The physics
Newton's second law in full is F = dp/dt. Force is how fast momentum changes. When mass flows in or out, momentum can change even at a steady speed.
stream picked up or stopped: F = v · dm/dt
water jet: dm/dt = ρAv. Stopped: F = ρAv². Turned back: F = 2ρAv².
rocket thrust = u · dm/dt rain in a cart: M v₀ = (M + Δm) v
rocket, fuel burned to the end: v = u ln(M₀/M) − g t
chain let go onto a scale: reading = landed weight + (M/L) v² = 3 × landed weight
Sand that leaks out of a cart leaves at the cart's own speed. It takes its own momentum away. So the cart keeps its speed.
Energy is harder to follow. Sand landing on a belt slides, and rain landing in a cart sticks. Both waste kinetic energy as heat. Momentum is the safe quantity to follow.