Pathline and Streamline problem

[Abigail1997]

1. Homework Statement
As above

Homework Equations

Not sure.

The Attempt at a Solution

I've only ever seen one of these problems and it was in the form of V=Axi-Ayj, so much simpler and even then it was poorly explained by the lecturer. I understand what a velocity field is but not much more.

 

[BvU]

Hi, Abigail,

Try A=0 to get started. The velocity vector at point $(1,1)$ is ?

 

[BvU]

statement, all variables and given/known data
I have completed question a, getting e^(t+((t^2)/4)) and e^t respectively and found the streamline for t=0, getting x=Cy, c being a constant- but am totally out of idea for finding it when t=1. I have been told the answer is e^3/2 but not sure how to get there

Homework Equations

dx/u=dy/v[/B]

first paragraph counts as an attempt at solution, I would say. (Choosing C as parameter is unfortunate, though, if the problem statement already has a C.)
Can't guess what u and v are; the components of $\vec v$ ?
You found the streamlines at t =0 from $\vec v = Bx\hat\imath + Cy\hat\jmath$
Aren't the streamlines for t=1 given by simply substituting t=1 and doing the same thing ?

 

[Abigail1997]

first paragraph counts as an attempt at solution, I would say. (Choosing C as parameter is unfortunate, though, if the problem statement already has a C.)
Can't guess what u and v are; the components of $\vec v$ ?
You found the streamlines at t =0 from $\vec v = Bx\hat\imath + Cy\hat\jmath$
Aren't the streamlines for t=1 given by simply substituting t=1 and doing the same thing ?

Yeah I realized that and changed it to D :) correct, u and v represent the x and y components of V. As for the subbing in t=1, that's what I thought but I cannot seem to get the correct answer (e^3/2) but I'm probably making a silly mistake somewhere and just can't see it

 

[BvU]

Check the non-moving dashes in the first picture here (watch out for headaches).
These dashes at fixed grid points you can draw for t=1 in your exercise. They should suggest the $e^{3\over 2}$