223.00-3

Fluid Mechanics - Course 223

FRICTION IN FLUID FLOW

In fluid flow, where liquids are concerned, we shallconsider the flow to be incompressible. That is, there isno change of volume with pressure. The total energy that afluid possesses when the flow is incompressible is made upof the following energi.es:

(a) Potential Energy - energy due to position.(b) Pressure Energy - energy due to pressure.(c) Kinetic Energy - energy due to motion.

In level 3 we saw that we could express the total energy, afluid possessed, in a mathematical form:

ET = Ep + EK + EpR

gh + v2

+P

= 2" 1:

where these values are in Joules/k.g.

In an ideal situation the total energy at one pointin the system is equal to the total energy at another pointin the system. In practice this is not the case. Some ofthe energy possessed by the fluid is converted into lowgrade heat, due to fluid internal friction and pipe friction.This heat energy is considered lost because there is noeasy method, whereby the heat energy may be reconverted intoPE, KE or Pressure Energy.

The energy loss appears as a decrease in pressureenergy and has to be replaced. This is done by a pump,where the fluid is given high KE in the impeller which isconverted into pressure energy in the pump volute.

It should be understood that any changes in KE, PE orfriction loss - all appear as a change in static pressure.

There are several factors upon which the friction lossdepends. In practice, there are very few laminar flowconditions and turbulent flow is the most frequentlyencountered condition.

The friction loss in turbulent flow varies as follows:

Ca) Directly with t~e length of the pipe.(b) Almost as the square of the velocity.(c) Almost inversely as the diameter.

January 1977

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223.00-3

(c) Almost inversely as the diameter.(d) Depends upon the surface roughness of the

interior pipe wall.(e) Depends upon the fluid properties of density

and viscosity.(f) Is independant of the pressure.By now, it has become obvious that friction is a com-

plicated function with many variables and we will now havea closer look to determine how we may account for frictionmathematically.

We must be able to select a factor correctly so that itaccounts for the system pressure loss due to friction. Thisfactor, called the "friction factor" is not constant butvaries with

velocitydiameterdensity

dynamic viscosity

VDt]..I and

certain characteristics of the wall roughness, signified byE where E is a measure of the SIZE of the roughness projectionsand has the dimensions of length.

Thus the friction factor "f" is a function of (V, D, R"].1, E). Since "f" is a dimensionless quantity, the dependentvariables must be arranged to present a dimensionless ratio.

In a smooth pipe E = 0 which leaves "f" dependant uponthe first four quantities. These quantities may only bearranged in one way to give a dimensionless ratio, VDt - Whichas you will recognize is Reynolds' Number. --].1-

byof

For rough pipes 8 may be made dimensionless by dividingthe diameter D. Thus in the general case "f" is a function( VDR, )]..I'D

In rough pipes, E/D is called the "relative roughness"Charts of relative roughness against pipe diameter areavailable to determine the friction factor at fully turbulentflow. Figure 3.1 shows a typical chart.

Experimental r~::;UJ.x::; have a.L.Lowea 1:ne friction factorto be expressed as a function of the relative roughness andthe Reynolds' Number. This chart is called a "MoodyDiagram" and is illustrated in Figure 3.2.

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223.00-3

Relative Roughness of Pip" Materials and Friction FactorsFor Complete Turbulence 's

03

01

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.000008t=::::t=t=jH::H~~+)""~'o~=1=+=H=Ht:H~+t+t=+=t~~.000006 ! ! I! I I I ! I I ! -t1;e;1' 1 I!!! I I I , I I I I I I :' I.000005 L1-..l...-+2~~3~~4J.+5~6~~8"-:ll!:-O~...L-.--;2~O-l-~30~4~O l..;!S!;;-O'!r.60~BO~lO~O-...L---;:;2~OO~300

Pipe Diameter, in Inches - d

Figure 3.1- 3 -

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oo,w

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Relative ...\I'Houglmess -..0

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f ):I-- -

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