To calculate the flow rate in a system with a valve between the throttle body and intake manifold, one must analyze the mass flow rate of air as the valve area decreases. An anemometer can be used to measure the air velocity, which is crucial for determining flow rate. The flow rate in the restricted area is proportional to the ratio of the cross-sectional areas of the air streams. A mathematical model can be developed to represent the relationship between valve position and flow rate, considering that flow is unrestricted when the valve is fully open and ceases when the area is zero. Understanding these dynamics is essential for assessing engine performance under varying conditions.