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:

turbulantarlavudy

ud

min''

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 sizeOther variables are well known by now

g

V

D

Lfh f 2

2

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/sRe=1000(1.6)(.2)/0.001=320000

From Moody Chart f=0.019

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 10.6Estimate Q through the 50 cm diameter steel pipe..

Type one problems

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?

Type three problem