# Poiseuille's law for turbulent flow?

I have some data for the volumetric flow rate of a fluid for a given pressure gradient.

I was looking to use Poiseuille's law (which is only valid for laminar flow) to calculate a value for the dynamic viscosity of the fluid used.

However, after a Reynold's number analysis, i know the flow rates are turbulent.

Is there an equation that can use this data to extract a dynamic viscosity value for turbulent flow?

Dynamic viscosity is a property of the fluid and its thermodynamic state.

If you have turbulent flows in a pipe, it's likely that molecular viscosity plays a minor role, while the system is governed by other parameters, like the surface roughness.

You can have a look at the Moody's chart (see https://en.wikipedia.org/wiki/Moody_chart) of the friction coefficient $$f_D$$ as a function of the Reynolds number $$Re$$ and surface roughness $$\varepsilon$$, being:

• $$\frac{\Delta P}{\Delta x} = f_d \frac{1}{2}\rho V^2$$,
• $$Re = \frac{\rho V D}{\mu}$$,
• $$\varepsilon$$ is an adimensional measure of the surface roughness, as the ratio of a characteristic dimension of the roughness and the diameter of the pipe.

In Moody's chart you can recognize 4 regions:

1. laminar regime, where Poiseuille flow holds in pipes with circular sections; here $$f_d$$ is a function of $$Re$$ only, $$f_d^L(Re) \sim \frac{1}{Re}$$;
2. transition;
3. turbulent regime, where $$f^T_d(Re, \varepsilon)$$; some formulas exists, derived from the law of the wall and matching viscous, inertial and outer layers, like Colebrook equations: these expressions are usually implicit in $$f_d$$; on the other hand you can directly use a Moody's diagram; you can find a reference about the Colebrook equation here in wiki, https://en.wikipedia.org/wiki/Darcy_friction_factor_formulae#Colebrook%E2%80%93White_equation
4. complete turbulent regime, where $$f_d$$ is approximately independent on $$Re$$, and only depends on $$\varepsilon$$, $$f^{CT}_d(\varepsilon)$$.