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PRACTICAL, HEAD LOSSES IN SMALL BORE

 PRACTICAL 5: HEAD LOSSES IN SMALL BOR





HEAD LOSSES IN SMALL BORE PIPE SYSTEMS



INTRODUCTION

The minor losses are those which are caused by change in pipe cross section, presence of bends,valves and fittings.Although in long pipelines the losses due to the local disturbances caused by these fittings are of minor importance and often can be neglected,they may however outweigh the friction losses in short pipe.

The source of losses is usually confined to every short length of the pipe.A theoretical determination of the minor losses is seldom possible except for the loss due to sudden enlargement.Since the losses have been experimentally found to vary approximately as the square of the mean velocity, they are normally expressed in the form



HL =KL V2

          2g

In which KLis known as the loss coefficient. For a geometry,the value ifKL is practically constant at high Reynolds number, the magnitude of the loss coefficient is experimentally determined and is governed primarily by the shape of the obstruction or pipe fitting.

                                    

OBJECTIVES

  1. To examine the minor energy head losses ( i.e shock losses ) for :

  1. 900 elbow bend
  2. 900mitre bend
  3. 900 large radius bend
                        
    To verify that hshock= Dh

    Dh = k v2
    2g

  1. To show that the shock losses due to a sudden contraction are also proportional to the velocity head and to calculate the coefficient of contraction

HL =kv2= (1/Cc- 1)2 v2

           2g                    2g



whereCc = coefficient of contraction.



  1. To confirm the Borda-Carnot equation for hea6+d loss in a sudden expansion from experimental results.

                                                     HL = (v1- v2)2

                                                                 2g

PROCEDURES

  • The pump was started and both the bench supply valve and apparatus control valve were opened. The water was allowed to flow for two to three minutes.

  • Then the apparatus control valve was partially closed.
  • The manometer was purged using the vent valve.
  • Then the apparatus control valve was closed.
  • The air was pumped into the manometer to obtain zero pressure difference in the piezometer tubes at the convenient level.
  • At least seven readings for Q (discharge) and Hdiff(pressure head difference) were required, (Hdiff), being reduced in equal decrements.




DATA COLLECTION

                                 

Pipe system:Piezometric Head Losses at various Rates of flow



Pipe diameter D1 = 22.5mm             Pipe diameter D2 = 29.6mm





Volume
(L)
Time
(sec)
Mitre bend
Hdiff
1-2
(m)
Elbow Bend Hdiff
3-4
(m)
Sudden enlargement
Hdiff
5-6
(m)
Sudden contraction
Hdiff
7-8
(m)
Large radius bend Hdiff9-10
(m)
5
9.12
0.160
0.110
0.040
0.110
0.060
5
13.25
0.130
0.090
0.030
0.090
0.050
5
14.33
0.110
0.080
0.030
0.070
0.040
5
15.46
0.090
0.070
0.020
0.060
0.030
5
17.16
0.005
0.040
0.010
0.035
0.020
5
23.09
0.004
0.030
0.010
0.025
0.015

















Pipe system:Piezometric Head Losses at various Rates of flow



Pipe diameter D1 = 22.5mm             Pipe diameter D2 = 29.6mm

                       A1 = 3.98×10-4m2                             A2 = 6.88×10-4m2



Discharge
Q
×10-4
(m3/sec)
Velocity in D1 pipe
V (m/sec)
Velocity Head
V2
2g
(m)
Pressure Change
0.034V2
(m)
Sudden Enlargement
Hshock=
0.034V2 - Hdiff
(m)
Sudden Contraction
Hshock=
Hdiff  - 0.034V2
(m)
5.482
1.379
0.097
0.065
0.025
0.045
3.774
0.949
0.046
0.031
0.001
0.059
3.489
0.877
0.039
0.026
-0.004
0.044
3.234
0.813
0.034
0.022
0.002
0.038
2.914
0.733
0.027
0.018
0.008
0.017
2.165
0.544
0.015
0.001
-0.009
0.024





GRAPHS AND ANALYSIS FROM THE GRAPHS

For 900mitre bend












The value of k for mitrebend is 2.0661











For 900 elbow bend;






The value ofk for elbow bend is 1.5024













For900 large radius bend






The value of k for large radius bend is 0.7967










The value of k for large sudden enlargement is 0.1035










The value of k for large sudden contraction is 0.7793



The graph which shows the shock losses due sudden contraction are also proportional to the velocity head and to calculate the coefficient of contraction.



From the graph 

HL = K v2 = (1/Cc- 1)2v2

          2g                     2g

             (1/Cc- 1)2  = 0.7793

 1 – 1 =0.8828

 Cc

Cc = 0.531

The coefficient of contraction,Cc is 0.531



ANALYSIS AND CALCULATIONS

Given;              

D1 = 22.5mm

D2 = 29.6mm

A1 = 3.98×10-4m2

A2 = 6.88×10-4m2



Q =volume(m3)

time(s)



Q = 5×10-3m3  = 5.482×10-4m3/s

          9.12(sec)

The same for rest of volume and time and results were recorded as shown in the table.



Velocity

                Q =A1×V1

V = Q /A1



V = 5.482×10-4m3/s  = 1.377m/s

        3.98×10-4m2

The same procedure were repeated and tabulated



Velocity head  =V2     Given   g =9.81m/s2

                           2g

=  (1.377m/s)2

2×9.81m/s2

Velocity head = 0.0702m

For each value of velocity,velocity head was determined.



Hshock in sudden enlargement



Hshock = 0.034V2 - Hdiff



Hshock = 0.034×1.3772 – 0.04 = 0.024m

The same was repeated for each value of velocity and Hdiff and the results were recorded.





Hshock in sudden contraction



Hshock= Hdiff -0.034V2



           = 0.045m

For each value of velocity and Hdiff,shock value was determined and tabulated.



To confirm the Borda –Carnot equation for head loss in sudden expansion from experimental results



                                                                HL = (V1 – V2)2

                                                                             2g

    From continuity equation



V2 =A1V1

          A2

                               hL = (V1-{ A1V1/A2})2

                                                2g



hL= (1 - A1/A2)2V12

              2g

hL=kV2

       2g

But A2 = 688.1mm2, A1 = 398.mm2

k= (1 – (398mm2/688.1mm2)) 2

The theoretical value of k is 0.178



From the graph the value of k is 0.1035



The value of k obtained from Borda – Carnot equation and that obtained from graph varies greatly due to error which was previously made by neglecting of frictional losses in the pipe. Since Head losses the pipe is caused by friction which is the major loss and suddenly enlargement and contraction which are the minor loss.



SOURCES OF ERRORS

  • Parallax
  • Fluctuation of liquid level in manometer
  • Timing error while recording the quantity of discharge
  • Approximately of value in calculation


                   
    CONCLUSION
    Generally change in direction of fluid flow have always brought loss, but the loss brought about by the bends varies from high head loss in sharply bend to minimum losses in slightly bent pipes.The loss is highly brought about by the reaction which is exerted by water flowing at the bend.

    Also verification of Borda-Carnot equation has proved some failure since the value are neither close nor the same. This was caused by assuming that losses due to friction were not present in the pipes.





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