Use Continuity as well as Bernoullis Law / Principle / Equation to calculate the static pressure in a pipe after a reduction in the pipe diameter.
This problem assumes there is no frictional losses in the fluid.
Knowing the flow in the larger bore pipe as well as the pipe diameter, we can solve for the linear velocity of the flow. That velocity increases as the fluid moves through the taper into the smaller bore pipe. We can use Q=AV to solve for the velocities both upstream and downstream of the taper.
Knowing both velocities we apply Bernoulli's law to the flow. There is no change in hydrostatic pressure. This means that the increase in dynamic pressure as the fluid speeds up correlates to a decrease in static pressure as the fluid speeds up.
It is important to point out, that the 'static pressure' term is quantity most people associate with pressure (Force/Area). Dynamic and hydrostatic pressures are not actually what most people would think of as 'pressures'... They are actually energy per volume of fluid. Looking at the units that would be Joules / m^3 which reduces to Newton meters / m^3 which reduces to Newtons/m^2... They are pressures, but not what most people think of as pressures.
This problem commonly comes up in introductory physics courses including high school physics, AP Physics, and fluid mechanics courses.
