Suggested Response - Q2

*/** A yeast pitching main has an internal diameter of 80 mm. If a maximum average line velocity of 0.5 m/s is specified, what would the friction factor be and consequently, the pressure drop per metre due to friction alone?

The yeast slurry can be considered a Newtonian fluid with a constant dynamic viscosity of 0.05 kg/ms and a density of 1,300 kg/m3.

Response:

Before determining the friction factor, we need to determine the Reynolds number:

R e equals fraction numerator rho u d over denominator mu end fraction equals fraction numerator 1 comma 300 cross times 0.5 cross times 0.08 over denominator 0.05 end fraction equals 1040

Immediately, we can state that the flow would be laminar (Re < 2,100) and therefore we can determine the friction factor as a function of Re only:

phi equals fraction numerator 16 over denominator R e end fraction equals 16 over 1040 equals 0.015

The pressure drop due to friction is given by the Darcy-Weisbach equation:

increment P subscript f equals 4 phi L over d rho u squared

We wish to determine the pressure drop per metre run, i.e. L = 1 m:

increment P subscript f equals 4 cross times 0.015 cross times fraction numerator 1 over denominator 0.08 end fraction cross times 1 comma 300 cross times 0.5 squared

increment P subscript f equals 243.75 space P a divided by m

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