turbulent flow through pipes

7/27/2019 Turbulent Flow Through Pipes

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Turbulent Flow Through Pipes

Prof. Rohit Goyal

Professor, Department of Civil Engineering

Malaviya National Institute of Technology Jaipur

E-Mail: [email protected]


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Topics Covered

Pipe Roughness Hydraulically Smooth Pipes

Hydraulically Rough Pipes

Velocity Distribution in Pipes

Equations for Average Velocities

Darcy-Weisbach Equation

Friction Factor Nikuradses Diagram

Moodys Diagram


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Turbulent Flow Through Pipes

Laminar flow analysis through pipes orother types of channels may be complexbut is possible due to application of well

established law such as Newton's law ofviscosity.

However in nature, flow is normallyturbulent, which even for simple cases

may need 3-dimensional considerations. Usually the objective is to compute

frictional resistance to flow.


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Hydraulically Smooth/Rough Pipe

It has been observed that for turbulent flows, wall

roughness plays a crucial role, however even the

finest polished surface have roughness at

microscopic levels which may initiate eddies anddisturbances in turbulent flow which are further

escalated due to turbulence.

It has been observed that pipes of different Degree

of Smoothness behaves likely and so based onroughness of pipe material, pipes are classified as

hydraulically smooth orhydraulically rough.


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Criteria for Smoothness

It has been experimentally observed that thickness

of laminar sub-layer could be calculated by.

When the roughness projections are less than

thickness of laminar sub-layer then pipe is classified

as hydraulically smooth.

This is because roughness projections are now

completely submerged in laminar sub-layer and so

does not matter.

velcoityshearuviscositykinematicwhereu **

&

5


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Hydraulically Rough

When the roughness projections are more than

thickness of laminar sub-layer then pipe is classified

as hydraulically rough.

Now beyond every projection which is more than

laminar sub-layer, a turbulent wake is formed and

so resistance to flow is increased.

Since the classification depends upon thickness of

laminar sub-layer, which depends upon flowconditions, so same pipe may be hydraulically

smooth orhydraulically rough.


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Velocity Distribution (HS Pipes)

It has been observed that the equation derived for

turbulent flow near walls is also valid for

hydraulically smooth circular pipe with the value

of constant B = 5.5 (experimentally observed). andso

5.5log75.5

5.5ln5.2

*

*

*

*

yu

u

u

or

yu

u

u


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Velocity Distribution (HR Pipes)

Forhydraulically rough circular pipe however the

velocity distribution would also depend upon

average value of roughness projections (say k).

It has been experimentally observed that forHR

Pipes

5.8log75.5

5.8ln5.2

*

*

k

y

u

u

or

k

y

u

u


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Average Surface Roughness (k)

Value of k (in cm) for typical surfaces

are as follows

Concrete 0.03 to 0.3

Caste Iron 0.025

Galvanized Iron 0.015

Riveted Steel 0.09 to 0.9 Timber 0.03 to 0.09

Commercial Steel 0.005

9


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Average Velocity (V)

If we integrate velocity profile for circular pipe(taking y=R-r), where R is radius of pipe andthen compute average velocity (V) then

ForHydraulically Smooth Pipes

ForHydraulically Rough Pipes

These could also be written in log terms.

10

75.1ln5.2 *

*

Ru

u

V

75.4ln5.2*

k

R

u

V


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Darcys Weisbach Equation

Darcy and Weisbach almost simultaneouslyderived the equation for head loss throughcircular pipe as

Where hL is head loss between two sections ldistance apart, V is average velocity and d isdiameter of pipe.

f is known as friction factor. This equation isderived from continuity, momentum equation andis valid for both laminar and turbulent flows.

gdflVh

L2

2


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Friction Factor

Since , so it can be proved that

By combining equations, we can than obtain

Hydraulically Smooth Pipe

Hydraulically Rough Pipe

0

*u

8

* f

V

u

74.1log2

1

8.0log21

k

R

f

fRf

N

pipeofRadiusRandVd

RHereN


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Friction Factor f

Friction factor f has been studied in great

details by various scientists.

Nikuradse, a student of Prandtl, conductednumerous experiments for pipes with varying

surface roughness and derived graph between

Reynolds Number (RN) and friction factor (f) as

shown in next slide Relative Roughness is defined as (k/D), where

D is diameter of the Pipe.


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Nikuradses Diagram

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Observations

In the laminar flow region (RN


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Moodys Diagram

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Observations

In the highly turbulent flow region it can be observed thatf varies only with relative roughness and is independentof RN.

For Turbulent flow through smooth pipes, Blasius also

fitted a equation, which is simple to use and f is only onleft side

Balsius equation holds good till RN < 105.

Friction factor is found to change with age of pipes.Roughness is gradually increased due to rusting. Asimple equation is used to calculate k with time t

17

25.0

316.0

NR

f

pipenewofroughnessiskwheretkk00

turbulent flow through pipes

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