LAB COURSE WORK

Lab Course Work

Lab Course Work

Task 1

In order to have flow in a pipe system, a pressure difference is needed, as fluids flow from a high-pressure point to a low-pressure point. One can identify three components that define this pressure difference:

Hydrostatic pressure loss

Frictional pressure loss

Kinetic pressure loss

For most applications, kinetic losses are minimal and can be ignored. Thus, the equation that describes the overall pressure losses can be expressed as the sum of two terms:

?PT = ?PHH + ?Pf

There are a number of calculation methods used to account for hydrostatic and frictional fluid losses under a variety of flow conditions. The correlations that are included are as follows:

Single-phase flow

Multiphase flow

Single-Phase Flow

Density (Single-Phase)

Density (?) is used in hydrostatic pressure difference calculations. The method for calculating ? depends on whether flow is compressible or incompressible (multiphase or single-phase). It follows that:

For a single-phase liquid, calculating the density is easy, and ? is simply the liquid density.

For a single-phase gas, ? varies with pressure (since gas is compressible), and the calculation must be done sequentially, in small steps, to allow the density to vary with pressure.

During pipe flows, friction results from resistance of the fluid to movement. Friction can be thought as energy that is “lost” or “dissipated” (transformed into non-useful thermal energy) in the system. In single-phase flow scenarios, the frictional component can be found by the general Fanning equation:

This correlation can be used either for single-phase gas or for single-phase liquid pipe flows.

Osborne Reynolds (1842-1912) experimentally investigated the relationship between the pressure drop and flow rate in a pipe. He found that at low rates, the pressure drop was directly proportional to the flow rate. He also observed that as he increased the flow rate, the measured data started to behave erratically. It was only when he used extremely high rates that he was able to reproduce his experimental data again.

After introducing a dye into the flow, Reynolds observed that at low rates of flow, the dye described a smooth flow path (linear) along the pipe. After increasing the flow rate, the dye presented perturbations, and if the rate was increased even further, the dye fluctuated erratically throughout the pipe. He named the smooth (stable) flow 'laminar flow regime' and the disturbed (unstable) flow 'turbulent flow regime'. Reynolds proposed to make use of the dimensionless ratio of inertial to viscous forces (now named after him) as an indication of the transition from flow regimes:

In field units, the Reynolds number can be rewritten as:

Considering the interaction of the fluid with the pipe wall, the friction factor results from the analysis (momentum flux) of the wall shear stress and the kinetic energy per unit volume due to the movement of the fluid inside the pipe:

In other words, the friction factor depends on the fluid properties and flowing conditions in the system.

Task 2

This method can only be used to determine the internal forces in the members of statically determinate pin-jointed trusses. It consists of isolating each joint of the framework in the form of free-body diagram ...