Lynn Larsen
Lynn Larsen
I had tried to avoid this to argue with Cliff that anytime a fluid is passed through a tube (or even an open channel for that matter) there are going to be line losses caused by friction and normally expressed a h sub L (head loss). (Ref the Darcy-Weisbach equation, or the Fanning equation for the chemical engineers here.) Because of the difficulty in doing equations in this editor, I will omit the "sub L".
For a circular pipe (smooth or rough) of L length and D diameter flowing full of a liquid at a velocity of V
where:
h = head loss in feet of the liquid in the pipe
f= the friction number which is proportional to the Reynolds number R
R = LVp/µ where p is the density and µ is the dynamic viscosity
g = acceleration of gravity - 32.2 f/s²
So, losses are proportional to both length of the pipe L and viscosity and inversely proportional to the diameter. However when a ratio of two line losses is done, the viscosities (being the same in each path) will cancel (as will the densities and g) and be determined only on L, D and V.
Lynn
Ref: Chp. 8 Steady Incompressible Flow in Pressure Conduits, Fluid Mechanics with Engineering Appliccations; Daugherty, Franzini & Finnemore. © 1985 McGraw-Hill ISBN 0-07-015441-4
For a circular pipe (smooth or rough) of L length and D diameter flowing full of a liquid at a velocity of V
h = f(L/D * V²/2g)
where:
h = head loss in feet of the liquid in the pipe
f= the friction number which is proportional to the Reynolds number R
R = LVp/µ where p is the density and µ is the dynamic viscosity
g = acceleration of gravity - 32.2 f/s²
So, losses are proportional to both length of the pipe L and viscosity and inversely proportional to the diameter. However when a ratio of two line losses is done, the viscosities (being the same in each path) will cancel (as will the densities and g) and be determined only on L, D and V.
Lynn
Ref: Chp. 8 Steady Incompressible Flow in Pressure Conduits, Fluid Mechanics with Engineering Appliccations; Daugherty, Franzini & Finnemore. © 1985 McGraw-Hill ISBN 0-07-015441-4
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