Assumptions will be specifically declared when there are indications for influencing the outcome of an experiment.
To enable other scientists to replicate the experiment, they specify a particular value or condition. If the experiment, conducted under the specified assumptions, yields the same result, it indicates adequate control over the test conditions. A different result may prompt a reassessment of the assumptions.
When an equation is derived from experiments to provide a mathematical description of an expected outcome, it is only valid under the stated assumptions.