1. CE 230-Engineering Fluid Mechanics
Lecture # 29-30
Turbulent flow in circular pipes

2. Head loss for turbulent flow
Difficult to develop velocity distribution
Newton’s viscosity law does not apply, instead:

3. Head loss formula, Turbulent flow
Avoiding detail a formula that is widely used is Darcy-Weisbach equation:
Where :
f friction factor function of Re and material type and size
Other variables are well known by now

4. 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

5. Rough pipes
We can idealize the roughness in pipes using mean values which are reported for different materials as ks shown below

9. 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.

10. Type one problem

11. =0.12/200
V= Q/A=1.6 m/s
Re=1000(1.6)(.2)/0.001=320000
From Moody Chart f=0.019

12. If the head loss per kilometer for a 30-cm diameter asphalt
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..

13. What size of asphalt cast iron pipe is required to
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?