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Illustration Bernoulli's principle applied to a flowing liquid

Bernoulli principle applied to a flowing liquid
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A liquid (e.g. water, blood) of density \(\rho\) flows through a pipe. As an example, a cross-sectional area of the pipe is considered. The static pressure \(\mathit{\Pi}_{\text{s}}\) acts on this area, which is at the height \(h\) above the ground. The fluid moves through the cross-sectional area with the average flow velocity \(v\).

Bernoulli's principle states that the flow velocity \(v\) increases when the pressure \(\mathit{\Pi}_{\text{s}}\) decreases and vice versa.