The Fluid Flow Rate And Pressure Drop module is used to compute the flow rate and pressure drop due to fluid flow in a pipe. The pipe cross-section can be circular, annular or rectangular. Laminar or turbulent flow of an incompressible fluid (gas or liquid) can be computed.

This module calculates the flow rate for a prescribed pressure drop across a pipe of selected cross-section and dimensions. Conversely, the module computes pressure drop for a prescribed flow rate. The pipe cross-section can be circular, annular or rectangular.

The pressure drop DP due to the flow of an incompressible fluid (gas or liquid) in a pipe is computed using equation (1):

(1)

where r is fluid density, L is length of pipe and D is diameter. The friction factor f depends on the pipe cross-sectional geometry.

For fully developed laminar flow in a circular cross-section pipe, the friction factor can be computed analytically. The friction factor f is given by equation (2)

(2)

where Re is fluid Reynolds and is computed using equation (3)

(3)

where V is mean fluid velocity and m is fluid viscosity.

For turbulent flow the friction factor can be computed using the well known Colebrook-White correlation [1]. This correlation gives a transcendental equation for f. This requires an iterative solution for f. In the current formulation, an explicit equation for f is used. This equation is generally within 0.5% of the Colebrook-White equation and yields accurate results for most engineering applications.

(4)

where e is equivalent surface roughness height. This is defined as the characteristic height of sand grains which, when glued as closely together as possible on the inside of a pipe produce the same pressure loss per unit pipe spans as a test pipe of the same diameter transporting the same flow.

For laminar flow in noncircular pipes the shape of the pipe cross-section is taken into account. For a rectangular cross-section the friction factor is given by equation (5)

(5)

where a is the longer side of the rectangle and b is the shorter side. The diameter used in the computation of Re is replaced by the hydraulic diameter D_hr as given by equation (6).

(6)

For laminar flow in an annulus the friction factor is given by equation (7).

(7)

where a is outer radius and b is inner radius of the annulus. The diameter used in the computation of Re is replaced by the hydraulic diameter D_ha as given by equation (8).

(8)

For turbulent flow in noncircular cross-sections the diameter in equations (1), (3), and (4) is replaced by the hydraulic diameter for the cross-section.

The fluid flow rate and pressure drop module inputs are depicted in Figure 1. The inputs consist of pipe geometric dimensions, fluid flow properties and flow conditions.

Figure 1: ETBX inputs for Fluid Flow Rate And Pressure Drop module.

Figure 2: ETBX output for Fluid Flow Rate And Pressure Drop module.