Fluid Mechanics Laboratory

FLUIDMECHANICS LABORATORY

EXPERIMENT NO – 04

Minor LOSSES IN PIPE FITTINGS

OMKARAM .K

0800335

1

AIM: to find out frictional losses associated with pipe fittings such as valves and bends installed in a piping system.

Apparatus:

Figure 1.1

In the above shown diagram there are two tanks called sump tank and measuring tank .sump tank acts as reservoir for water .measuring tank is used for calculating volumetric flow rate of water. Water flow is controlled by two valves called control valve and By-pass valve. Here we are provided with nine fittings called pipe bend, enlargement, contraction,

Elbow, gate valve, ball valve, union-1, union-2, long radius bend. Pressure tapings are provided at inlet and outlet of these fittings at appropriate locations. A manometer is fitted to the pipeline to measure pipe loss due to installation of pipe fitting.

Given data:

Area of measuring tank , Atank = 0.1m2

Specific gravity of mercury = 13.6g

cm3

Acceleration due to gravity = 9.81m

s2

Diameter of small pipe, D1 = 0.0165 m

Diameter of larger pipe, D2 = 0.027 m

2

Cross sectional area of smaller diameter pipe, A1 =2.14∗10−4m2

Cross sectional area of larger diameter pipe, A2 =5.73¿10−4m2

Nomenclature:

D1 , Diameter of small pipe

D2 , Diameter of larger pipe

A1 , Cross sectional area of smaller diameter pipe

A2 , Cross sectional area of larger diameter pipe

hL , head loss

k L , pipe fitting loss coefficient

V 1 , velocity in smaller diameter pipe

V 2 , velocity in larger diameter pipe

g ,acceleration due to gravity

f, friction factor

LD

, equivalent length

∆ P, pressure drop

h, height of mercury in manometer

ρHg, density of mercury

ρ, density of water

t, average time taken to fill measuring tank

μ , kinematic viscosity of fluid

ε, Roughness

3

Theory and Formulae:

As the fluid flows along a long pipe there are losses due to friction .but in the short pipes friction doesn’t play much role for losses. But due to abrupt changes in cross section of pipe, presence of fittings such as elbow, gate valve ,bends, ball valves etc are forming secondary flows due to which the separation of flow from the boundary also formation of eddies occur. This results in minor head losses.

Head loss due to presence of a bend or elbow or a valve or a union in a pipe line is given by

hL=k LV 2

2 g (1)

Head loss due to sudden enlargement in pipeline is given by

hL=k L(V 1−V 2)

2

2g (2)

In terms of area of cross section above equation can also be written in the form of

hL=k L(1−A1A2

)2 V 1

2

2 g (3)

Headloss due to sudden contraction in the pipe line is given by

hL=k LV 1

2

2g (4)

The viscous head loss associated with flow in straight circular pipeof length L and diameter D is given as

h f=f ( LD )( V2

2g) (5)

Friction factor depends on pipe friction which depends on reynolds number of the pipe flow.

Compare 4 & 5

k L=f ( LD ) (6)

4

k Lis considered to be independent of both friction factor and reynolds number and is treated as constant for a fiven fitting or valve under any type of flow condition.

k Lis defined as number of velocity heads lost due to the valve or fitting. it is a measure of the following losses in a valve or fitting.

Pipe friction in the inlet and outlet straight portions of the valve or fitting Changes in direction of flow path Obstructions in the flow path Sudden or gradual changes in the cross-section and shape of the flow path

The ratio LD

is also constant for a fitting or valve at the same type of flow condition.

The ratio L/D is defined as the equivalent length of the valve or fitting in pipe diameters and L is the equivalent length itself.

Head loss in the pipe due to fitting can also be written as

hL=∆ P=ρHgh

ρ (7)

Results:

For height 10 cm

Average time=t1+t 2+ t33

=19.31+18.90+18.12

3=18.77 s

Volumetric flow rate= 0.0118.77

=5.327∗10−4 m3

s

Velocity in the smaller diameter pipe,V 1= 5.327∗10−4

2.14∗10−4 =2.489

ms

Velocity ion the larger diameter pipe,V 2=5.327∗10−4

5.73∗10−4 =0.9296 ms

Following table shows pressure drop across various pipe fittings

Pipe fitting Pressure drop h(in mm of Hg)

Head loss Pipe fitting loss coefficient(experimental)

Pipe fitting loss coefficient (theoretical)

Elbow(threaded)

48 0.6528 2.065 0.57

Expansion 13 0.1768 0.559 0.36Contraction 48 0.6528 0.25 0.26

5

Union-1 26 0.3536 1.118Ball valve 23 0.3128 0.9898 2.85Bend (90) 51 0.6936 2.1949 0.95Gate valve 35 0.476 1.5063 0.152Union -2 24 0.3264 1.033Long radius bend

34 0.4624 1.4633 0.38

Table 1.1

Reynolds numbers are

For smaller diameter pipe (ρV 1d1μ

) =4.1068*104

For larger diameter pipe (ρV 2d2μ

) = 2.5024*104

Total head loss= 4.1072

Total Pipe fitting loss coefficient (experimental) =11.1793

ε for commercial steel is 0.045 and diameter of pipe is 16.5mm therefore ϵd

is 2.72*10−3

From the intersection point of Reynolds number and ϵd

is 0.019 which is friction factor. From

the multiplication of friction factor with equivalent length gives us pipe fitting loss coefficient. So for elbow 0.019*30=0.57 is pipe fitting loss coefficient.

Second time:

For height 10 cm

Average time =29.38+28.65+29.91

3=29.31 s

Volumetric flow rate =0.0129.31

=3.41*10−4m3

s


2.14∗10−4 =1.6

ms


5.73∗10−4 =0.595 ms


Pipe fitting Pressure drop Head loss Pipe fitting loss Pipe fitting loss

6

h(in mm of Hg) coefficient(experimental)

coefficient (theoretical)

Elbow 21 0.2856 2.187 0.6Expansion 6 0.0816 0.6248 0.36Contraction 20 0.272 0.26 0.28Union-1 10 0.136 1.04Ball valve 9 0.1224 0.9372 3Bend (90) 23 0.3128 2.40 1Gate valve 16 0.2176 1.66 0.16Union -2 10 0.136 1.04Long radius bend

14 0.19 1.455 0.4

Table 1.2



) =2.64*104


) = 1.6065*104

Total head loss = 1.754

Total Pipe fitting loss coefficient (experimental) = 9.944

Third time:

For height 10 cm


=50.38+48.12+50.53

3=49.67 s


=2.01¿10−4 m3

s


2.14∗10−4 0.9392

ms


5.73∗10−4 =0.35 ms





Elbow 8 0.1088 2.417 0.6

7

Expansion 2 0.0272 0.38 0.36Contraction 7 0.0952 0.29 0.28Union-1 5 0.068 1.51Ball valve 3 0.0408 0.906 3Bend (90) 4 0.0544 1.208 1Gate valve 6 0.0816 1.813 0.16Union -2 2 0.0272 0.60Long radius bend

5 0.068 1.51 0.4

Table 1.3



) =1.5496*104


) = 0.9450*104



Fourth time:

For height 10 cm


=31.72+32.28+33.47

3=32.49 s


=3.07¿10−4 m3

s


2.14∗10−4 =1.47897

ms


5.73∗10−4 =0.5357 ms





Elbow 19 0.2584 2.34 0.6Expansion 5 0.068 0.38 0.36

8

Contraction 17 0.2312 0.29 0.28Union-1 10 0.136 1.236Ball valve 9 0.1224 1.112 3Bend (90) 20 0.272 2.47 1Gate valve 13 0.1768 1.60 0.16Union -2 9 0.1224 1.112Long radius bend

13 0.1768 1.60 0.4

Table 1.4





) = 2.44*104


) = 1.4463*104

0.5 1 1.5 2 2.5 3 3.5 4 4.51.8

1.9

2

2.1

2.2

2.3

2.4

2.5

reynolds number vs pipe fitting loss coefficient

reynolds number vs pipe fitting loss coefficient

Figure 1.1 Reynolds number Vs pipe fitting loss coefficient for elbow

9

0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.5

1

1.5

2

2.5

3

reynolds number Vs pipe fitting loss coefficient

reynolds number Vs pipe fitting loss coefficient

Figure 1.2 Reynolds number Vs pipe fitting loss coefficient for bend

0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.5

1

1.5

2

2.5

3

reynolds number vs pipe fitting loss coefficientreynolds number Vs pipe fitting loss coefficient (theoretical)

10

Figure 1.3 theoretical and experimental pipe fitting loss coefficient comparisons

0.5 1 1.5 2 2.5 3 3.5 4 4.50

2

4

6

8

10

12

14

reynolds number Vs total pipe fitting loss coefficientreynolds number Vs total head loss

Figure 1.4

0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

reynolds number Vs head loss for elbow

reynolds number Vs head loss for elbow

Figure 1.5

DISCUSSIONS:

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1. If we look at the values of k Lin the all tables value of k Lis constant for a fitting or valve which proves that value of k Ldoesn’t depend on velocity or Reynolds number. It merely depends on valve or fitting under any flow condition.

It is also observed in figure 1.1 where variation of pipe fitting loss coefficient is almost negligible.

2. High difference between theoretical and experimental value is due to frictional losses that exist in addition to the minor losses.

Figure 1.3 shows the comparison of experimental value and theoretical value.

3. In figure 1.2 variation of pipe fitting loss coefficient is high which may be due to experimental error

4. As the Reynolds number increases pipe fitting loss coefficient increases for any valve or fitting. Obviously total pipe fitting loss coefficient also increases with the Reynolds number.

The reason may be tendency of fluid to behave like turbulent flow.

5. But interestingly as Reynolds number increases head loss is decreasing, but here we have to agree with the fact that in this experiment as the Reynolds number increased velocity is decreased. So total head loss is also decreasing with Reynolds number.

References:

1. Fox R.W. and McDonald A.T., Fluid Mechanics, John Wiley International, 2005.2. White F. M., Fluid Mechanics, Tata McGraw Hill, 2008.3. Gupta V. and Gupta S.K., Fluid Mechanics, Narosa, 2005

Internet resources:1. A Pipeline Sizing Program athttp://www.roymech.co.uk/Related/Fluids/Fluids_Pipe.html2. An e-book on the application to sizing piping systemshttp://www.scribd.com/doc/6205083/Pipe-Selection-Friction-Loss

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Fluid Mechanics Laboratory