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ME 123: Mechanical Engineering Lab II: Fluids

Laboratory 4: Head Losses in Pipe Flow1

MAE 123 : Mechanical Engineering Laboratory II - Fluids

Laboratory 4: Head Losses in Pipe FlowDr. J. M. Meyers | Dr. D. G. Fletcher | Dr. Y. Dubief



Viscous Pipe Flow

Again, think about the size of the probe relative to the gradients. In the entry region, is the probe

able to measure accurately the velocity profile near the wall?

Do your early profiles allow you to determine the entrance length? Is the static pressure distribution

better for that?

Did you look down the pipe to see if the wall is smooth or rough? How would ascertain whether or

not the pipe were smooth or rough? How certain is your judgment?

Lab is always open during the day if you need to make additional observations for your report.

RECAP: Velocity Profile Development in Pipe Flow



Viscous Pipe Flow

Make sure you can interpret the static pressure distribution as you have been asked. Don’t forget to

address:

• Determination of shear stress in the fully developed flow region

• Estimation of the entrance length

• Method(s) for determining shear stress and which is more reliable

• Check log-law

• Asses momentum and friction contributions to velocity development

RECAP: Velocity Profile Development in Pipe Flow



Viscous Pipe FlowRECAP: Velocity Profile Development in Pipe Flow

• This plot, known as a Moody chart (Figure 6.13, White, Fluid Dynamics), gives friction factor as a

function of roughness and of Re and allows you to estimate the head loss due to friction.

• This is done for air and water. (How does the change in liquid effect Re??)

• How does your determination of friction factor compare with this chart?



Reynold’s Number: The primary dimensionless parameter correlating the viscous behavior of all

Newtonian fluids. This is one of the most important non-dimensional parameters in fluid

dynamics.

Re = �� = ��

� ≡ fluid inertia

fluid viscosity

� ≡ velocity scale

� ≡ length scale

� ≡ viscosity

� ≡ kinematic viscosity (�/�)

Reynold’s Number

Very low ReReReRe⇒ viscous creeping motion (high viscosity with low inertia)

Moderate ReReReRe⇒ smoothly varying laminar flow

High ReReReRe⇒ turbulent flow

Laminar: Re < 2300Transient: 2300 < Re < 4000Turbulent: 4000 < Re

The precise value depends on whether any small disturbances are present

Flat Plate Pipe Flow

Laminar: Re < ~500,000Turbulent:~500,000 < Re



Head Loss in Pipe Flow

Last lab and lecture we focused on losses due to friction from the pipe wall.

Additional losses in pipe flows beyond friction include:

1. Pipe entrances and exits

2. Sudden expansions or extractions

3. Bends, elbows, tees and other junctions

4. Valves, whether they’re partially opened or closed

5. Gradual contractions or expansions in the flow



Head Loss

�� +

��2� + �� = ��

�� +��2� + �� = constant

Consider the following form for the Bernoulli equation for steady incompressible flow along a streamline

This is widely used for frictionless flow as the energy along the streamline is assumed to be constant

(NO LOSSES).

You were introduced to the term of stagnation enthalpy which can be evaluated at points 1 and 2:

Incompressible Flow

( = const.const.const.const.)

1

2

streamlines

It can be shown that if there is heat transfer, shaft work, or viscous work (see Chapter 3) between

points 1 and 2 then "� ≠ "�

" = ℎ% + 12�� + �� ℎ% ≡ enthalpy

" ≡ stagnationenthalpy



Head Loss

�� + -� ��

�2� + �� − ��

�� + -� ��

2� + �� = ℎ/012345 − ℎ/012345 + ℎ6137/384

It is common to work in units of length whereby the enthalpy losses and gain are designated to be

“heads”

Assuming there is no energy addition and only losses in the system we arrive at Eq. 6.7:

• Here the velocities represent average velocities.

• The term - represents the kinetic energy correction

factor.

• For fully developed laminar pipe flow this value is

about 2.0.

• For fully developed turbulent pipe flow this value is

normally between 1.04 and 1.11.

ℎ9 ≡ total head loss�� + -� ��

�2� + �� − ��

�� + -� ��

2� + �� = ℎ9

Fig. 6.10 Control volume of steady,

fully developed flow between two

sections in an inclined pipe



Head Loss

ℎ9 = :;2�

2�: = ∆�

12��

The head loss represents a total pressure loss just before and just after a fitting such as an elbow, a

valve, a constriction, an expansion, etc…

The head loss is normally defined in terms of a loss coefficient, ::

Experimentally, the pressure difference between

upstream and downstream stations of the fitting can

be monitored by using a manometer bank:

∆� = ∆ℎcos=�>�

Nominal values for K can be found for various

fittings in most all fluid mechanics textbooks



Head Loss: Inlets

ℎ9 = :;2�

2�: = ∆�

12��



Head Loss: Tube Bends and Elbows

Resistance coefficient for

smooth-walled bends at

Re?=200,000 (Fig. 6.21)

ℎ9 = :;2�

2�: = ∆�

12��

BEND

ELBOW: much of the loss id due to

centrifugal forces. Guide vanes in the bend

section can lessen this loss



Head Loss: Valves

ℎ9 = :;2�

2�: = ∆�

12��



Head Loss: Restriction Meters

Restriction meters are common flow metering devices that take advantage of this pressure drop

phenomenon

(friction loss)

(orifice loss)



@ = AB�� = C?ABD� 2∆�� 1 − EF

@ ≡ volume flow rate [m3/s]

� ≡ bulk velocity measured at station 3 [m/s]

∆� ≡ variation of pressure across the orifice [Pa]

� ≡ density of fluid [kg/m3]

E = BD/B ≡ ratio of orifice radius to pipe radius [-]

The calibration requires the determination of the degree of deviation from the ideal Bernoulli

equation.

This deviation is defined as a discharge coefficient, C?, a dimensionless parameter accounting for the

discrepancies in the approximate analysis.

The flow rate obtained by the modified Bernoulli equation for an orifice with flanged taps is:

Head Loss: Restriction Meters

Eq. 6.124



Experiment

Pipe experimental facility in angled configuration for head loss measurements

Inserts and inlets



Experiment

1) Using two different flanged 80 mm diameter 90° elbows between station 6 and 7, determine the

resistance coefficient

200 mm radius elbow Mitered elbow with

turning vanes

Discuss the results based on the literature (compare

with existing plots!!) and show all uncertainties



Experiment

2) Use the orifice to perform a restriction meter-based flow rate measurement

Orifice Plate

Again, discuss the results based on the literature

(compare with existing plots!!) and show all

uncertainties



Experiment

� = @G = 1

AB�H H I J, = JKJK=L

D

MN�O

MND

Recall, if a velocity profile is known, the average velocity can be calculated from :

For laminar pipe flow the parabolic profile can be simply integrated. However, for turbulent flow, the

profile needs to be numerically integrated with empirical data:

� = 2AG PI(J)J∆J Use this relation for your bulk/average velocity calculations

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