1. Force = rate of change of momentum
2. Mass of water delivered per unit time is proportional to velocity
3. Momentum of water delivered per unit time = mass*velocity
4. Substitute 2 in 3 you get momentum of water delivered per unit time is proportional to square of the velocity, which from 1, says it is proportional to the force/pressure
So, we have pressure P proportional to V^2, substituting 4V for V you get 16V.