### Viscosity

Viscosity is defined as the quantitative measure of tendency of a fluid to resist the forces of shear or deformation. Meaning, a fluid that can flow easily (e.g. water) has low viscosity, and a fluid that resist to flow (like cold honey, or Dunlop adhesive) is highly viscous.

Reference point for viscosity scale is water at 20°C (68°F), which is equal to 1.0 centipoise. (1 poise = 1gm/cm s). The poise or centipoise is referred to as absolute viscosity.

Other units of viscosity used in the petroleum industries include Kinematics viscosity, expressed in Stokes (or centistokes) and Saybolt. Universal or Saybolt Furol viscosity expressed in seconds. These units are readily converted from one to the other when calculations required their use and values are given in other units.

The viscosity of a fluid depends primarily on temperature and to a lesser degree on pressure. Viscosity of liquids generally decrease with increasing temperature, and gas viscosity normally increase as temperature increase. The effect of pressure on viscosity of a liquid is very small, however, particularly at high pressure, it does effect the viscosity very significantly.

### Density

Density of a substance is defined as its mass per unit volume.

The unit derived from this formula is kg/m3. However, there are other units used, such as pounds per cubic inch, ounces per gallons. Liquids densities change considerably with temperature, but relatively very small with pressure because liquids are considered uncompressible.

For gases and vapours, pressure and temperature affected greatly in their densities. Therefore, in measuring the flow, mass-flow measure is most desired method to use.

### Specific Gravity

Normally called ‘SG’, is the fluid weight (or mass) ratio to a standard one. For liquids (or solids), the standard referral is water (s.g. = 1.0) at 4°C (60°F). For gases and vapours, the standard used is air (s.g. = 1.0) at 4°C (60°F) under atmospheric pressure (14.7 psi).

#### Specific gravity correction of flow

It is necessary to compensate for changes in specific gravity because of temperature. Correction factor, C_{f} is used, multiplied against the D.P. (diff. pressure flowmeter) to provide the compensation. Example;

### Super-compressibility

Liquids are considered incompressible except at high-pressure ranges but it normally not applicable to most liquids flow measurement methods. However, for gases, the compressibility factor should be taken much into consideration in its calculation since the percentage error is remarkably high.

Compressibility Factor is a function of molecular weight, temperature, and pressure. Follow the following;

The Ideal Gas Law (Boyle’s + Charles Laws) ;

Assume at this moment, the gas is at a normal temperature and pressure. The molecules of gas is moving randomly constantly in the container. When pressurised, the molecules have lost the space to move and become more attached to each other. These changes in behaviour of gas is called the Super-compressibility (Z).

The general gas law written to include the Z factor

## Head loss

Head loss occurs after a fluid passed through a restriction of an orifice or venturi, and does not quite return to its original pressure. Hydraulic energy cannot be transferred through pipes without losses.

Friction occurs at the pipe surface and within liquid, which then generates heat. The loss created this way in hydraulic energy actually means that a pressure loss occurs within the system/pipe itself.

### Discharge co-efficient, C, Viscous friction

If we examine a real calibrated flow meter and plot recorded flow, against calculated flow, we find there is a constant difference over the whole flow range.

Note that C will normally be less than 1, the closer value to 1 the more ideal.

Typical values of C are; about 0.6 for an orifice plate, and about 0.99 for a venturi.

### Beta ratio ( β )

It is a ratio between the diameter of orifice bore and the internal diameter of the pipe.

The range of β values is restricted to between 0.2 and up to 0.7 max. for accuracy and linearity in flow measurement.

### Laminar and turbulent fluid flow (Reynolds number)

Laminar referred to an orderly motion of flow where every particle of the fluid moves in parallel to the pipe. However, the fluid flowing close to the wall slows down due to friction and viscosity.

The flow is said to become turbulent when it speeds up even more. The two types can be demonstrated easily by injecting a small jet of coloured water slowly into a clear liquid stream in a transparent pipe.

At low flow rate, the coloured water shows an even and with little diffusion in the surrounding stream. When a similar jet is released in a high velocity stream, the diffusion is almost immediate and uniform across the section.

#### The Reynolds number (Re) tells us if the flow is laminar or turbulent;

- If less than 2000, it is laminar
- If more than 4000, it is turbulent

Reynolds Number is given by;

Therefore, Reynolds number depends on;

i. Velocity of the flow (velocity of the flow ∝ turbulence)

ii. Diameter of the pipe, D

iii. Density, ρ

iv. Viscosity of the liquid, η

### Minimum and Maximum Volumetric Flow (Qmin/Qmax) Calculation

Where ;

- ρ = density in kgm
^{-3} - Q = volumetric flow in m
^{3}/h - d
_{i}= internal diameter of pipe in mm

Credits : N Asyiddin

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