Fluid flow student handout material engineers Mopco Course

Fluid Flow

The transfer of fluids through piping and equipment is accompanied by friction and may result in changes in pressure, velocity, and elevation. These effects require input of energy to maintain flow at desired rates. In this chapter, the concepts and theory of fluid mechanics bearing on these topics will be reviewed briefly.

Properties

Pressure

When a uniform pressure p acts on a flat plate of area A and a force F pushes the plate, then

p = F/AThe unit of pressure is the pascal (Pa), but it is also expressed in bars or meters of water column (mH,O).' The conversion table of pressure units is given in Table 1. In addition, in some cases atmospheric pressure is used:

Table 1 Conversion of pressure units

Absolute pressure and gauge pressure

There are two methods used to express the pressure: one is based on the perfect vacuum and the other on the atmospheric

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pressure. The former is called the absolute pressure and the latter is called the gauge pressure.

Then,

In gauge pressure, a pressure under 1 atmospheric pressure is expressed as a negative pressure. This relation is shown in Fig.1. Most gauges are constructed to indicate the gauge pressure.

Fig. 3 Absolute pressure and gauge pressure

Vacuum

The term vacuum is used to express pressures less than atmospheric pressure (sometimes represented as a negative psi on pressure gauges).

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DensityDensity is defined as the mass of the substance per unit of volume. The density of a gas changes according to the pressure and temperature, but that of a liquid may be considered unchangeable in general. The density of air in summer is less than the density in winter. This explains the need to more power of compressors in summer than in winter to compress the same amount of air. Also the density of air on mountain is less than the density of air at the sea level.

The ratio of the density of a material ρ to the density of water ρw , is called the specific gravity

Viscosity

Similar to the presence of frictional force between two solid contacting surfaces, there is a certain amount of shear force between two adjacent layers of fluids. This shear or viscous force affects the fluid flow characteristics significantly. The viscous force was found to depend on the viscous nature of the fluid. It becomes important to understand the viscous property of a fluid and how it affects the magnitude of the viscous force.

When fluid flows inside a pipe, the layer of fluid nearest to the wall of the pipe does not move relative to the pipe. The next layer above this infinitesimal layer moves slightly to the right relative to the bottom layer. As the layers approach the center of the pipe, it gains more and more velocity. This is shown in Fig. 2.

fluid layer with the maximum velocity

fluid layer with zero velocity

axis of pipe

pipe wall

Fig. 2 Velocity distribution among various fluid layers

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The coefficients of viscosity of liquids vary greatly with temperature. Raising the temperature of a liquid decreases the viscosity.

A velocity profile is created radially across the fluid as shown in Fig. 3. The velocity of the fluid layers ranges from zero at the wall to a maximum flow velocity at the axis of the pipe.

v = 0

maximum velocity

δ

Fig. 3 Velocity profile of fluid inside a pipe

The viscosity of gases varies with temperature just in the opposite way, that is, increasing the temperature increases the viscosity. It becomes meaningless to state viscosity of a liquid or a gas without specifying the temperature.

ENERGY BALANCE OF A FLOWING FLUID

The energy terms associated with the flow of a fluid are

1. Elevation potential (g/gc)z,2. Kinetic energy, u2/2gc,3. Internal energy, U,4. Work done in crossing the boundary, PV,5. Work transfer across the boundary, W6. Heat transfer across the boundary, Q.

Figure 4 represents the two limiting kinds of regions over which energy balances are of interest: one with uniform conditions throughout (completely mixed), or one in plug flow in which gradients are present. With single inlet and outlet streams of a uniform region, the change in internal energy within the boundary is

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Fignre 4 Energy balances on fluids in completely mixed and plug flow vessels. (a) Energy balance on a bounded space with uniform

conditions throughout, with differential flow quantities dm, and dm,. (b) Differential energy balance on a fluid in plug flow in a tube

of unit cross section.

Pressure drop

Velocities in pipe lines are limited in practice because of

1. The occurrence of erosion.2. Economic balance between cost of piping and equipment and the cost of power loss because of friction which increases sharply with velocity.

Although erosion is not serious in some cases at velocities as high as 10-15 ft/sec, conservative practice in the absence of specific knowledge limits velocities to 5-6 ft/sec.

Economic optimum design of piping will be touched on later, but the rules of Table 2 of typical linear velocities and pressure drops provide a rough guide for many situations.

The correlations of friction in lines that will be presented are for new and clean pipes. Usually a factor of safety of 20-40% is advisable because pitting or deposits may develop over the years.

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There are no recommended fouling factors for friction as there are for heat transfer, but instances are known of pressure drops to double in water lines over a period of 10 years or so.

In lines of circular cross section, the pressure drop is represented by

TABLE 2 Typical Pressure Drops in Pipelines

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TABLE 2 (Continued) Typical Pressure Drops in Pipelines

TABLE 3 Typical Velocities in Pipelines

For other shapes and annular spaces, D is replaced by the hydraulic diameter

For an annular space, Dh = D1 – D2

Fittings and valves

Friction due to fittings, valves and other disturbances of flow in pipe lines is accounted for by the concepts of either their equivalent lengths of pipe or multiples of the velocity head. Accordingly, the pressure drop equation assumes either of the forms

Values of coefficients K and, equivalent lengths Li are given in Tables 4 and 5

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Orifices

In pipe lines, orifices are used primarily for measuring flow rates but sometimes as mixing devices. The volumetric flow rate through a thin plate orifice is

TABLE 4 Equivalent Lengths of Pipe Fittings

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TABLE 5 Velocity Head Factors of Pipe Fittings

POWER REQUIREMENTS

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A convenient formula in common engineering units for power consumption in the transfer of liquids is

For example, with 500 gpm, a pressure difference of 75 psi, pump efficiency of 0.7, and driver efficiency of 0.9, the power requirement is 32.9 HP or 24.5 kw.

Flow through nozzles and diffusers

A nozzle is a variable-area passage that accelerates fluid from low speed to high speed. It transforms thermal energy into kinetic energy. Nozzles are one of the more common fluid flow devices. They are used in turbines, gas turbine engines, and wind tunnels.

A diffuser is a component of a fluid flow system designed to reduce the flow velocity and thereby increase the fluid pressure.

All turbo-machines and many other flow systems incorporate a diffuser the duct following the impeller of a centrifugal compressor

Parameters affecting the mass flow rate

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The volume flow rate is the volume of fluid flowing past a pipe section in one second.The mass flow rate is the amount of fluid flowing past a pipe section in one second

Mass flow rate of gases depends on:

1- Temperature of the gas2- Pressure of the gas3- Flow area4- Flow velocity

While Mass flow rate of liquids depends on

1- Liquid density 2- Flow area3- Flow velocity

Water hammer

Water is slightly compressible. Because of this characteristic, shock waves can occur and propagate through confined water systems. Shock waves in pipe systems can result from sudden changes in flow such as:

• rapid opening or closing of control valves;• starting and stopping of pumps;• the recombination of water after water column separation; or• the rapid exhaustion of all air from the system

When sudden changes in flow occur, the energy associated with the flowing water is suddenly transformed into pressure at that location. This excess pressure is known as surge pressure and is greater with large changes in velocity. Characteristics of the pipe such as the materials used in construction, the wall thickness, and the temperature of the pipe all affect the elastic properties of the pipe and how it will respond to surge pressures.

Steam distribution systems may also be vulnerable to a situation similar to water hammer, known as steam hammer.

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In a steam system, water hammer most often occurs when some of the steam condenses into water in a horizontal section of the steam piping.

How to minimize the effects of water hammer on a system

To help minimize surge pressures the maximum velocity of water in the pipeline should be limited

Entrapped air in a pipeline can cause problems. Air is very compressible and can compress and expand in the pipeline, resulting in varying velocity conditions, and, thus, significant pressure variations. Water-column separation can also produce significant surge pressures due to the high velocities encountered when the column rejoins.

Problems associated with air entrapment can be minimized by preventing air from accumulating in the system. This can be accomplished by using air-relief valves positioned at the high points of the piping system. In areas of relatively flat terrain these should also be used in the vicinity of the pump discharge, near the middle of the line, and at the downstream end of the line.

Additional design considerations include:

• surge arrestors (devices such as small pressure tanks which can absorb shock waves) or automatic pressure reducing valves at flow regulators and at the pump discharge;

• flow controllers used to minimize the rate of filling and to reduce start-up surge in filled lines;

• in cycling systems, design pipelines, if possible, to keep out all air, and then to restart with a filled system

Water hammer cannot be completely eliminated in an economical design, but, by taking precautions during management and operation, the effects can be minimized. Start-up is critical, especially when pipe lines are empty. Empty lines should be filled as slowly as possible to allow entrapped air to escape. In addition the following cautions should be observed:

• Open all manual valves except at the pump discharge. The pump discharge valve should be opened slowly to allow slow filling of the pipe line. Caution should be observed when filling is interrupted and restarted because a quick surge may develop

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during the restart which could slam into a stationary or slow moving body of water. This situation could result in damaging water hammer pressures, especially if air becomes entrapped between the water fronts. Therefore, follow the same precautions on restart as during initial starting of the system.

• Make sure that all air has been discharged from the system before operating the system at full throttle.

• Close all manual valves slowly. No valve should ever be closed in less than 10 seconds; 30 seconds or more is preferable.

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