Bernoulli Principle -
Flow Rate Derivation

The flow rate is the ratio of mass to time.

Since the fluid is flowing steadily and not pooling, the flow rate into any section of the pipe is the same as the flow rate out of that section of the pipe, which is in turn the flow rate into the next section of pipe.

Therefore, the flow rate at any point a is

f = f0

where
f - flow rate (kilograms per second)
f0 - constant flow rate (kilograms per second)