Using scaling analysis, eliminate the non$-$essential terms to derive the hydrodynamic boundary layer equations, for high Reynolds number, starting from the equation set given below for a flat plate as it experiences a uniform velocity $U_{}$ at its leading edge.

$\frac{\text{d}\text{e}\text{l}\text{u}}{\text{d}\text{e}\text{l}\text{x}}+\frac{\text{d}\text{e}\text{l}\text{v}}{\text{d}\text{e}\text{l}\text{y}}=0$;$,u\frac{\text{d}\text{e}\text{l}\text{u}}{\text{d}\text{e}\text{l}\text{x}}+v\frac{\text{d}\text{e}\text{l}\text{u}}{\text{d}\text{e}\text{l}\text{y}}=-\frac{\text{d}\text{e}\text{l}\text{p}}{\text{d}\text{e}\text{l}\text{x}}+(\frac{de{l}^{2}u}{del{x}^2}+\frac{de{l}^{2}u}{del{y}^2})$;

$u\frac{\text{d}\text{e}\text{l}\text{v}}{\text{d}\text{e}\text{l}\text{x}}+v\frac{\text{d}\text{e}\text{l}\text{v}}{\text{d}\text{e}\text{l}\text{y}}=-\frac{\text{d}\text{e}\text{l}\text{p}}{\text{d}\text{e}\text{l}\text{y}}+(\frac{de{l}^{2}v}{del{x}^2}+\frac{de{l}^{2}v}{del{y}^2})$