Pipeflow / Pumps / Turbines        (continued)

 

Turbulent Flow through single pipes  (Start with the energy equation.)

 

In general between sections of a pipe     Energy In + Net Work Rate = Energy Out + Loss

 

Consider sections one and two with two being downstream of one.  Express this energy

equation in terms of head (ft or m).  Assume  steady, viscous, incompressible, uniform flow.

 

       P1/γ  +  V12/2g  +  z1  + net work rate in head loss  =  P2/γ  +  V22/2g  +  z2  + head loss

or

       P1/γ  +  V12/2g  +  z1  +  dW/dt)/Qγ  =  P2/γ  +  V22/2g  +  z2  + HL

 

where  P1 and P2    =  the static pressures at sections 1 and 2  (lb/ft2, N/m2)

                         γ   =  specific weight of fluid (lb/ft3 or N/m3)

           V1 and V2   =  the fluid velocities at sections 1 and 2   (ft/sec, m/sec)

                        g   =  acceleration of gravity  (32.2 ft/sec2,  9.8 m/sec2)

           z1  and  z1   =  elevations at stations 1 and 2

                  dW/dt  =  net work rate in  (ftlb/sec, Nm/sec)      + for pump and – for turbine

                         Q  =  flowrate  (ft3/sec, m3/sec)

Note:              Qγ  =  mass flowrate  (slugs/sec, Kg/sec)

                       HL  =  f L/D (V2/2g)

                          f  =  friction factor;  f depends on the Reynolds number and the

                               relative roughness of the pipe using the Moody Chart  (figure below)

                        L  =  length of pipe between sections 1 and 2    (ft, m)

                       D  = diameter of the pipe (ft, m)

                       V  = fluid velocity in pipe between sections 1 and 2  (ft/sec, m/sec)

                                                        The Moody Diagram (below)

 

                                          

 

Click here to continue discussion.

 


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