Pipe Fitting Losses

Pipework fittings such as bends, tees, reducers etc., cause pressure loss or resistance in a heating system.

When making approximate calculations 10%, 15%, 20% or more may be added to the pressure loss in straight pipe runs.

For accurate calculations the fitting loss should be determined separately for each fitting, as outlined below.

The concept of equivalent length is used and is defined as the length of straight pipe which would give a friction pressure loss equivalent to one velocity head.

The D’Arcy equation is;

H         =          4  .  f  .  l  . v2            /          2  . g  .  d

Where;            H = head loss due to friction in a straight pipe (m)

                        f = friction coefficient

                        l = length of pipe (m)

                        d = diameter (m)

                        v = velocity of fluid (m/s)

                        g = acceleration due to gravity (m/s2)

The D’Arcy equation can be rewritten for pressure instead of head.

Pressure drop (dpl)          =          ( 4 .  f  . l ) / d     x      ( v2  .  r  .  g ) / 2 . g

Where;            dpl       =          Pressure loss in a pipe section (Pa)

f           =          friction coefficient for pipe

                                    l           =          length of pipe (m)

                                    d          =          diameter of pipe (m)

                                    v          =          water velocity (m/s)

                                    r           =          density of water (kg/m3)

                                    g          =          acceleration due to gravity (m/s2)

 

To simplify the above equation we get;

Pressure drop (dpl)          =          ( 4 .  f  . l ) / d     x      ( v2  .  r ) / 2

or;       Pressure drop (dpl)          =          ( 4 .  f  . l ) / d     x     ( ˝  .  r  .  v2 )

For the friction pressure loss to equal one velocity head;

Velocity pressure               =          ( ˝  .  r  .  v2 )

Then                  1.0               =          ( 4 .  f  . l ) / d    

The length (l) is now called equivalent length (le) and by rearranging the above formula we get;

1.0 x d         =       4 .  f  . le

le       =       d  /  4 .f

 

Values of equivalent length are given in the FLOW of WATER in PIPES TABLE for water at 75oC, see CIBSE guide C (2001) section 4 , Flow of  Fluids in Pipes and Ducts, Tables 4.9 to 4.33 for various types of pipes.

These values should be corrected for each particular type of fitting.

The correction factors of Velocity pressure loss factors are called z(Zeta) factors.

The resistance in a fitting is converted to equivalent straight lengths of pipe, e.g. a bend may have a resistance equivalent to 1.2 metres of straight pipe.

The Total Equivalent Length of a Fitting    =    Equivalent Length    x    Pressure Loss factor z(Zeta).

Total Equivalent Length of a Fitting (T.E.L.) (m)     =    (le)   x    z (Zeta factor).

See CIBSE guide C (2007) section 4.4.1 and section 4.10 for more details of fittings zeta factors.

Examples Of z Zeta Factors

The following are some examples of pressure loss (z zeta) factors for pipe fittings:

Some Pipe Cross Sectional Areas

Area  =   p .d2  /4

Area (28mm)  =  p .0.0282  / 4  =  0.0006158 m2.

Area (22mm)  =  p .0.0222  / 4  =  0.0003801 m2.

Area (15mm)  =  p .0.0152  / 4  =  0.0001767 m2.

Some Ratios of Pipe Areas

For 22mm x 15mm reduction

The ratio of area A2/A1  =  0.0001767   /  0.0003801      =   0.465.    

Therefore for reduction z = 0.35 approximately from the above table.

For 28mm x 22mm reduction

The ratio of area A2/A1  =  0.0003801   /   0.0006158   =   0.617.

Therefore for reduction z = 0.25 approximately from the above table.