Question

A steady, two-dimensional, incompressible flow field in the xy-plane has the following stream function: ? = ax2 + bxy + cy2, where a, b, and c are constants. (a) Obtain expressions for velocity components u and ?. (b) Verify that the flow field satisfies the incompressible continuity equation. 

          A steady, two-dimensional, incompressible flow field in the xy-plane has the following stream function: ? = ax2 + bxy + cy2, where a, b, and c are constants. (a) Obtain expressions for velocity components u and ?. (b) Verify that the flow field satisfies the incompressible continuity equation.
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University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
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A steady, two-dimensional, incompressible flow field in the xy-plane has the following stream function: ? = ax2 + bxy + cy2, where a, b, and c are constants. (a) Obtain expressions for velocity components u and ?. (b) Verify that the flow field satisfies the incompressible continuity equation.
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Transcript

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00:01 Here we can say that the given stream function is si is equal to a x square plus b xy plus c of y square then the velocity component can be calculated as v is equal to curly si divided by the curly x so we'll be equal to curly divided by the curly x of si that is a x square plus b xy plus c y square so from here the value of v will become equals to 2 a x plus b y so from here also we know that u is equal to minus curly side divided by the curly y so from here you will be equals to minus curly divided by the curly y of a x square plus b xy plus c y so from here you will become equal to minus bx minus 2c y so from here uh…
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