4 flow in a circular pipe 1 p1 p 2 p 339 g x g sin

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Unformatted text preview: nd correct later for entrance effects. Then the kinetic-energy correction factor 1 V2 from (6.23), Eq. (6.24) now reduces to a 2, and since V1 simple expression for the friction-head loss hf hf z1 p1 g p2 g z2 z p g z p g (6.25) The pipe-head loss equals the change in the sum of pressure and gravity head, i.e., the change in height of the hydraulic grade line (HGL). Since the velocity head is constant through the pipe, hf also equals the height change of the energy grade line (EGL). Recall that the EGL decreases downstream in a flow with losses unless it passes through an energy source, e.g., as a pump or heat exchanger. Finally apply the momentum relation (3.40) to the control volume in Fig. 6.10, accounting for applied forces due to pressure, gravity, and shear p R2 g( R2) L sin w(2 R) L m (V2 ˙ V1) 0 (6.26) This equation relates hf to the wall shear stress p g z hf 2 w g L R (6.27) where we have substituted z L sin from Fig. 6.10. So far we have not assumed either laminar or turbulent flow. If we can correlate w with flow conditions, we have solved th...
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