Final answer:
The flow in the shower decreases due to decreased water pressure when the toilet is flushed, as the increased demand for water leads to a drop in pressure in the shared line which manifests as a reduced shower stream.
Step-by-step explanation:
When someone flushes the toilet while you are taking a shower, the flow in the shower decreases because of decreased water pressure. This is tied to the continuity equation and the concept that when the cross-sectional area of a pipe (or water channel) increases due to the toilet being flushed, the velocity must decrease to maintain the constant product of area, velocity, and density. Since water is an incompressible fluid, its density does not change, meaning the system must adjust in velocity and area. In your shower, this translates to lower water pressure resulting in a reduced flow rate.
Moreover, during high-velocity fluid flow, regions of lower pressure can occur leading to pressure drops. For instance, when the toilet flushes, it demands a substantial amount of water quickly, drawing from the overall supply and consequently dropping the pressure available to your shower. The high demand of water flow into the toilet reduces the pressure in the shared water line, and so the showerhead outputs less water, leading to a weaker shower stream.