1. The problem asks which type of fluid has a velocity potential that satisfies Poisson's equation $$\nabla^2 \phi + \rho = 0$$. 2. Poisson's equation appears in fluid dynamics for incompressible, irrotational, ideal fluids with distributed sources. 3. Here, $$\phi$$ is the velocity potential, and the fluid is irrotational and ideal. 4. Incompressible fluids satisfy $$\nabla \cdot \mathbf{u} = 0$$, where $$\mathbf{u} = \nabla \phi$$ is the velocity vector, meaning $$\phi$$ satisfies Laplace or Poisson's equation. 5. Therefore, the fluid must be incompressible. Final answer: **c. incompressible**