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The equipment described in this manual ismanufactured and distributed by

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.TBCQUIPMENT LIMl"l'HU

Suppliers of technological laboratoryequipment designed for teaching.

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BONSALL STREET, LONG EATON, NO'rrINGHAM, NG1O 2AN, ENGLAND

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Tel: (0115) 9722611 : Fax: (0115) 9731520...

@ TecQuipment Limited

1No part of this publication may be reproduced ortransmitted in any form or by any means, electronic or

mechanical, including photocopy, recording or anyinformation storage and retrieval system without the expresspermission of TecQuipment Limited. Exception to thisrestriction is given to bona fide customers in educational ortraining establishments in the normal pursuit of theirteaching duties.

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Whilst all due care has been taken to ensure that the contentsof this manual are accurate and up to date, errors or

omissions may occur from time to time. H any errors are

discovered in this manual please inform TecQuipment Ltd.

so the problem may be rectified.

A Packing Contents List is supplied with the equipment and

it is recommended that the contents of the package(s) are

carefully checked against the list to ensure that no items are

missing, damaged or discarded with the packing materials..In the event that any items are missing or damaged, contactyour local TecQuipment agent or TecQuipment direct assoon as possible.

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.Figure 1. General Arrangement of Apparatus.

Pagel

H34 LOSSFS IN PIPE JlTJ-J'JNGS

INTRODUCTION Almost all runs of pipework contain fittings such as bends,

changes in diameter, junctions and valves. The

constrictions, and changes in direction of flow through such

fittings, cause losses which are additional to those due to

friction at the pipe wall. Since these losses at fittings

usually contribute significantly to the overall loss through

the pipework, it is important to have reliable information

about them. In this experiment, losses in various typical

fittings are investigated over a range of flow rates....

Description of

Apparatus

The equipment illustrated in Fig I provides a run ofpipework, made up of components manufactured in rigidplastic material, supported in the vertical plane from abaseboard with a vertical panel at the rear. Water issupplied to the pipe inlet from an HI Hydraulic Bench, andis discharged at the exit to the measuring tank of the bench.In the run of the pipe there are the following fittings:--

,a.

,.

90° mitre bend

90° elbow bend

90° large radius bend

Sudden enlargement in pipe diameter

Sudden contraction in pipe diameter..

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Piezometer tappings are provided in the pipe wall, at clearlengths of 4 pipe diameters, upstream and downstream ofeach of the fittings. The tappings are connected to amultitube manometer which may be pressurised by use of acycle pump. The system may be purged of air by venting toatmosphere through the manometer. The flow rate throughthe equipment may be varied by adjusting the valve nearthe pipe exit.

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H34 wss~ IN PIPE lI'n-I'INGS

----fr

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c rTV u2/2g

r--~ i&H

r"'~.

V d2/2g

"', !' "

r~"1'

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Figure 2. Schematic Representation of Loss at a Pipe Jlitting.

11

11Page 4

H34 LOS~ IN PIPE rJNGS

Measurement of Loss

of Total Head at a

Fitting

Fig 2 shows water flowing at speed V u along a pipe of

diameter Du towards some pipe fitting such as a bend or a

valve, but shown for simplicity as a simple restriction in the

cross-section of the flow. Downstream of the fitting, the

water flows along a pipe of some other diameter Dd, along

which the velocity of flow is V d. The figure indicates the

variation of piezometric head along the pipe run, as would

be shown by numerous pressure tappings at the pipe wall.

In the region of undisturbed flow, far upstream of the

fitting, the distribution of velocity across the pipe remains

unchanged from one cross-section to another; this is the

condition referred to as 'fully developed pipe flow'. Over

this region, the piezometric head falls, with a uniform,

mild gradient, as a result of the effect of constant friction at

the pipe wall in fully developed pipe flow. Close to the

fitting, however, there are sharp and substantial local

disturbances to the piezometric head, caused by rapid

changes in direction and speed as the water passes through

the fitting. In the downstream region, these disturbances die

away, and the line of piezometric head returns

asymptotically to a

slight linear gradient, as the velocity distribution gradually

returns to the condition of fully developed pipe flow.

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If the upstream and downstream lines of linear frictiongradient are now extrapolated to the plane of the fitting, aloss of piezometric head ~h due to the fitting is found. Toestablish the corresponding loss of total head ~H it isnecessary to introduce the velocity heads in the upstreamand downstream runs of pipe. From Fig 2 it is clear that:

AH = Ah + Vu2/2g - Vd2/2g 1~

It is conveniant to express this as a dimensionless losscoefficient K, by dividing through by the velocity head ineither the upstream or the downstream pipe (the choice

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1H34 LOSS~ IN PIPE JI"n-J"INGS

depending on the context, as we shall see later).

The result is thus4H 4HK= or 2a

For the case where Du = Dd, the flow velocities in the

upstream and downstream are identical, so we may simplifythe definition to:

Mi ~K = 2 or 2 2bV /2g V /2g

where V denotes the flow velocity in either the upstream orthe downstream pipe run. *

To obtain results of high accuracy, long sections of straightpipe (of 60 pipe diameters or more) are needed to establishwith certainty the relative positions of the linear sections ofthe piezometric lines. Such long upstream and downstreamlengths are impracticable in a compact apparatus. However,if just two piezometers are placed, one upstream and onedownstream of the fitting, outside the region of severedisturbance, reasonable accuracy is obtained simply bytaking Ah as the differential reading between the two. 0

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[* The velocity head v2/2g used here is based simply on

the mean flow velocity V. Because the velocity variesacross the pipe cross-section, from zero at the wall to amaximum at the centre, the velocity head in this non-uniform flow is somewhat higher, being typically 1.05 to

I.O7V2/2g.

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(a) 908 bend

.(c) Sudden contraction

-Figure 3. Flow in a Bend, Sudden Enlargement an Sudden Contraction.-

~Charactermics of a

}low Through Bends

and at Changes in

Diameter

Fig 3(a) illustrates flow round a 900 bend which has aconstant circular cross-section of diameter D. The radius of

the bend is R, measured to the centre line. The curvature of

the flow as it passes round the bend is caused by a radial

gradient of piezometric head, so that the piezometric head

is lower at the inner surface of the pipe than at its outer

surface.

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Page 7

lH34 LOSS~ IN PIPE .l4rJ-rINGS

As the flow leaves the bend, these heads start to equalise asthe flow loses its curvature, so that piezometric head beginsto rise along the inner surface. This rise causes the flow toseparate, so generating mixing losses in the subsequentturbulent reattachment process. Additionally, the radialgradient of piezo-metric head sets up a secondary cross-flow in the form of a pair of vortices, having outwarddirected velocity components near the pipe centre, andinward components near the pipe walls. When

superimposed on the general streaming flow, the result is adouble spiral motion, which persists for a considerabledistance in the downstream flow, and which generatesfurther losses that are attributable to the bend. Clearly, thevalue of the loss coefficient K will be a function of the

geometric ratio RID; as this ratio increases, making thebend less sharp, we would expect the value of K to fall.The smallest possible value of RID is 0.5, for which thebend has a sharp inner comer. For this case, the value of Kis usually about 1.4. As RID increases, the value of K falls,reducing to values which may be as low as 0.2 as RIDincreases up to 2 or 3. There is also a slight dependence onReynolds Number Re, but for most purposes this is smallenough to be ignored.

Fig 3(b) shows the flow in a sudden enlargement. The flowseparates at the exit from the smaller pipe, forming a jetwhich diffuses into the larger bore, and which reattaches tothe wall some distance downstream.

The vigorous turbulent mixing, resulting from theseparation and reattachment of the flow, causes a loss oftotal head. The piezometric head in the emerging jet,however, starts at the same value as in the pipe immediatelyupstream, and increases through the mixing region, sorising across the enlargement. 0

Page 8

H34 LQSSFS IN ~F1 TI'lNGS

These changes in total and piezometric head, neglecting the

small effect of friction gradient, are illustrated in Fig 3(b).

Assuming that the piezometric pressure on the face of the

enlargement to be equal to that in the emerging jet, and that

the momentum flux is conserved, the loss of total head may

be shown to be:

4H = (Vo (3)

The corresponding rise in piezometric head is:

.db = 2V d(V u - V d>/2g (ii)...

The loss coefficient K is, in this case, best related to theupstream velocity Vu, so that:.

.(5)

. This shows K increasing from zero when Au/~ = 1.0, to1.0 when Au/~ falls to zero.

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Consider lastly the case of the sudden contraction shown in

Fig 3(c). The flow separates from the edge where the face

of the contraction leads into the smaller pipe, forming a jet

which converges to a contracted section of cross-sectional

area Ac. Beyond this contracted section there is a region of

turbulent mixing, in which the jet diffuses and re-attaches

to the wall of the downstream pipe. The losses occur almost

entirely in the process of turbulent diffusion and re-

attachment. The losses are therefore expected to be those

due to an enlargement from the contracted area Ac to the

downstream pipes area ~. Following the result of equation

(3), the expected loss of total head in contraction is:J.

4H = (V c - V d)2/2g .(6)

H34 LOSS~ IN PIPE ~"'l-l'INGS

The obvious choice of reference velocity in this case is V d,

so the loss coefficient K becomes:

IC == [<"c"/d) - 1]2 == [(~'1lC) - 1]2 (7)

Consider now the probable range of values of Ad' Ac. If the

value of the pipe contraction ratio is 1.0, viz if Ad' Au =

1.0, there will be no separation of the flow, so Ad' Ac =

1.0 also. Equation (7) then gives a zero value of K. If,

however, the contraction is very severe, viz. Ad' Au -+ 0,

then the upstream pipe tends to an infinite reservoir in

comparison with the downstream one. We might then

reasonably expect the flow at the entry to the downstreampipe to resemble that from a large reservoir through an

orifice of area Ad. For such an orifice, the contraction

coefficient has the value 0.6 approximately, so that

~/Ac = 1/0.6 = 1.667

Substituting this value in equation (7) gives:

K = 0.44

It might therefore be expected that K would rise from zerowhen the pipe area ratio ~I Au = 1 to a value of about

0.44 as ratio ~I Au falls towards zero.

1 H34 LOSS~ IN PIPE l4Tl-l"JNGS

1 Installation

Instructions

1

Connect the supply hose of the HI Hydraulics Bench to the

inlet of the unit. Fix a further hose to the outlet of the unit,

to direct the discharge to the measuring tank of the bench.

Ensure that the connections are made correctly by referring

to the mimic diagram, which shows the direction of flow.

Ensure that the hose clip connecting the inlet hose to the

apparatus is tight. Start the pump, and open fully the

control valve at the exit from the unit, to allow water to

circulate through the pipework. Check the system for leaks.

...

Now use the following procedure to ensure that all air is

expelled from the system. Depress the Schrader valve,

which is situated in the manometer manifold. Partially close

the control valve at the exit from the unit. Air bubbles will

be seen to be carried upwards by the water currents along

the manometer tubes into the manifold, from which they

escape to atmosphere through the depressed Schrader valve.

Adjust the control valve at the exit from the unit to produce

vigorous flow up the manometer tubes, so ensuring that the

system is thoroughly purged of air. When this is complete,

close the Schrader valve, and close the valve at the exit

from the unit. Now connect the air pump to the Schrader

valve, and carefully pump air into the manifold. Continue

to pump until air is driven down the manometer tubes to a

convenient height. Again check for leaks by observing that

the water levels in the manometer tubes remain constant

over a period of time.

Page 11

H34 LOSSFS IN PIPE lIII-rINGS

Routine Care andMaintenance

I

Clean water should always be used with the unit. If used inconjunction with a TQ Hydraulic Bench (HI or HID) thewater should be changed periodically in line with themanufacturers instructions, and a suitable stain and depositremover used. To clean the apparatus externally it shouldonly be necessary to wipe with warm water and a lint-freecloth; do not use detergents or any abrasives as these maydamage the smooth fibreglass and painted surfaces. Theequipment is designed for trouble-free operation andservice, but if for any reason damage does occur thenTecQuipment or their accredited Agent should be informedimmediately to advise and arrange for the appropriate

repair.

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Page 12

H34 LOSS~ IN PIPE I1U-."INGS

EXPERIMENTALPROCEDUREn Set up the unit and level it as described in the Installation

Instructions. Note the diameters of the pipes and

dimensions of the fittings, as shown on the mimic diagram.

Open the exit valve carefully, watching the water levels inthe manometer tubes. Admit or release air as necessary tokeep all the readings within the range of the scale. Whenthe maximum feasible flow rate is reached, record thedifferential readings across each of the fittings, whiletiming the collection of a known quantity of water in themeasuring tank of the bench.

Repeat these measurements at a number of rates of flow. Itmay be necessary to pump in more air to the manometer tokeep the readings within bounds as the exit valve is closed;alternatively the bench valve may be used to effect part ofthe flow reduction.

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H34 LOSS~ IN PIPE J4'r.-rINGS

Dimensions of Pipes and Fittings~UL TS ANDCALCULA nONS

m2m2

Diameter of smaller bore pipe

Diameter of larger bore pipe

Radius to centre line of mitre

Radius to centre line of elbow

Radius to centre line of bend

Dl =D2 =

Rm=Re=Rb =

mm Al =mm A2 =mmmmmm

DifferentialTotal Head

Readings and ofPiezometer Loss

If the measured flow rate is Q l/s, then the velocities VI

and V 2 along the pipes of cross-sectional A 1 and A2 m2

areas are :

VI = lQ-3QtAI mts and V2 = lQ-3Q/A2 m/s

The laboratory readings are recorded as follows (note thatthe reading for the enlargement is negative):

Differential Piezometer Reading (mm)

Enlarge-mentS-6

Contract-ion7-8

Qty

0)

Time

(s)

Q

(l/s)

Mitre

1-2

Eloow

3-4Bend

9-10

24 43.3 0.554 154 113 -28 104 62

Table 1 Piezometric Head Losses at Various Rates of Flown.

Page 14

H34 LOSS~ IN PIPE J4I...'INGS

Next, velocities and velocity heads are calculated at eachrate of flow, for both the smaller and larger diameter pipes.

The calculations are tabulated as follows. (Values are basedon Dl = 22.5mm and D2 = 29.6mm).

I

Note that, for the case of the enlargement and of thecontraction only, the loss of total head differs from thedifferential piezometer reading, as shown in equation 1.For example, the sample entries in the tables show, in thecase of the sudden enlargement:

Ah

V u2/2g

Vd2/2g

So 4H

VuA~/~ "':;./. ~+-~ - ~

~I..A...'T OL~

.61-1 :.=)

Q.

VI :'A.

Q..

~:~~ Loss of Total Head (mm)

VI(mls)

V12/2g(mm)

Vr/2g(mm)

V2(m/s)

Mitre1-2

Elbow3-4

Bend9-10

EnJarge-ment

5-6 ~-.

38

Cootract-ion .7-8. - II..

43

J.~

Q

,~

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1.394 0.806 99 33 154 113 62

Table 2 Total Head Loss at Various Rates of Flow

Page 15

1H34 WSS~ IN PIPE i4I.-.'INGS

1Calculation of Loss

Coefficients KTo obtain the loss coefficients of each of the fittings, values

of total head loss shown in Table 2 are plotted against

values of velocity head V 12/2g, which is the velocity head

in the pipe of smaUer diameter. For every fitting other than

the sudden contraction, V 12/2g represents the velocity head

in the upstream pipe, and so conforms with the relevant

definition of K. For the contraction, V 12/2g represents the

velocity head in the downstream pipe, which again

conforms with the relevant definition. The slopes of the

lines through the origin give the values of K for each of the

fittings in turn, as shown in Figs 4 and 5.

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jI-X<2-g

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~/

A

$/

If/y1

/40 ..A"r

0, .

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r" I I I I I0 20 40 ~ 80 100

VeJodty head va /2g (mm)

Figure 4. Total Bead Loss in 90° Bends of Various Radii.J

JPage 16

120

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-.H34 LOSSF$ IN PIPE Frj-j'1NGS

60

~-:I:~

]""fa:g'0

~0

~

-.+::~~~=3 v u

Du = 29.6 mm4H=k~

29i-~-<]

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0-

'0

II)

.§

p~~d =22.5 mm

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0 0 ~ I 20 I 40 ' (,0 , ~ I 100

Ix,wnsb'eam velocity head v: / (mm)729

Figure S. Total Head Loss at a Sudden Enlargement and a Sudden Contraction

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