The twodimensional velocity field of circular streamlines ar

The two-dimensional velocity field of circular streamlines around the origin (0, 0) is given by u = y (m/sec) and v = -x (m/sec), where u and v are the x- and y-components of the velocity, respectively. If the pressure at the origin is 35 kPa, what it the pressure at the location x = 5, y = 0? What is the pressure at x = 0, y = 5?

Solution

Let us consider the 2D flow of a perfect fluid.It is given that v is the velocity in y direction and u is the velocity in x direction.

In case I,x =5 and y = 0 I.e. Streamline is horizontal u is the velocity and ds is dx. u = y(m/s)

= UX+vy

= y*5 -x*0= 5y and,

Y*0 -x*5 = 5x

We know that, Equation of streamline flow as dx/u = dy/v for 2D flow.

Therefore,lnx= lny + lnc,

lnx=lnyc

Cancelling ln,

x=yc

At x=5,y =0 and x=0,y=5

C =0