Suggested Response - Q3

**Consider further, the yeast pitching main in question two. Prior to yeast pitching, interface water flows down the yeast main at the same maximum average velocity. What would be the pressure drop per metre? The absolute roughness is 0.002 mm. (µ = 1x10-3 kg/ms and ρ = 1,000 kg/m3).

Response:

Interface water has very different physical properties to yeast slurry, so we will need to determine the Re again:

R e equals fraction numerator rho u d over denominator mu end fraction equals fraction numerator 1 comma 000 cross times 0.5 cross times 0.08 over denominator 0.001 end fraction equals 40 comma 000

We can see straight away that the flow is highly turbulent Re > 4,000 (compare this with the laminar flow regime for the yeast slurry). Therefore, we will need to use a Moody diagram to determine the friction factor. To do this, we need to know the relative roughness of the pipe:

R e l a t i v e space R o u g h n e s s space ϵ equals fraction numerator A b s o l u t e space R o u g h n e s s space e over denominator P i p e space I n s i d e space D i a m e t e r space d end fraction equals fraction numerator 0.002 over denominator 80 end fraction equals 0.000025

Plotting this and the Re on a Moody diagram (below) gives a friction factor of 0.0060.

pipe friction chart

Substituting values into the Darcy-Weisbach equation:

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

increment P subscript f equals 4 cross times 0.0060 cross times fraction numerator 1 over denominator 0.08 end fraction cross times 1 comma 000 cross times 0.5 squared

increment P subscript f equals 75 space P a divided by m

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