CE 230-Engineering
Fluid Mechanics
Lecture # 29-30
Turbulent flow in circular pipes
Head loss for turbulent flow
Difficult to develop velocity distribution
Newton’s viscosity law does not apply,
instead:


du
 
  u ' v '   la min ar   turbulant
dy
Head loss formula, Turbulent flow
Avoiding detail a formula that is widely
used is Darcy-Weisbach equation:
2
LV
hf  f
D 2g
Where :
f friction factor function of Re and
material type and size
Other variables are well known by now
Factors affecting f
Smooth pipes only Re is important
Rough pipes Re as well as ks/D
Fully turbulent Re is not important
See Moody chart or equations
Rough pipes
We can idealize the roughness in pipes
using mean values which are reported
for different materials as ks shown
below
Classes of problems handled
Given size and type of pipe and Q find
head loss.
 Given size and type of pipe and head
loss find Q.
 Given type of pipe, Q and head loss
find size.

Type one problem
=0.12/200
V= Q/A=1.6 m/s
Re=1000(1.6)(.2)/0.001=320000
From Moody Chart f=0.019
Type one problems
Example 10.5:
If the head loss per kilometer for a 30-cm diameter asphalt
cast iron pipe is 12.2 m, estimate Q.
Example 10.6
Estimate Q through the 50 cm diameter steel pipe..
Type three problem
Example 10.6:
What size of asphalt cast iron pipe is required to
carry Q=3cfs with a head loss of 4 ft per 1000 ft of pipe?