Sia

{'context': "[{'Student': 'my name is 张45321, and I am currently at College (Senior) ', 'Sia': 'awesome!'}, {'Student': '\\n11. 证明在二维不可压缩流体中，对于任意的流线积分，若流函数 $\\\\psi$ 是时间相关的，则流速可以表示为：\\n\\\\[\\n\\\\vec{v} = \\begin{pmatrix} -\\\\frac{\\partial \\\\psi}{\\\\partial y} \\\\  \\\\frac{\\partial \\\\psi}{\\\\partial x} \\end{pmatrix} \\n\\\\]\\n\\n其中，流体的速度与流函数的偏导数有关。\\n12. 证明：在稳态条件下，对于不可压缩流体，流量守恒条件可以表示为：\\n\\\\[\\n\\\\nabla \\\\cdot \\vec{v} = 0 \\n\\\\]\\n\\n即流体在任意小体积内的体积流量之和为零。\\n228', 'Sia': ' step 1 ⋮ The flow velocity in a two-dimensional incompressible fluid is given in terms of the stream function. step 2 ⋮ Here, \\\\vec{v} denotes the flow velocity vector and \\\\$\\\\psi$ is the stream function. '}] ", 'question': 'how to find the flow velocity using the stream function ?'}