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 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

H_L =K_L V²

          2g

In which K_Lis known as the loss coefficient. For a geometry,the value ifK_L 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 h_shock= 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

H_L =kv²= (1/C_c- 1)² v²

           2g                    2g

whereC_c = coefficient of contraction.

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

                                                     H_L = (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 H_diff(pressure head difference) were required, (H_diff), 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 

H_L = K v² = (1/C_c- 1)²v²

          2g                     2g

             (1/C_c- 1)²  = 0.7793

 1 – 1 =0.8828

 C_c

C_c = 0.531

The coefficient of contraction,C_c 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.

H_shock in sudden enlargement

H_shock = 0.034V² - H_diff

H_shock = 0.034×1.377² – 0.04 = 0.024m

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

H_shock in sudden contraction

H_shock= H_{diff -}0.034V²

           = 0.045m

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

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

                                                                H_L = (V₁ – V₂)²

                                                                             2g

    From continuity equation

V₂ =A₁V₁

          A₂

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

                                                2g

h_L= (1 - A₁/A₂)²V₁²

              2g

h_L=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.