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?


1 Answer 1


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.

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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 $\varepsilon$, $f^{CT}_d(\varepsilon)$.

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