Flow of Fluid in Pipes: The nature of the flow in a pipe depends upon the value of the Reynolds number. If Re is less than 2100, then flow is laminar, otherwise flow is turbulent if Re is greater than 4000. The skin frictional loss for flowing fluids is given by
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where f is a Fanning friction factor that depends upon the Reynolds number and relative roughness of the pipe. Reynolds number (Re) is given as
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Friction factor relationship has been plotted in the graphical form in Figure 4.3 (McCabe and Smith, Figure 5-10). It is helpful to merge roughness, ε, and diameter, d, into one parameter, relative roughness RR that is defined as
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It should be noted that Moody's friction factor (4 times Fanning friction factor) is also in use in other fields of engineering.
For laminar flow, friction factor (f) is given by
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And frictional losses are given by Hagen Poiseuille equation:
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Case1: Velocity unknown for given pressure drop.
Assume velocity of the fluid in the pipe (V).
Calculate Reynolds number (Re)
Read friction factor (f) from Figure 4.3
Calculate frictional loss (hf) using Equation 4.12
Determine pressure drop (ΔP) using Bernoulli equation.
Compare calculated pressure drop with the given value.
Repeat the steps till an agreement is achieved.
We recommend that you use the following steps:
Use Bernoulli equation to obtain frictional head (hf)
Calculate the value of a group ReÖf given as
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Read friction factor (f) from Figure 4.4.
Calculate Reynolds number (Re).
Calculate velocity of the fluid (V) using Equation 4.12.
Case 2: Pipe diameter unknown for given flow rate and pressure drop:
Assume a value of friction factor (say 0.005).
Estimate the diameter of the pipe (d) using the following equation.
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Calculate Reynolds number (Re).
Read friction factor using Figure 4.3
Compare the revised and assumed friction factor values
Repeat the steps till convergence for d is achieved.
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