Changing a Flow's Momentum Produces a Force
A jet of water strikes a plate. Drag the jet's strength to feel where the force on the plate comes from as the jet hits and turns.
The jet hits the plate and scatters sideways. Drag the jet's strength and the force on the plate grows. As much momentum as the plate stops in the water, the plate is pushed back by the reaction.
Wrap a control volume around it and watch the momentum in and out. The incoming momentum arrow, the outgoing one, and their difference is exactly the force applied to the flow. Momentum is not lost, only redirected, and that change shows up as a force.
Drag the deflection angle. The more you turn the flow, the larger the momentum change and the larger the reaction force. Reverse it fully at 180° and the change, and the force, are at their maximum, twice as large.
As an equation, F = ṁ Δv, the mass flow rate times the change in velocity. Since ṁ = ρAv, F = ρAv·Δv. Drag v and it grows in two places, so the force climbs with v squared.
Look at a fire hose. The more water it throws out fast, the harder the reaction shoves the firefighters back. Drag the flow up and the recoil jumps. A rocket works the same way, throwing gas backward to drive itself forward.