From 6c3382080c68f3ffad1a5d6ac52a9d51ce46cad2 Mon Sep 17 00:00:00 2001 From: Eise Nota Date: Wed, 18 Sep 2024 12:07:01 +0200 Subject: [PATCH] Update chapter_2.md --- course/practicals/chapter_2.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/course/practicals/chapter_2.md b/course/practicals/chapter_2.md index 9949600..b664a8b 100644 --- a/course/practicals/chapter_2.md +++ b/course/practicals/chapter_2.md @@ -426,7 +426,7 @@ $$ \tau_c = \frac{1}{8} \rho f u^2_c = \rho g \left( \frac{u^2}{C^{/2}}\right) $$ (Eq_2_9) -where $u_c$ is the flow velocity of the current, which we consider equal to the flow velocity $u$ (Eq. {eq}`Eq_1_1`; subscript w could be for orbital velocity amplitude of waves). Note that $C^/$ implies a Chezy for grain friction and is therefore not equal to $C$ (you can therefore not use Eq. {eq}`Eq_1_2` here). Finding a good predictor for the friction factor $f$ or $C^/$ is a challenging problem in civil engineering, because of the interactions between flow, flow turbulence, the added resistance of transported sediment, and most importantly roughness elements such as grains on the bed and bed forms. $f$, $C$ or $C^/$ is therefore commonly used as calibration parameter in flow models, or derived from measurements of other parameters in. Therefore, there is a large number of available predictors for $f$, which have applicability ranges determined by the data set they were derived from. Here we use the general and well-verified predictor called the Colebrook-White function, which is semi-empirical and is related to boundary layer theory for flow over rough bed ([Silberman et al., 1963](https://ascelibrary.org/doi/10.1061/JYCEAJ.0000865)): +where $u_c$ is the flow velocity of the current, which we consider equal to the flow velocity $u$ (Eq. {eq}`Eq_1_1`; subscript w could be for orbital velocity amplitude of waves). Note that $C^/$ implies a Chezy for grain friction and is therefore not equal to $C$ (you can therefore not use Eq. {eq}`Eq_1_2` here). Finding a good predictor for the friction factor $f$ or $C^/$ is a challenging problem in civil engineering, because of the interactions between flow, flow turbulence, the added resistance of transported sediment, and most importantly roughness elements such as grains on the bed and bed forms. Either $f$, $C$ or $C^/$ is therefore commonly used as calibration parameter in flow models, or derived from measurements of other parameters. Therefore, there is a large number of available predictors for $f$, which have applicability ranges determined by the data set they were derived from. Here we use the general and well-verified predictor called the Colebrook-White function, which is semi-empirical and is related to boundary layer theory for flow over rough bed ([Silberman et al., 1963](https://ascelibrary.org/doi/10.1061/JYCEAJ.0000865)): $$ \sqrt{\frac{8}{f}} = \frac{C^/}{\sqrt{g}} = 5.74 \log_{10} \left( 12.2