Question

PTUURBIJ + 5. Velocity field of a 2-dimensional flow motion of an inviscid and incompressible fluid is given by, u=x', v=y', w=0 a) Fluid velocity and the magnitude of velocity at a point M(-3,2). b) Fluid acceleration and its magnitude at a same point.

Answer 1

Write the velocity equation in vector form. ū = uî +vſ+ wk=(x)i +(y)+(0)ế=xi+y?ſ +O Substitute the given coordinate values. V =(-3) i +(2) j+Ok=-127ỉ +8j+o Calculate the magnitude of velocity at given point. 171= v(-127)2 +(8)* +(0)* = 127.25 m/s Calculate the x-component of acceleration. =(x) [x]+(v) [+]+(0) [ ] =(x")-3x² +(vº).0+(0).0 = 3x +0+0 > a = 3x Calculate the y-component of acceleration.

=C2)(*]+(3) L"]+020] =(x®).0+(yº)-3y2 +(0) 0 = 0 +3y3 +0 =a, = 3y3 Calculate the z-component of acceleration. =(29)[0+(30) ,001+0)2.00 = (x2).0+y®.0+(0).0 = 0+0+0 >>. = 0 Write the acceleration equation in vector form. a =a î +a, j+a_Ã = (3x){ +(3v") +(0) Â = 3x'i +3y'+Of Substitute the given coordinate values. a =3(-3) i +3 (2) j+0k=-729 +963 +O Â Calculate the magnitude of acceleration at given point. lāl= (-729) * +(96) +(0)2 = 735.29 m/s2