I have a flow through a pipe that changes in diameter to become narrower. I can measure the pressure P1 at the wider end where it is applied and I want to calculate the pressure P2 at the narrow end. I can't directly apply Bernoulli's equation here because I have no way of measuring the flow rate at either end. I do however know all of the relative dimensions of the pipe (i.e. I know the cross-secional area through which the water flows at P1 and the smaller area at P2), and assuming the water is incompressible the volume flow is constant, I can substitute v2 = (A1/A2)v1. But simplfying leaves P2 in terms of v1: - P2 = P1 + 0.5*rho*( V1^2 - ( (A1/A2)*V1 )^2 ) Is the pressure at the narrow end simply scaled linearly by the ratio of the cross sections? I have a feeling I have solved this problem before and found this to be the case, I just can't see it at the moment.