Viscous Flow in Pipes.pdf

8.2.4 Energy Consideration• Consider the energy equation for incompressible, steady flowbetween flow locations.p V p Vγ 2gγ 2g2 21 1 2 2+ α1 + z1 = + α2 + z2 + h2• For fully developed flowα = α , V = V1 2 1 2p1 ⎛ p2⎞+ z1− ⎜ + z2⎟=hLγ ⎝ γ ⎠Δ p 2τ2τl4lτ= ∴whL= , hL=l r γ r γ D(Recall p = p +Δp, z − z =l sinθ)1 2 2 1EX. 8.3 Laminar pipe flow properties⎛Δp−γ l sin θ 2τ⎞⎜=l r⎟⎜⎟Δpl sin θ 2τ− =⎜ γrγ⎟⎝ l ⎠Which indicates that it is the shear stress at the wall ( which isdirectly related to the viscosity and the shear stress throughoutthe fluid ) that is responsible for the head loss.