in a flow field the velocity vector is given by v 3y 2 i 6xj the stream line passes through 1 1

Name: in a flow field the velocity vector is given by v 3y 2 i 6xj the stream line passes through 1 1 determine the equation of the stream line 29002
Uploaded: 2022-05-22T03:38:28-08:00
Duration: 5 min 55 s
Channel: Marinus Kenechukwu
Description: in a flow field the velocity vector is given by v 3y 2 i 6xj the stream line passes through 1 1 determine the equation of the stream line 29002

To determine the equation of the stream line for the given velocity vector field (vec{V} = -3y

In a flow field the velocity vector is given by v 3y 2 i 6xj...

Transcript

00:01 Hello.

00:03 So for this problem, we are given the velocity vector of a fluid as v is equal to minus y square i minus 6xj.

00:14 And then we are told to find the equation of streamline at the point 1 -1.

00:30 Generally, we know that this velocity vector can be written in this form.

00:39 And so when we look at this, we can simply say comparing the problem.

00:43 We were given and this general form of the velocity vector i can say therefore that u is equal to minus y squared and v is equal to minus 6 x now what is the equation of a streamline the equation of a streamline is simply the x over u is equal to the y over v which is equal to the z over w now because we have a two -dimensional problem here in terms of only u and v we will not have anything to do with this term.

01:33 And so i can take just the first two terms and i can say that for this are streamline, we'll have this equation and putting in what the values of u and v are, i will simply have the x over minus y squared is equal to the y over minus 6x.

01:57 Now when i simplify this by cross multiplying, i will get 6.

02:02 6x the x is equal to y squared the y i've cancelled the minus because it's on both sides now what do i do i simply because this is a separable variable differential equation ordinary differential equation actually so this is a separable variable and i've already separated the variables so what i simply have to do is to integrate both sides and so i'll put the integral for 6x the x is equal to the integral for y squared the y.

02:46 When i perform this integral here, i'll get 6x squared over 2 is equal to y cube over 3 plus c...

Question

In a flow field the velocity vector is given by ⃗𝑉 = −3𝑦 2 𝑖̂ − 6𝑥𝑗̂. The stream line passes through (1, 1). Determine the equation of the stream line.

Question

In a flow field the velocity vector is given by ⃗𝑉 = −3𝑦 2 𝑖̂ − 6𝑥𝑗̂. The stream line passes through (1, 1). Determine the equation of the stream line.

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