Poiseuille’s law was first obtained experimentally (1840s),

without dimensional analysis. Later works introduced scaling arguments:

1. Horace Lamb (1879) – Hydrodynamics

Early hydrodynamics treatise; uses scaling before full equations.

https://ia802804.us.archive.org/25/items/hydrodynamics00horarich/hydrodynamics00horarich.pdf

2. Osborne Reynolds (1883) – Experimental Investigation of Flow in Channels

Introduced the Reynolds number; discussed scaling with viscosity, velocity, diameter.

https://www.homepages.ucl.ac.uk/~uceseug/Fluids3/Extra_Reading/Reynolds_1883.pdf

or read from the Royal Society:

https://royalsocietypublishing.org/doi/10.1098/rspl.1883.0018

3. Edgar Buckingham (1914) – On Physically Similar Systems

Classic statement of the π-theorem; includes viscous pipe flow as example.

https://link.aps.org/doi/10.1103/PhysRev.4.345

https://www.scribd.com/document/732827860/Buckingham-1914-on-Physically-Similar-Systems-Illus

To: Lahsen Ourbaa

Thank you kindly for replying and providing this helpful information. I could not find a comparably helpful answer on searching the internet.