Classical Mechanics
# Dimensional Analysis

As shown in the above figure, a liquid with density \( \rho \) and viscosity \( \mu \) flows through a pipe with diameter \( d. \) In a section of the pipe with length \( L, \) the liquid flows with a speed of \( v. \) Using the Buckingham \(\pi\) theorem, determine the pressure difference \( \Delta P = P_1 - P_2 \) in terms of the fluid properties \( d, L, \rho, \mu \) and \( v .\)

**Details**

- the function \(f\) is unitless, so that it outputs a pure number.

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