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The velocity components describe a 2-D flow as u=10x^3 and v=-10x^2y draw a flonwnet by using a combination of atleast 4 stream line and 4 equipotential lines . aslo verify the continous equatioon for the above flow field?
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The velocity components describe a 2-D flow as u=10x^3 and v=-10x^2y d...
Flownet for 2-D Flow with given velocity components:
To draw a flownet for the given velocity components u = 10x^3 and v = -10x^2y, we need to plot a combination of streamlines and equipotential lines. Streamlines represent the flow direction, while equipotential lines represent the pressure distribution in the flow field.
Drawing Streamlines:
Streamlines can be obtained by integrating the given velocity components. We integrate u with respect to x and v with respect to y to obtain the stream function, ψ.
Integrating u = 10x^3 with respect to x, we get ψ = 2.5x^4 + C1.
Integrating v = -10x^2y with respect to y, we get ψ = -5x^2y^2 + C2.
Equating the two stream functions, we get 2.5x^4 + C1 = -5x^2y^2 + C2. Rearranging the equation, we have C1 - C2 = -2.5x^4 - 5x^2y^2.
We can choose different values for C1 - C2 to obtain different streamlines. Let's consider four streamlines with values of C1 - C2 as -10, -5, 0, and 5.
For C1 - C2 = -10, the equation becomes -2.5x^4 - 5x^2y^2 = -10. We can plot this equation on a graph to obtain the first streamline.
Similarly, we can plot the equations -2.5x^4 - 5x^2y^2 = -5, -2.5x^4 - 5x^2y^2 = 0, and -2.5x^4 - 5x^2y^2 = 5 to obtain the other three streamlines.
Drawing Equipotential Lines:
Equipotential lines can be obtained by integrating the given velocity components. We integrate u with respect to y and v with respect to x to obtain the potential function, φ.
Integrating u = 10x^3 with respect to y, we get φ = 10x^3y + C3.
Integrating v = -10x^2y with respect to x, we get φ = -10/3x^3y^2 + C4.
Equating the two potential functions, we get 10x^3y + C3 = -10/3x^3y^2 + C4. Rearranging the equation, we have C3 - C4 = -10/3x^3y^2 - 10x^3y.
We can choose different values for C3 - C4 to obtain different equipotential lines. Let's consider four equipotential lines with values of C3 - C4 as -10, -5, 0, and 5.
For C3 - C4 = -10, the equation becomes -10/3x^3y^2 - 10x^3y = -10. We can plot this equation on a graph to obtain the first equipotential line.
Similarly, we can plot the equations -10/3
To draw a flownet for the given velocity components u = 10x^3 and v = -10x^2y, we need to plot a combination of streamlines and equipotential lines. Streamlines represent the flow direction, while equipotential lines represent the pressure distribution in the flow field.
Drawing Streamlines:
Streamlines can be obtained by integrating the given velocity components. We integrate u with respect to x and v with respect to y to obtain the stream function, ψ.
Integrating u = 10x^3 with respect to x, we get ψ = 2.5x^4 + C1.
Integrating v = -10x^2y with respect to y, we get ψ = -5x^2y^2 + C2.
Equating the two stream functions, we get 2.5x^4 + C1 = -5x^2y^2 + C2. Rearranging the equation, we have C1 - C2 = -2.5x^4 - 5x^2y^2.
We can choose different values for C1 - C2 to obtain different streamlines. Let's consider four streamlines with values of C1 - C2 as -10, -5, 0, and 5.
For C1 - C2 = -10, the equation becomes -2.5x^4 - 5x^2y^2 = -10. We can plot this equation on a graph to obtain the first streamline.
Similarly, we can plot the equations -2.5x^4 - 5x^2y^2 = -5, -2.5x^4 - 5x^2y^2 = 0, and -2.5x^4 - 5x^2y^2 = 5 to obtain the other three streamlines.
Drawing Equipotential Lines:
Equipotential lines can be obtained by integrating the given velocity components. We integrate u with respect to y and v with respect to x to obtain the potential function, φ.
Integrating u = 10x^3 with respect to y, we get φ = 10x^3y + C3.
Integrating v = -10x^2y with respect to x, we get φ = -10/3x^3y^2 + C4.
Equating the two potential functions, we get 10x^3y + C3 = -10/3x^3y^2 + C4. Rearranging the equation, we have C3 - C4 = -10/3x^3y^2 - 10x^3y.
We can choose different values for C3 - C4 to obtain different equipotential lines. Let's consider four equipotential lines with values of C3 - C4 as -10, -5, 0, and 5.
For C3 - C4 = -10, the equation becomes -10/3x^3y^2 - 10x^3y = -10. We can plot this equation on a graph to obtain the first equipotential line.
Similarly, we can plot the equations -10/3
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The velocity components describe a 2-D flow as u=10x^3 and v=-10x^2y draw a flonwnet by using a combination of atleast 4 stream line and 4 equipotential lines . aslo verify the continous equatioon for the above flow field?
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The velocity components describe a 2-D flow as u=10x^3 and v=-10x^2y draw a flonwnet by using a combination of atleast 4 stream line and 4 equipotential lines . aslo verify the continous equatioon for the above flow field? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The velocity components describe a 2-D flow as u=10x^3 and v=-10x^2y draw a flonwnet by using a combination of atleast 4 stream line and 4 equipotential lines . aslo verify the continous equatioon for the above flow field? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The velocity components describe a 2-D flow as u=10x^3 and v=-10x^2y draw a flonwnet by using a combination of atleast 4 stream line and 4 equipotential lines . aslo verify the continous equatioon for the above flow field?.
The velocity components describe a 2-D flow as u=10x^3 and v=-10x^2y draw a flonwnet by using a combination of atleast 4 stream line and 4 equipotential lines . aslo verify the continous equatioon for the above flow field? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The velocity components describe a 2-D flow as u=10x^3 and v=-10x^2y draw a flonwnet by using a combination of atleast 4 stream line and 4 equipotential lines . aslo verify the continous equatioon for the above flow field? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The velocity components describe a 2-D flow as u=10x^3 and v=-10x^2y draw a flonwnet by using a combination of atleast 4 stream line and 4 equipotential lines . aslo verify the continous equatioon for the above flow field?.
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