According to Bernoulli’s law, with a reduction in diameter, the pressure will decrease (velocity will increase). What happens if we increase the diameter: will the velocity decrease and the pressure increase?

Answer

When you consider a steady flow of an incompressible fluid and viscous losses are negligible, Bernoulli’s law states that the kinetic energy and thus the velocity of a fluid particle can increase if the pressure decreases or if the height decreases and vice versa can decrease if the pressure rises or the altitude increases.

Indeed, with a decrease in diameter of a horizontal pipe, the speed increases and the pressure decreases, and with an increase in diameter, the speed decreases and the pressure increases. If there are viscous losses, the pressure decrease will be slightly more pronounced and the subsequent pressure increase will be less, ie when the original diameter is reached again, the pressure will have decreased somewhat. If the fluid is compressible, another law applies which is sometimes called Bernoulli’s generalized law, but there too you get that the pressure decreases with an increase in speed and vice versa, only the relationship is quantitatively different.

So if you start from a compressed air reservoir where there is no velocity and the gas accelerates to the compressed air pipe, the pressure in the compressed air pipe will be lower than the pressure in the compressed air reservoir, because the gas has gained a velocity. By widening the pipe, the pressure can then rise again, but never exceed the original pressure in the compressed air reservoir.