We found this fountain in Williamson Park in Lancaster. I'm estimating that the water fountain goes up 4 metres. By using the idea that kinetic energy turns into gravitational potential energy or 1/2mv^2=mgh, you get v = sqrt(2gh). So the velocity of the water coming out of the nozzle is about 9 metres per second. Volume flow rate in cubic metres per second = cross-sectional area of hole x velocity. I'm going to estimate a cross-sectional area of 1 square centimetre or 1 x 10^-4 square metres so volume flow rate = 9 x 10^-4 cubic metres per second. Mass flow rate = density of water x volume flow rate = 0.9 kg per second since the density of water is 1000 kg per cubic metre. Newton's second law says that force = rate of change of momentum = mass flow rate x velocity = 0.9 x 9 = 8N. Pressure = force per unit area = 8/1 x 10^-4 = 80000Pa.
