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Chapter 7: Problem 1

A mixing basin in a sewage filtration plant is stirred by mechanical agitation (paddlewheel) with a power input \(\dot{W}(\mathrm{ft} \cdot \mathrm{lb} / \mathrm{s})\) The degree of mixing of fluid particles is measured by a "velocity gradient" \(G\) given by $$G=\sqrt{\frac{\dot{W}}{\mu V}}$$ where \(\mu\) is the fluid viscosity in \(\mathrm{Ib} \cdot \mathrm{s} / \mathrm{ft}^{2}\) and \(\mathrm{V}\) is the basin volume in \(\mathrm{ft}^{3}\). Find the units of the velocity gradient.

Short Answer

Expert verified
The units of the velocity gradient are \(\mathrm{ft}/\mathrm{s}\).

Step by step solution

01

Substituting Units in Equation

Replace each variable in the equation with their corresponding units: \(G=\sqrt{\mathrm{ft}\cdot\mathrm{lb}/\mathrm{s}/(\mathrm{Ib}\cdot\mathrm{s}/\mathrm{ft}^{2}\cdot\mathrm{ft}^{3})}\)
02

Simplify Units

Simplify units within the radical: \(G=\sqrt{\mathrm{lb}\cdot\mathrm{ft}^{2}/\mathrm{Ib}\cdot\mathrm{s}^{2}}\)
03

Apply Square Root

Apply the square root to the units, which will result in \(G=\mathrm{ft}/\mathrm{s}\)

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