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Update README.md
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aumpierre-unb committed Jul 18, 2024
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Expand Up @@ -300,7 +300,13 @@ Compute the Reynolds number *Re* and the Darcy friction factor *f* given the sam

`hQeps2fDRe` computes both the Darcy friction factor *f* and the Reynolds number *Re* given the head loss *h*, the pipe's length *L* and relative roughness *ε*, the volumetric flow rate *Q*, the gravitational acceleration *g*, and the fluid's density *ρ* and dynamic viscosity *μ*. Replacing hydraulic diameter *D* in the Darcy-Weisbach equation by the Reynolds number *Re*,

$${Re^5 f}={2ghQ^3 \over\displaystyle {{ \left({\pi \over 4} \right) }^3 {\left({\mu \over \rho} \right)}^5 L }}$$
$$
{Re^5 f}={2ghQ^3 \over\displaystyle {{ \left( {\pi \over 4} \right) } }}
$$

$$
{Re^5 f}={2ghQ^3 \over\displaystyle {{ \left( {\pi \over 4} \right) }^3 { \left( {\mu \over \rho} \right) }^5 L }}
$$

Along with the Colebrook-White equation, this version of the Darcy-Weisbach equation produces a system of two equations with two variables. Solution is computed iteratively.

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