Looking for an equation to find resulting pressure

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To determine the resulting pressure and velocity at the smaller diameter B in a pipe reduction from A, the Bernoulli equation is essential. Input data at point A, including flow rate and pressure, can be used to calculate these values. For a more accurate analysis, incorporating pressure losses due to friction and turbulence is necessary, which requires resistance coefficients for the reducers. Understanding these coefficients will enhance the precision of the calculations. Accurate modeling of fluid dynamics in pipe systems is crucial for effective engineering solutions.
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Picture a pipe reduction from a diameter A down to B. I'm looking for an equation that can tell me the resulting pressure and velocity out of B from input data at point A such as flow and pressure. I've would really appreciate it :)
 
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Bernoulli equation.

If you want to get more detailed with the pressure losses, you'll need to have a source for resistance coefficients of reducers, etc...
 
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