-
Seoul National University
457.309.02 Hydraulics and Laboratory
.09 Turbulent flow in rough pipe
Prepared by Jin Hwan Hwang(2019.04.03)
-
Seoul National University
Today’s objectives
§ Similarly to the smooth pipe case, turbulent flow in rough
pipe will be understood.
§ Classifying the pipes whether they are smooth or rough§
Evaluating pipe friction factors in the given condition
2
-
Seoul National University
§ Pipe friction in rough pipe will be governed by the size and
patterns of the roughness (like as sediment particles)
§ As we learned through the last class, velocity profile follows
logarithm no matter what flow is laminar or turbulent.
§ When roughness is high, the viscous layer will be canceled and
viscosity may not be the important parameter.
§ Experiment proved that the viscosity can be replaced by the
roughness in the rough wall condition.
§ In this condition Q (flow rate) can be determined as
Turbulent flow – Rough pipes
3
uu*
= 5.75 log ye+ 8.5 (Rough pipe, when e is roughness)
Q = u(2πr dr)0
R
∫ = 2πu* 5.75 logR − re
⎛⎝⎜
⎞⎠⎟ + 8.5
⎡⎣⎢
⎤⎦⎥r dr
0
R
∫
-
Seoul National University
§ Therefore, the mean velocity is
§ Since
§ With experimental adjustment,
Rough pipes’ friction factor
Turbulent flow – Rough pipes
4
Vu*
= 5.75 log Re+ 4.75
u* =Vf8
1f= 2.03log R
e+1.68
1f= 2.0 log d
e+1.14
-
Seoul National University
§ The mean velocity in a 300 mm pipeline is 3m/s. The relative
roughness of the pipe is 0.002 and the kinematic viscosity of the
water is 9 x 10-7 m2/s. Determine the friction factor, the
centerline velocity, the velocity 50 mm from the pipe wall, and the
head lost in 300 m of this pipe under the assumption that the pipe
is rough.
– Friction factor– Centerline velocity– The velocity at 50 mm
from the wall– Head loss
Example
5
-
Seoul National University
– Friction factor
– Centerline velocity
– The velocity at 50 mm from the wall
– Head loss
Example
6
1f= 2.0 log d
e+1.14
ucu*
= 5.75 log Re+ 8.5, u* =V
f8
u50u*
= 5.75 log y50e
+ 8.5
hL = fldV 2
2gn
-
Seoul National University
§ What parameters do we need to compare to know whether flow is
smooth or rough?
§ To cancel this, we need to see the ratio between this and
that.– This is viscous sublayer thickness and roughness height
§ What is the viscous sublayer thickness in Laminar flow?– Since
viscosity governs overall depth in pipe, R should be the
thickness.– Therefore, in a Laminar flow, no matter what smooth or
rough,
§ In turbulent flow,
Classification of smoothness and roughness
7
f = 64Re
eδν
= e / dδν / d
= e / d32.8 / Re f
= ed
⎛⎝⎜
⎞⎠⎟Re f32.8
edRe f = 32.8 e
δν
-
Seoul National University
§ Now we can plot the results with
Classification of smoothness and roughness
8
edRe f and 1
f− 2.0 log d
e
1f− 2.0 log d
e= 1.14
Fully rough flow
1f= 2.0 log Re f( )− 0.8
1f− 2.0 log d
e= 2.0 log e
dRe f⎛⎝⎜
⎞⎠⎟ − 0.8
Smooth flow
1f− 2.0 log d
e= 1.14 − 2log 1+ 9.28
Re(e / d) f⎡
⎣⎢
⎤
⎦⎥ (For commertial highly turbulent flow)
-
Seoul National University
§ Classifications
Classification of smoothness and roughness
9
For smooth flow: ed
Re f ≤10
For transition flow: 10< ed
Re f < 200
For rough flow: 200 ≤ ed
Re f
-
Seoul National University
Classification based on velocity profile
§ Another means of classification of the roughness effects is to
use the velocity profiles directly. In all pipes (page 331),
§ In rough pipes,
10
uc − uu*
= 5.75 log Ry
uu*
= 5.75 log ye+ 8.5
ucu*
= 5.75 log Re+ 8.5 (At center)
uc − uu*
= 5.75 log Re− log y
e⎛⎝⎜
⎞⎠⎟
= 5.75 log Ry
-
Seoul National University
Classification based on velocity profile
§ Now let’s modify the equation – For both (smooth and
rough)
§ In smooth flow, A=8.5 from experiment.§ Check the page 332,
equation 9.17,
11
uu*
= ucu*
+ 5.75 log yR
= ucu*
+ 5.75 log eR+ 5.75 log y
e
= A + 5.75 log ye
A = ucu*
+ 5.75 log eR
uu*
= 5.75 log u*yν
+ 5.5 (Smooth pipe)
= 5.5 + 5.75 log u*eν
+ 5.75 log ye
= A + 5.75 log ye
A = 5.5 + 5.75 log u*eν
-
Seoul National University
Classification based on velocity profile
§ In the previous equation is the Roughness Reynolds Number.
12
u*eν
11.6 /δν( )e = u*e /ν ≤ 3.5 Smooth flow3.5< 11.6 /δν( )e =
u*e /ν < 70 Transition flow70 ≤ 11.6 /δν( )e = u*e /ν Wholly
rough flow
