- #1
johnt447
- 9
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Blasius equation help :(
Hello so I'm working on the blasius solution for incompressible viscous flow. So far I have solved for f' and successfully plotted a graph of flow speed against [tex]\eta[/tex]. So from what I understand this is correct I got a gradient of velocity from 0 to the flow speed. Now i want to extend it to different values of x. Now this is my issue, the book I have has a equation for du/dy so my plan was find the gradient for each different value of x, hence since i know it always starts at 0 and ends at the flow speed i could find the points in between. Although when trying the equation out I found my gradient was in fact decreasing as x increases. As far as I understood the gradient (du/dy) should become larger as x increases. The equation I'm using is this
[tex]\frac{du}{dy}=V_{\infty}\sqrt{\frac{V_{\infty} }{\nu x}}f''(0)[/tex]
where [tex]V_{\infty}[/tex] is flow speed, [tex] \nu [/tex] is kinematic viscosity, u is speed and why y and x are the coordinates.
So what I did was use the equation with f''(0) bit included I wasn't sure if that has to change I thought since the gradient in a incompressible flow is constant.
I was thinking would it be ok (and not cheating :P) to just find the gradient manually say we know at the edge of a boundary layer u=10 and at the surface u=0 and hence we also know the value of y for each one we could find the gradient that way instead of using the above formula
Hello so I'm working on the blasius solution for incompressible viscous flow. So far I have solved for f' and successfully plotted a graph of flow speed against [tex]\eta[/tex]. So from what I understand this is correct I got a gradient of velocity from 0 to the flow speed. Now i want to extend it to different values of x. Now this is my issue, the book I have has a equation for du/dy so my plan was find the gradient for each different value of x, hence since i know it always starts at 0 and ends at the flow speed i could find the points in between. Although when trying the equation out I found my gradient was in fact decreasing as x increases. As far as I understood the gradient (du/dy) should become larger as x increases. The equation I'm using is this
[tex]\frac{du}{dy}=V_{\infty}\sqrt{\frac{V_{\infty} }{\nu x}}f''(0)[/tex]
where [tex]V_{\infty}[/tex] is flow speed, [tex] \nu [/tex] is kinematic viscosity, u is speed and why y and x are the coordinates.
So what I did was use the equation with f''(0) bit included I wasn't sure if that has to change I thought since the gradient in a incompressible flow is constant.
I was thinking would it be ok (and not cheating :P) to just find the gradient manually say we know at the edge of a boundary layer u=10 and at the surface u=0 and hence we also know the value of y for each one we could find the gradient that way instead of using the above formula