Pressure drop in a pipe

The frictional pressure drop per unit length of smooth pipe, Apt/1, is expected to be a function of the pipe diameter d, mean flow velocity ft across the cross-section and fluid density p and viscosity p (neglects end effects, i.e. I d). Thus, 

These five variables (considering Apflas a single variable), m = 5, may be expressed in terms of n = 3 fundamental dimensions, i.e. mass, length and time. Using Buckingham s n theorem, these five variables may be rearranged into m — n = 5 — 3 = 2 new dimensionless variables  

Note for different flow situations, the Reynolds number may take different forms. See Chapter 3, Concepts of Fluid Flow for a discussion of the role of Reynolds number. 

1 Problem. Methanol at 50°C flows at a mean velocity of 2 m s 1 through a smooth pipe of 25 mm internal diameter and 12 m length. Calculate the frictional pressure drop. 

2 Solution. The solution to this problem is given in Table 3. 

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The pressure drop in a pipe, due to friction, is a function of the fluid flow-rate, fluid density and viscosity, pipe diameter, pipe surface roughness and the length of the pipe. It can be calculated using the following equation ... 

For heterogeneous flow, one approach to determining the pressure drop in a pipe is... 

The extrusion pressure could be further modulated by choice of dies or screens with appropriate L/D ratios. The pressure differential between points of die entry and exit due to viscosity for a Newtonian material moving within a cylinder is represented by Equation (4), derived from the Hagen-Poisuille expression for pressure drop in a pipe of constant diameter as (41)... 

This section illustrates the use of material presented earlier to determine the pressure drop in a pipe system, mating of a pump to the pipe system and the head loss over a control valve. 

Table 3 Solution, pressure drop in a pipe problem...

Figure 8-3 illustrates the friction frictor versus GRe relationship for power law fluids under laminar flow conditions. It can also be used for Newtonian fluids in laminar flow with the Reynolds number being used in place of GRe. In fact, the Newtonian/ versus Re relationship was established much earlier than extension to non-Newtonian fluids. Once the magnitude of the friction factor is known, the pressure drop in a pipe can be estimated from Equation 12. 

C THIS PROGRAM CALCULATES PRESSURE DROP IN A PIPE INCLUDING ... 

For example, if you have a pressure drop in a pipe of 16 psi, and the conversion factor 1 psi = 6.895 kPa, your calculator will give 16 x 6.895 = 110.32. However, your answer should be 110 kPa because your starting value was only given to a precision of two figures. The conversion factor cannot add accuracy ... 

Extent of reaction specified Two-phase, chemical equilibrium Multiphase, chemical equilibrium Continuous-stirred tank reactor Plug-flow tubular reactor Pump or hydraulic turbine Compressor or turbine Pressure drop in a pipe Stream multiplier Stream duplicator... 

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