Page 59 - Fluid mechanics, heat transfer, and mass transfer

PIPING, SEALS, AND VALVES
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& Smooth pipes: ➢ For extremely rough pipes

p ffiffiffi p ffiffiffi
1= fÞ 0:4: ð3:5Þ
f ¼ 4log ðN Re
10 f ¼ 0:013: ð3:13Þ
This equation requires iterative techniques.
& Use of equations has become more convenient in the
➢ Blasius equation:
present scenario of computerization compared to the
5
0:25
f ¼ 0:079=N Re ; 4000 < N Re < 10 : ð3:6Þ past when use of charts has been the practice.
& Figure 3.1 represents Moody diagram.
& Rough pipes: & The values of roughness for different materials are
listed in Table 3.1.
p ffiffiffi p ffiffiffi
1= f ¼ 2log ½f«=D=3:7gþ 2:51=N Re ð1= fފ: . What are the recommended pipe surface roughness
10
values for steel piping at different stages of its life?
ð3:7Þ
& New pipe: 0.04 mm.
This equation also requires an iterative technique
& After longer use: 0.2 mm.
such as Newton–Raphson method for estimating f.
& Slightly rusted condition: 0.4 mm.
➢ Rough pipes—noniterative equation:
& Severely rusted condition: 4.0 mm.
p ffiffiffi . Arrange the following pipe materials in the order of
1= f ¼ 0:8686 ln ½0:4587N Re =ðs=s s þ 1 ފ; ð3:8Þ
increasing surface roughness: Polyethylene, stainless
steel, concrete, GI, copper, commercial steel, cast iron,
where s ¼ 0:1240ð2 =DÞN Re þ lnð0:4587N Re Þ: Teflon-coated carbon steel, severely rusted steel, and
Maximum error of 1% is claimed in the estimation glass.
of f. & Glass, Teflon-coated carbon steel, copper, polyeth-
& Churchill equation for smooth and rough pipes:
ylene, stainless steel, GI, cast iron, concrete, and
severely rusted steel.
p ffiffiffi 0:9
1= f ¼ 4log ½0:27ð«=DÞþð7=N Re Þ Š; . Name different types of fittings used in piping.
10
ð3:9Þ

& Flanges, elbows (90 and 45 ), bends, tees, reducers,
N Re > 4000:
crosses, nipples, unions, valves, and so on.
This equation is noniterative and applies to both . Friction losses are more in a bend or in an elbow?
laminar and turbulent flows, by putting «/D ¼ 1 for & In an elbow, as it involves sudden change in direction,
laminar flow. promoting energy losses through eddy formation.
& Colbrook equation: . “Pressure drop in a fitting for sudden enlargement (e.g.,
tankinlet)ishigherthanforsuddencontraction(e.g.,tank
p ffiffiffi
1= f ¼ 4log ½ð«=3:7DÞþð1:256=N Re fފ; outlet) for the same size ratio.” True/False?
10
& True. The number of diameters equivalent to straight
N Re > 4000: ð3:10Þ pipe for sudden enlargement is 50, while it is 25 for
sudden contraction.
This equation formed the basis for the Moody
. “Friction factor has a linear relationship with Reynolds
chart.
Number under turbulent conditions.” True/False?
& Approximate relationships for Fanning friction fac-
& False.
tors are as follows:
. “In laminar flow friction factor f is dependent on
➢ For laminar flow
roughness factor «/D.” True/False?
f ¼ 16/N Re . & False.
. Is there any effect of temperature on friction factors for
➢ For commercial pipes
flow through a pipe?
& Yes. As temperature decreases, for example, fluid
0:2
f ¼ 0:054=N : ð3:11Þ
Re
viscosity increases and also fluid density. But
➢ Smooth pipes viscosity increase is much more in magnitude than
density increase, with the net result that Reynolds
f ¼ 0:46=N 0:2 : ð3:12Þ
Re number decreases. A look at Moody diagram