- #1

Type1civ

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This is my first post so I hope this in the right place. I am fairly sure this is quite a straight forward question but I having trouble working out the details of it.

"State the boundary conditions for an inviscid fluid at an impermeable fixed boundary

[tex] x_3-h(x_1,x_3)=0 [/tex]

where we do not permit normal velocity but permit non-zero tangential velocity"

So my attempt is quite limited as I feel if I could get started I'd be able to make some progress. But I believe that since the wall is stationary then the velocity of the fluid at the wall must also be stationary. And since it says that normal velocity is zero i guess this means that in the [itex] x_3 [/itex] direction the velocity is always zero.

so:

[tex] \mathbf{u}\cdot \mathbf{\hat x}_3 =0[/tex]

Then the velocity of the fluid only has components in the other two directions...

I was then also thinking that the [itex] \hat x_1 [/itex] component of velocity wouldn't change with [itex] x_1 [/itex] but I am not really sure why I think that. I am just getting a bit confused as you might be able to tell, any help would be really appreciated!

Edit: I am also not sure why my tex commands aren't working so if somebody could point out what I am doing wrong that would also be great...

"State the boundary conditions for an inviscid fluid at an impermeable fixed boundary

[tex] x_3-h(x_1,x_3)=0 [/tex]

where we do not permit normal velocity but permit non-zero tangential velocity"

So my attempt is quite limited as I feel if I could get started I'd be able to make some progress. But I believe that since the wall is stationary then the velocity of the fluid at the wall must also be stationary. And since it says that normal velocity is zero i guess this means that in the [itex] x_3 [/itex] direction the velocity is always zero.

so:

[tex] \mathbf{u}\cdot \mathbf{\hat x}_3 =0[/tex]

Then the velocity of the fluid only has components in the other two directions...

I was then also thinking that the [itex] \hat x_1 [/itex] component of velocity wouldn't change with [itex] x_1 [/itex] but I am not really sure why I think that. I am just getting a bit confused as you might be able to tell, any help would be really appreciated!

Edit: I am also not sure why my tex commands aren't working so if somebody could point out what I am doing wrong that would also be great...

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