Question

# Use dimensional analysis to show that in a problem involving shallow water waves, both the Froude number and the Reynolds number are relevant dimensionless parameters. The wave speed c of waves on the surface of a liquid is a function of depth h, gravitational acceleration g, fluid density $ho$, and fluid viscosity $\mu$. Manipulate your $\Pi s$ to get the parameters into the following form: $\mathrm{Fr}= rac{c}{\sqrt{g h}}=f(\mathrm{Re}) \quad ext { where } \mathrm{Re}= rac{ ho c h}{\mu}$.

Solution

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Given Data

The wave speed $c$ of waves on the surface of a liquid is a function of depth $h,$ gravitational acceleration $g$, fluid density $\rho,$ and fluid viscosity $\mu .$

We can write the relationship as

$c=f(h, \rho, \mu, g)$

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