$$P_1 + \frac{1}{2} \rho v_1^2 = P_2 + \frac{1}{2} \rho v_2^2$$
where:
* $$P_1$$ is the pressure at point 1
* $$\rho$$ is the density of the gas
* $$v_1$$ is the velocity of the gas at point 1
* $$P_2$$ is the pressure at point 2
* $$v_2$$ is the velocity of the gas at point 2
As the gas flows through the pipe, the velocity of the gas increases as the pipe diameter decreases. This is because the same amount of gas must flow through a smaller area, so the gas must move faster. As the velocity of the gas increases, the pressure of the gas decreases.
Therefore, when a pipe is changed from a large diameter to a small diameter, the pressure of the gas will decrease.
