Question

设不可压缩流体平面无选流体速度势为X立方Y减去XY立方.那它是否满足流体连续条件,求流函数

Answer 1

u=x³y-xy³

∂²u/∂x²+∂²u/∂y²=6xy-6xy=0

满足流体连续条件

设f(z)=u(x,y)+iv(x,y)

∂u/∂x=∂v/∂y,∂u/∂y=-∂v/∂x

dv=(∂v/∂x)dx+(∂v/∂y)dy=(-∂u/∂y)dx+(∂u/∂x)dy

v(x,y)=∫dv=-∫(x³-3xy²)dx+∫(3x²y-y³)dy

=(3/2)x²y²-(x^4+y^4)/4