Problem 57497. Locate image wells

Created by ChrisR

Solve Later

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The method involves reflecting each well about the boundary as shown below: the image well lies on a line running through the real well and perpendicular to the boundary, and the distances between the wells and the boundary are equal. </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>If a well is pumping water near an impermeable soil unit, then the image well pumps in the same sense (i.e., either both extract water or both inject water): the components of the water velocity perpendicular to the boundary cancel each other and satisfy the condition of no flow across the boundary. If the well is pumping near a river, then the image well pumps in the opposite sense (i.e., one well extracts and the other injects). At the boundary, the water injected by one well replaces the water extracted by the other, and the head, which is related to the water level, is constant on the boundary.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Write a function that takes coordinates of the real wells and coordinates of two points on the boundary and returns the coordinates of the image wells. For this problem you do not have to indicate the sense of the pumping. </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"401\"/><w:attr w:name=\"width\" w:val=\"610\"/><w:attr w:name=\"verticalAlign\" w:val=\"baseline\"/><w:attr w:name=\"altText\" w:val=\"\"/><w:attr w:name=\"relationshipId\" 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","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div 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; "><div style="block-size: 664.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 332.35px; transform-origin: 407px 332.35px; vertical-align: baseline; "><div style="block-size: 84px; 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 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span 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: 369.933px 8px; transform-origin: 369.933px 8px; unicode-bidi: normal; "><span style="">A mathematical model of wells pumping groundwater near a boundary can be constructed using the method of images, which is also used in fluid mechanics, electrodynamics, and other fields. The method involves reflecting each well about the boundary as shown below: the image well lies on a line running through the real well and perpendicular to the boundary, and the distances between the wells and the boundary are equal. </span></span></div><div style="block-size: 105px; 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 52.5px; text-align: left; transform-origin: 384px 52.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span 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: 370.7px 8px; transform-origin: 370.7px 8px; unicode-bidi: normal; "><span style="">If a well is pumping water near an impermeable soil unit, then the image well pumps in the same sense (i.e., either both extract water or both inject water): the components of the water velocity perpendicular to the boundary cancel each other and satisfy the condition of no flow across the boundary. If the well is pumping near a river, then the image well pumps in the opposite sense (i.e., one well extracts and the other injects). At the boundary, the water injected by one well replaces the water extracted by the other, and the head, which is related to the water level, is constant on the boundary.</span></span></div><div style="block-size: 42px; 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; "><span 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: 365.892px 8px; transform-origin: 365.892px 8px; unicode-bidi: normal; "><span style="">Write a function that takes coordinates of the real wells and coordinates of two points on the boundary and returns the coordinates of the image wells. For this problem you do not have to indicate the sense of the pumping. </span></span></div><div style="block-size: 406.7px; 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 203.35px; text-align: left; transform-origin: 384px 203.35px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><img class="imageNode" style="vertical-align: baseline;width: 610px;height: 401px" 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" 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A mathematical model of wells pumping groundwater near a boundary can be constructed using the method of images, which is also used in fluid mechanics, electrodynamics, and other fields. The method involves reflecting each well about the boundary as shown below: the image well lies on a line running through the real well and perpendicular to the boundary, and the distances between the wells and the boundary are equal. 
If a well is pumping water near an impermeable soil unit, then the image well pumps in the same sense (i.e., either both extract water or both inject water): the components of the water velocity perpendicular to the boundary cancel each other and satisfy the condition of no flow across the boundary. If the well is pumping near a river, then the image well pumps in the opposite sense (i.e., one well extracts and the other injects). At the boundary, the water injected by one well replaces the water extracted by the other, and the head, which is related to the water level, is constant on the boundary.
Write a function that takes coordinates of the real wells and coordinates of two points on the boundary and returns the coordinates of the image wells. For this problem you do not have to indicate the sense of the pumping.

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Problem 57497. Locate image wells

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