The other reply is mistaken about where exactly that constant comes from. When solving an exact differential equation in the "total differential" form, (stuff) = df, you automatically also have df=0. So when you find f(x,y,z) from the first equation (the "total differential"), you also have f(x,y,z)=C by integrating the second equation (df=0). The point is, the streamline expression is equal to a constant because all solutions to exact differential equations resulting from integrating a total differential pop out as a function equal to a constant.
Thank you for watching. For the stream function, the v-component of velocity is v = - partial psi / partial x. With the computed stream function this gives v=-2xy. Unlike computing velocity from the potential function, computing the v-component of velocity from the stream function introduces a minus sign.
![Streamlines and stream function [Aerodynamics #6]](http://i.ytimg.com/vi/LWpSGsOYxPI/mqdefault.jpg)
The equation being drawn at 5:44. I am confused as to why it makes sense.
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thank you so much sir,your video is really help me to understanding the basic of fluids mechanics. subscribed
Why u substitute c(y) in c(x) not reverse
Hi, why is the equation of the streamline equal to a constant? (See 10:05) Thanks.
That constant is for C(x) which is obtained upon integration. In this case, C(x) is some arbitrary constant and not a function of x
The other reply is mistaken about where exactly that constant comes from. When solving an exact differential equation in the "total differential" form, (stuff) = df, you automatically also have df=0. So when you find f(x,y,z) from the first equation (the "total differential"), you also have f(x,y,z)=C by integrating the second equation (df=0). The point is, the streamline expression is equal to a constant because all solutions to exact differential equations resulting from integrating a total differential pop out as a function equal to a constant.
solid explanation, now I get it
In the example, v=2xy. Besides that, great lecture!
Thank you for watching. For the stream function, the v-component of velocity is v = - partial psi / partial x. With the computed stream function this gives v=-2xy. Unlike computing velocity from the potential function, computing the v-component of velocity from the stream function introduces a minus sign.
@@ronhugo6225 Thank you for the clarification.
More videos please
people.ucalgary.ca/~hugo/WEBPAGES/fluid%20mechanics/fluidmech_lecture_list.html#head2
available there :)