1 Pipe Flow Calculations R. Shankar Subramanian Department of Chemical and Biomolecular Engineering Clarkson University We begin with some results that we shall use when making friction loss calculations for steady, fully developed, incompressible, Newtonian flow through a straight circular pipe. Volumetric flow rate 2 4 Q DV π = where D is the pipe diameter, and V is the average velocity. Reynolds Number: 4 4 Re DV DV Q m D D ρ µ ν π ν π µ = = = =  where ρ is the density of the fluid, µ is its dynamic viscosity, and / ν µ ρ = is the kinematic viscosity. The pressure drop P ∆ is related to the loss in the Engineering Bernoulli Equation, or equivalently, the frictional head loss f h , through loss f P h ρ γ ∆ = × = Here, the specific weight g γ ρ = , where g is the magnitude of the acceleration due to gravity. Power The power required to overcome friction is related to the pressure drop through Power PQ =∆ or we can relate it to the head loss due to pipe friction via Power f hQ γ = Head Loss/Pressure Drop The head loss f h is related to the Fanning friction factor f through 2 2 f L V h f D g     =         or alternatively we can write the pressure drop as ( ) 2 2 L P f V D ρ   ∆ =     Friction Factor In laminar flow, 16 Re f = . In turbulent flow we can use either the Colebrook or the Zigrang-Sylvester Equation, depending on the problem. Both give equivalent results well within experimental uncertainty. In these equations, ε is the average roughness of the interior surface of the pipe. A table of roughness