When a fluid moves through a pipe two distinct types of flow are possible, laminar and turbulent. Laminar flow occurs in fluids moving with small average velocities and turbulent flow becomes apparent as the velocity is increased above a critical velocity. In laminar flow the fluid particles move along the length of the pipe in a very orderly fashion, with little or no sideways motion across the width of the pipe.
Turbulent flow is characterised by random, disorganised motion of the particles, from side to side across the pipe as well as along its length. There will, however, always be a layer of laminar flow at the pipe wall - the so-called 'boundary layer'. The two types of fluid flow are described by different sets of equations. In general, for most practical situations, the flow will be turbulent.
The properties relevant to fluid flow are summarized below.
Density: This is the mass per unit volume of the fluid and is generally measured in kg/m3. Another commonly used term is specific gravity. This is in fact a relative density, comparing the density of a fluid at a given temperature to that of water at the same temperature.
Viscosity: This describes the ease with which a fluid flows. A substance like treacle has a high viscosity, while water has a much lower value. Gases, such as air, have a still lower viscosity. The viscosity of a fluid can be described in two ways.
• Absolute (or dynamic) viscosity: This is a measure of a fluid's resistance to internal deformation. It is expressed in Pascal seconds (Pa s) or Newton seconds per square metre (Ns/m2 ). [1Pas = 1 Ns/m2 ]
• Kinematic viscosity: This is the ratio of the absolute viscosity to the density and is measured in metres squared per second (m2 /s).
Reynolds Number: A useful factor in determining which type of flow is involved is the Reynolds number. This is the ratio of the dynamic forces of mass flow to the shear resistance due to fluid viscosity and is given by the following formula. In general for a fluid like water when the Reynolds number is less than 2000 the flow is laminar. The flow is turbulent for Reynolds numbers above 4000. In between these two values (2000<Re<4000) the flow is a mixture of the two types and it is difficult to predict the behavior of the fluid.
Re= ρ × u×d / 1000 ×µ
Where: ρ = Density (kg/m3 )
u = Mean velocity in the pipe (m/s)
d = Internal pipe diameter (mm)
µ = Dynamic viscosity (Pa s)
Pressure Loss in Pipes
Whenever fluid flows in a pipe there will be some loss of pressure due to several factors:
a) Friction: This is affected by the roughness of the inside surface of the pipe, the pipe diameter, and the physical properties of the fluid.
b) Changes in size and shape or direction of flow
a) Obstructions: For normal, cylindrical straight pipes the major cause of pressure loss will be friction. Pressure loss in a fitting or valve is greater than in a straight pipe. When fluid flows in a straight pipe the flow pattern will be the same through out the pipe. In a valve or fitting changes in the flow pattern due to factors (b) and (c) will cause extra pressure drops. Pressure drops can be measured in a number of ways. The SI unit of pressure is the Pascal. However pressure is often measured in bar.
This is illustrated by the D’Arcy equation:
hf = fLu^2 / 2gd
L = Length (m)
u = Flow velocity (m/s)
g = Gravitational constant (9.81 m/s²)
d = Pipe inside diameter (m)
hf = Head loss to friction (m)
f = Friction factor (dimensionless)
Before the pipe losses can be established, the friction factor must be calculated. The friction factor will be dependant on the pipe size, inner roughness of the pipe, flow velocity and fluid viscosity. The flow condition, whether ‘Turbulent’ or not, will determine the method used to calculate the friction factor.
Standard Pipe dimensions
There are a number of piping standards in existence around the world, but arguably the most global are those derived by the American Petroleum Institute (API), where pipes are categorised in schedule numbers. These schedule numbers bear a relation to the pressure rating of the piping. There are eleven Schedules ranging from the lowest at 5 through 10, 20, 30, 40, 60, 80, 100, 120, 140 to schedule No. 160. For nominal size piping 150 mm and smaller, Schedule 40 (sometimes called ‘standard weight’) is the lightest that would be specified for water, compressed air and steam applications. High-pressure compressed air will have schedule 80 piping. Regardless of schedule number, pipes of a particular size all have the same outside diameter (not withstanding manufacturing tolerances). As the schedule number increases, the wall thickness increases, and the actual bore is reduced. For example:
• A 100 mm Schedule 40 pipe has an outside diameter of 114.30 mm, a wall thickness of 6.02 mm, giving a bore of 102.26 mm.
• A 100 mm Schedule 80 pipe has an outside diameter of 114.30 mm, a wall thickness of 8.56 mm, giving a bore of 97.18 mm.
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