Q & A – Fluid Mechanics – Flow of Incompressible Fluids in Pipelines – Q.1

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Q & A – Fluid Mechanics – Flow of Incompressible Fluids in Pipelines – Q.1

Q & A – Fluid Mechanics – Flow of Incompressible Fluids in Pipelines – Q.1

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Question No.1

Topic : Flow of Incompressible Fluids in Pipelines

Crude oil of density 925 kg/m3 and absolute viscosity 0.065 N.sec/m2 at 20oC is pumped through a horizontal pipeline 100 mm in diameter, at a rate of 10 lit/sec. Determine the head loss in each kilometer of pipeline and the shear stress at the pipe wall. What power is supplied by the pumps per kilometer length ?

Given :

  • ρ=925  kg/m3
  • μ=0.065  N.sec/m2
  • D=100  mm=0.1  m
  • L=1,000  m
  • Q=10  lit/sec=0.01  m3/sec

Solution :

Average flow velocity through the pipe :

v=QA=Qπ4D2=0.01π0.12=1.273  m/sec

Calculate Reynolds number to determine the type of flow :

Re=ρvDμ=9251.2730.10.065=1,812

Since Re is less than 2,000, therefore the flow is laminar.

Calculate the friction coefficient through the following equation :

f=64Re=641,812=0.0353

Friction losses using Darcy-Weisbach equation :

hf=8fLπ2gD5Q2 hf=80.03531,000π29.810.150.012=29.19  m

Shear stress at the pipe wall (boundary shear stress) :

τo=γRSf

Calculate the hydraulic radius for the full circular pipe :

R=D4=0.14=0.025  m

Calculate the slope of the total energy line :

Sf=hfL=29.191000

Therefore, the shear stress at the pipe wall (boundary shear stress) :

τo=γRSf=9259.810.02529.191000=6.622  N/m2

Power supplied by the pumps per kilometer length :

Power=γQhf=9259.810.0129.19=2,648.77  Watt

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