The flow of fluid through a pipe is governed by Bernoulli's equation. In layman's language, this means that the sum of the velocity head (i.e., kinetic energy on account of the fluid velocity), pressure head and level head (i.e., potential energy on account of the level of the fluid above a reference datum)is constant.
Now, when there is a restriction in the pipeline (such as is produced by the orifice), the velocity head increases at the orifice (because the fluid is constrained to flow through a lesser area. As a result, the pressure head will have to decrease (assuming, a horizontal pipe, to simplify things - so that the level head remains unaltered).
Moreover, the decrease in pressure head will be equal to the increase in velocity head.
Now, the flowrate is the velocity times the area of cross-section of the orifice.
When you solve the equation, you will find in the end that the flowrate in the pipeline will decrease as the orifice bore is decreased more and more.