# 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 :

Solution :

Average flow velocity through the pipe :

Calculate Reynolds number to determine the type of flow :

$Re=ρvDμ=925∗1.273∗0.10.065=1,812$

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 :

$hf=8fLπ2gD5Q2$ $→$

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

$τo=γRSf$

Calculate the hydraulic radius for the full circular pipe :

Calculate the slope of the total energy line :

$Sf=hfL=29.191000$

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

Power supplied by the pumps per kilometer length :