A three-bladed propeller is used to mix a fluid in the laminar region. The stirrer is 0.3 m in diameter and is rotated at 1.5 Hz. Due to corrosion, the propeller has to be replaced by a flat two-bladed paddle, 0.75 m in diameter. If the same motor is used, at what speed should the paddle rotate?

Question

Accepted Answer

For mixing in the laminar region, the power requirement is:

[latex]P =k^{\prime} N^2 D^3[/latex] (equation 7.17)

where [latex]k^{\prime}=1964[/latex] for a propeller and 1748 for a flat paddle.
Thus, for a propeller 0.3 m in diameter rotating at 1.5 Hz:

[latex]P =\left(1964 imes 1.5^2 imes 0.3^2 ight)=\underline{119.3 W }[/latex]

and for a paddle, 0.75 m in diameter using the same motor:

[latex]119.3=\left(1748 N^2 imes 0.75^3 ight)[/latex] and [latex]N=\underline{\underline{0.403 Hz }}[/latex] (24 rpm)

Question 7.P.2: A three-bladed propeller is used to mix a fluid in the lamin...

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