Exercise: Bernoulli equation for flow in a pipe

Gravity will cause the flow to move from point Ⓐ to Ⓑ, so Ⓐ is upstream of Ⓑ.

Using the fact that locations Ⓐ and Ⓑ are both at the same pressure, Bernoulli’s equation reduces to the following:

\[\frac{1}{2} \left(v_{Ⓑ}^{2} - v_{Ⓐ}^{2} \right) + g \, (z_{Ⓑ} - z_{Ⓐ})= 0\]

This equation can be rearranged to solve for \(v_{2}\),

\[v_{Ⓑ} = \sqrt{ v_{Ⓐ}^{2} - 2g \, (z_{Ⓑ} - z_{Ⓐ}) }\]

Substituting in numerical values, yields

\[v_{Ⓑ} = \SI{19.45}{m/s}\]