Final answer:
As the velocity in a pipe increases, the pressure generally becomes lower, according to Bernoulli's principle. However, turbulence can cause an increase in pressure due to energy loss. The continuity equation also shows the inverse relationship between velocity and pressure in incompressible flows.
Step-by-step explanation:
As the velocity increases due to undersized pipes, the pressure in the pipes becomes lower. This phenomenon is described by Bernoulli's principle, which states that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy.
It's important to note that if turbulence occurs, this can disrupt the flow and cause the pressure to increase due to the energy loss in the system, which makes the flow less efficient. Furthermore, the continuity equation helps explain that in an incompressible fluid, the product of the cross-sectional area and velocity at one point must equal the product of those at another point; if the pipe narrows and velocity increases, the pressure decreases.
Therefore, when the tube narrows, and the fluid's velocity increases, the pressure decreases. This is because the work done on the fluid translates into increased kinetic energy, leaving less energy to be manifest as pressure. However, if factors such as turbulence come into play, they can decrease the flow rate, necessitating an increased pressure difference to maintain flow, thus leading to higher pressure.