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Lecture 23 - 8.5 Friction Losses in Non-Circular Conduits...

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1 8.5 Friction Losses in Non-Circular Conduits Many of the conduits that are used for conveying fluids are not circular in cross section. Although the details of the flows in such conduits depend on the exact cross-sectional shape, many round pipe results can be carried over, with slight modification, to flow in conduits of other shapes.
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2 Recall from section 8.2.1 origin of l w (friction losses): (1) (2) L R F x = 0 x P 1 A P 2 A τ w A s 𝐴𝐴 = 𝜋𝜋𝑅𝑅 2 𝐴𝐴 𝑠𝑠 = 2 𝜋𝜋𝑅𝑅𝜋𝜋 = 𝑃𝑃𝑃𝑃 . 𝜋𝜋 𝑃𝑃 1 𝜋𝜋𝑅𝑅 2 − 𝑃𝑃 2 𝜋𝜋𝑅𝑅 2 − 𝜏𝜏 𝑤𝑤 2𝜋𝜋𝑅𝑅𝜋𝜋 = 0 𝑃𝑃 1 − 𝑃𝑃 2 𝜋𝜋 = 2 𝜏𝜏 𝑤𝑤 𝑅𝑅 ∆𝑃𝑃 𝜋𝜋 = 4 𝜏𝜏 𝑤𝑤 𝐷𝐷 Eq. 8-2 perimeter 8.5 Friction Losses in Non-Circular Conduits ∆𝑃𝑃 𝜋𝜋 = 4 𝜏𝜏 𝑤𝑤 𝐷𝐷 = 𝜏𝜏 𝑤𝑤 𝐷𝐷 4 = 𝜏𝜏 𝑤𝑤 𝐴𝐴 𝑃𝑃𝑃𝑃
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3 So we define a hydraulic diameter, D h : 8.5 Friction Losses in Non-Circular Conduits
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