ANALYSIS OF FLOW IN PIPES

 

-􀂙Flows completely bounded by solid  

 surfaces are called INTERNAL

-FLOWS which include flows through  pipes (Round cross section),

 ducts (NOT Round cross section),  nozzles,  diffusers, sudden contractions  and  expansions, valves, and fittings.

􀂙-The basic principles involved are    independent of the cross-sectional

 shape, although the details of the flow  may be dependent on it.

􀂙-The flow regime (laminar or turbulent) of  internal flows is primarily

 a function of the Reynolds number.

-Laminar flow: Can be solved analytically.

-Turbulent flow: Rely Heavily on semi-  empirical theories and

 experimental data.

 

 

PIPE SYSTEM

 

-A pipe system include the pipes themselves (perhaps of more than one diameter), the various

 fittings, the flowrate control devices valves) , and the pumps or turbines.

                        

 

LAMINAR OR TARBULENT FLOWS

 

 

• The flow of a fluid in a pipe may be Laminar ?

     Turbulent ?

• Osborne Reynolds, a British scientist and mathematician, was the first to distinguish the difference between thes classification of flow by using a simple apparatus as shown.

 

LAMINAR FLOWS

 

 

There are numerous ways to derive important results pertaining to fully developed laminar   flow:

-From F=ma applied directly to a fluid        element.

-From the Navier-Stokes equations of  motion

-From dimensional analysis method.

-Laminar flow can be thought of as very  

 small   but finite sized

 fluid particles flowing smoothly in layer,  one over

  another.

-The only randomness and mixing take  place on the molecular scale and result  in  relatively small heat,

 mass, and momentum transfer rates.

 

 

TURBULENT FLOWS

 

 

• Turbulent pipe flow is actually more likely to occur than laminar flow in practical situations.

• Turbulent flow is a very complex process.

• Numerous persons have devoted considerable effort in an attempting to understand the variety of baffling aspects of turbulence. Although a considerable amount if knowledge

      about the topics has been    

      developed, the field of turbulent flow         still remains the least understood area       of fluid mechanics.

• Turbulent flows involve randomly fluctuating

      parameters.

• The character of many of the important properties of the flow (pressure drop, heat transfer, etc.) depends strongly the turbulent fluctuations or randomness.

• Laminar: pressure drop in pipe, aerodynamic drag on airplane.