Why does flow decrease in your shower when someone flushes the toilet?

The Poiseuille’s law defines the resistance of flow. The greater the pressure differential between two points, the greater the flow rate. The discharge through laminar flow in pipe is given by:

\[Q = \frac{{{P_2} - {P_1}}}{R}\]

Here, R is resistance of flow, Q is the discharge, P₁ and P₂ is the pressure at points 1 and 2 resp.

The cold water is diverted to refill the tank when the toilet is flushed which causes pressure drop in the water line. The pressure-balancing valve senses the drop-in cold-water pressure which then restricts the hot water pressure. There is drop in water pressure for the period until the toilet bowl is filled back up. During the pressure drop, the water may turn very hot as the valve do not get all the cold water it requires.