In FSAE events we need to use a restrictor of 20mm diameter in the upstream of intake manifold. it is to restrict the intake mass flow rate. my question is how it affects the engine power output? any mathematical formula is welcomed.
The output power is m_dot*g*h_flow. m_dot is the mass flow rate, g=9.81 m/s^2 the gravitational acceleration and h_flow is the head of flow. By using the restrictor, the h_flow (can be converted to pressure) is reduced. The mass flow rate is already reduced therefore you should expect lower power (and not constant power) output.
In the internal combustion engine, the power generated by the engine is influenced by the amount of fuel and air being burned, which is about the amount of stoichiometry.