.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBernoulli's equation states that for an incompressible fluid the following summation is constant across the flow: v^2/2 + g*z + P/rho, where v = fluid velocity, g = gravitational constant, z = elevation, P = pressure, and rho = density (constant throughout the fluid due to incompressible nature). The values of v, z, and P change at points along the flow whereas values for g and rho are assumed constant.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAssuming all units are congruent, fill in the holes (zero values) in the given matrix of v, z, and P values, in three respective rows for n measured points (3 x n matrix). Use g = 9.81. Rho will be given for each test case. The input matrix will contain one complete set of values to calculate the constant. 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