When you close a valve, the decrease in flow is primarily due to an increase in resistance within the system, rather than a direct consequence of the equation Q = A * V.
The equation Q = A * V represents the continuity equation, where Q is the volumetric flow rate, A is the cross-sectional area through which the fluid is flowing, and V is the velocity of the fluid. According to this equation, if the area decreases, the velocity of the fluid should increase to maintain a constant flow rate.
While this equation holds true in idealized, frictionless conditions, real-world systems involve factors such as viscosity, turbulence, and pressure differentials that affect the flow behavior.
Closing a valve introduces additional resistance to the flow path, which can be understood by considering the pressure drop across the valve. As you close the valve, the available cross-sectional area for the fluid to pass through decreases, resulting in an increase in the velocity of the fluid as per the equation Q = A * V. However, this increase in velocity also leads to an increase in pressure drop due to the fluid's interaction with the valve.
The increased pressure drop and resistance in the system create a backpressure that opposes the flow and reduces the overall flow rate. The net effect is that the system adjusts to a new equilibrium with a reduced flow rate, even if the velocity has increased due to the reduced area.
Therefore, while the equation Q = A * V provides a useful framework for understanding the relationship between flow rate, area, and velocity, it does not account for the additional factors that affect the flow resistance and ultimately reduce the flow rate when a valve is closed.