(Solved): Q4. For incompressible fluids, the dot product of the Del operator and velocity vector \( (V) \) e ...

Q4. For incompressible fluids, the dot product of the Del operator and velocity vector \( (V) \) equals to zero: \( \nabla \cdot V=0 \). For which combination of constants, a, b, c, and d can the velocity components (e.g., \( \mathrm{V}_{\mathrm{X}}, \mathrm{V}_{\mathrm{Y}} \), and \( \mathrm{V}_{\mathrm{Z}} \) ) be used to describe an incompressible flow field? \[ \begin{array}{l} \mathrm{V}_{\mathrm{X}}=\mathrm{ax}+\mathrm{by} \\ \mathrm{V}_{\mathrm{Y}}=\mathrm{cx}+\mathrm{dy} \\ \mathrm{V}_{\mathrm{Z}}=0 \end{array} \]