For incompressible liquids, flow work could usually be neglected in the steady-f
ID: 2991575 • Letter: F
Question
For incompressible liquids,flow work could usually be neglected in the steady-flow
energy equation. In the trans-Alaska
pipeline, the high viscosity of the oil and long distances
cause significant pressure drops, and it is reasonable
to question whether flow work would be significant.
Consider an L = 100 km length of pipe of diameter
D = 1.2 m, with oil flow rate m(dot) = 500 kg/s. The oil properties
are Density, p = 900 kg/m3, cp = 2000 J/kg K, and (mu) u = 0.765
N s/m2. Calculate the pressure drop, the flow work, and
the temperature rise caused by the flow work.
Explanation / Answer
Volume flow rate Q = m(dot)/ = 500/900 = 0.555 m3/s
Velocity V = Q/A = 0.555/(/4*1.22) = 0.49 m/s
Reynolds no. Re = VD/ = 900*0.49*1.2/0.765 = 694 (Flow is laminar since Re<2300)
Friction factor, f = 64/Re = 64/694 = 0.0922
Pressure drop = fL/D*V2/2 = 830512 Pa
Flow work = Pressure drop/ = 922.7
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