Acceleration of fluid flowing down a slope [closed]

You have a fluid flowing down an inclined plane. Assuming drag increases with the square of velocity, and knowing the following properties:

initial velocity $v₀$, mass m, fluid density ρ, depth d, surface area A, angle θ, drag coefficient of surface k

How would you calculate the final velocity $vf$ of the surface of the fluid after time $t$ since acceleration wouldn't remain constant and would decrease as the fluid's velocity increases? What about the distance traveled after time $t$?