Snapshot 1: oil in a smooth pipe in laminar flow

Snapshot 2: water in a smooth pipe in turbulent flow

Snapshot 3: water in a rough pipe in turbulent flow

Snapshot 4: concentrated dextrin solution in a smooth pipe in turbulent flow

This Demonstration calculates the pressure of a liquid in a pipe,

(in kPa), as a function of its volumetric flow rate,

(in

/min), the pipe's diameter,

(in cm), length,

(in m), and degree of roughness,

(dimensionless), and the liquid's density,

(in kg/

), and viscosity,

(in Pa s). It also calculates and displays the liquid's mass flow rate,

(in kg/s), the Reynolds number,

(dimensionless), and the friction factor,

(dimensionless).

A Reynolds number of less than 2100 implies laminar flow, in which case, according to the Hagen–Poiseuille equation,

*.* A Reynolds number greater than 4000 implies turbulent flow, for which there are different ways to estimate the friction factor,

. The one used in this Demonstration, commensurate with the Moody diagram in the cited references, is based on the numerical solution of the equation

*.*A transition from laminar to turbulent flow or vice versa occurs when

, in which case the use of either equation should be done with caution. This region is shaded in pink on the

versus

plot.

The displayed plot type is chosen with one of the following setters:

vs.

(the Moody diagram),

versus

,

versus

, or

versus

. Use the sliders to enter the current values of the parameters

,

,

,

,

, and

. The conditions corresponding to the current settings of the parameters are marked as colored dots on the plots. The numerical values of

,

,

, and

are displayed in a box above each plot.

Note that the pipe's roughness only affects the friction factor in the turbulent regime.

To apply the Demonstration to pipe lengths greater than 100 m, simply scale a smaller result.

D. W. Green and R. H. Perry,

*Perry's Chemical Engineer's Handbook*, New York, NY: McGraw–Hill, 2008.

C. J. Geankoplis,

*Transport Processes and Unit Operations*, 2nd ed., Boston: Allyn and Bacon, 1983.