00:01
As we know u is equals to 2c x y and v is equals to c multiplied by a square plus x square minus y square.
00:08
These are the two equations.
00:10
In a part we will differentiate u with respect to x partial differentiate u with respect to x and this value is equals to 2c y partial differentiate v with respect to y and this value is equals to c multiplied by minus 2 y.
00:23
On adding these two equations we get du divided by dx plus dv divided by del v divided by del y is equals to where this is v and this is equals to 2c y minus 2c y and this is equals to 0.
00:36
Therefore we can say flow is incompressible.
00:42
Flow is incompressible.
00:45
Now v part in v part we know omega g is given by equals to 1 divided by 2 multiplied by del v divided by del x here v is partial differentiating with respect to x minus del u divided by del y partial differentiation of u with respect to y.
01:06
On putting values we get del v divided by del x is equals to c multiplied by 2x.
01:12
This is we know on partial differentiating and del u divided by del y is equals to 2c x.
01:30
2c x this is equals to 0.
01:33
Therefore we can say flow is irrotational.
01:36
Flow is irrotational.
01:40
Here v part flow is irrotational.
01:43
Now we will solve c part.
01:46
In c part we know u is equals to minus del phi divided by del x partial differentiation of phi with respect to x.
01:54
This implies del phi is equals to minus u dx.
01:59
On integrating both side this equation integration of del phi is equals to here del phi is equals to integration of minus 2c x y del x.
02:11
On integration we get phi is equals to minus 2c x square by divided by 2 plus k.
02:19
Again further solving phi is equals to minus x square y plus k.
02:24
Let this be first equation.
02:25
Now we will differentiate it with respect to y.
02:28
We get del phi divided by del y partial differentiation and this is equals to minus x square plus del k divided by y.
02:38
This is second equation.
02:40
Now using the second equation we also know del phi is equals to del phi divided by del y that is partial differentiation of phi with respect phi with respect to y is equals to minus v which is equals to minus c multiplied by a square plus x square minus y square...