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Hi,

I`m seeking for help in the following problem.

A flat vertical board is travelling in water which is to be considered as ideal. One of its ends is in water, the other one is outside the water. Its velocity is v with respect to its normal. What is the velocity of the water stream directed up the board?

I made the following attempts to solve the problem...

Go to the frame of reference of the board. In this reference frame water is simultaneously approaching the board from one direction with velocity v.

This water must leave that area somehow so it has to move up or down with some other velocity. Let this velocity be: u.

This is only possible if a steady layer of water is created in front of the board.

Let the thickness of it be: d.

Now if I write the continuity equation for that layer i.e. the total amount of fluid entering=leaving then I get an equation between d, u and v.

At this point I stuck. I don`t know what else should I use. Conservation of momentum tells me that the velocity downwards= the velocity upwards=u. But It doesen`t contribute to the solution.

Then I`m not sure if I could/should use energy conservation or not. Maybe Bernoulli`s equation?

I know that the solution is u=v regardless of any dimensions.

If someone could help me with that I would really appreciate it :D

Then the b part is: what is the velocity u if the board is making an angle with the horizontal, but I think I could solve that as myself if I have the solution for part a.

Thanks,

I`m seeking for help in the following problem.

A flat vertical board is travelling in water which is to be considered as ideal. One of its ends is in water, the other one is outside the water. Its velocity is v with respect to its normal. What is the velocity of the water stream directed up the board?

I made the following attempts to solve the problem...

Go to the frame of reference of the board. In this reference frame water is simultaneously approaching the board from one direction with velocity v.

This water must leave that area somehow so it has to move up or down with some other velocity. Let this velocity be: u.

This is only possible if a steady layer of water is created in front of the board.

Let the thickness of it be: d.

Now if I write the continuity equation for that layer i.e. the total amount of fluid entering=leaving then I get an equation between d, u and v.

At this point I stuck. I don`t know what else should I use. Conservation of momentum tells me that the velocity downwards= the velocity upwards=u. But It doesen`t contribute to the solution.

Then I`m not sure if I could/should use energy conservation or not. Maybe Bernoulli`s equation?

I know that the solution is u=v regardless of any dimensions.

If someone could help me with that I would really appreciate it :D

Then the b part is: what is the velocity u if the board is making an angle with the horizontal, but I think I could solve that as myself if I have the solution for part a.

Thanks,