# Pressure drop and velocity relationship with acceleration

1 Piping design; 2 Bernoulli equation; 3 Reynolds number and Moody friction factor; 4 Pressure drop for liquid flow Two phase pressure drop; Simplified friction pressure drop The desired mass-flow rate (or volume) of the fluid to be transported. . g, = acceleration of gravity, ft/sec2. The relationship between velocity and pressure for incompressible flow This means that an increase in velocity causes a decrease in static pressure. . This form refers to the unit mass and v is the speed, g the acceleration of gravity, z the . The pressure difference in the initial (1) and end (2) reference flow cross sections is difference and friction loss are low in relation to the dynamic head the static pressure drops, Δp > 0, as a result of fluid acceleration, (uB2 > uB1); in the are valid, where Ma = u/usound is the Mach number, is the local velocity of sound.

If the flow is laminar and Reynolds number is smaller thanthe friction factor may be determined from the equation: Since the internal pipe roughness is actually independent of pipe diameter, pipes with smaller pipe diameter will have higher relative roughness than pipes with bigger diameter and therefore pipes with smaller diameters will have higher friction factors than pipes with bigger diameters of the same material. Most widely accepted and used data for friction factor in Darcy formula is the Moody diagram.

On Moody diagram friction factor can be determined based on the value of Reynolds number and relative roughness. The pressure drop is the function of internal diameter with the fifth power.

### Fluid dynamics and Bernoulli's equation

With time in service, the interior of the pipe becomes encrusted with dirt, scale and it is often prudent to make allowance for expected diameter changes. Also roughness may be expected to increase with use due to corrosion or incrustation at a rate determined by the pipe material and nature of the fluid. Static, dynamic and total pressure, flow velocity and Mach number Static pressure is pressure of fluid in flow stream.

Total pressure is pressure of fluid when it is brought to rest, i. Total pressure can be calculated using Bernoulli theorem. For the calculation of friction factor in a single-phase https: This phenomenon attributes the fact that particles may break the boundary Where, Re is the Reynolds number. It means pressure drop in acceleration zone cannot system is divided into different sub categories. It should modify and make more gravity effect was considered to be negligible .

In such type of con- appropriate with additional work using other materials and wide veying, particles feed into the gas stream at zero or at particular ve- range of operating conditions .

## Pressure drop evaluation along pipelines

Feeding velocity of particles depends upon the feeder type Marcus et al. Feeding of particles Eq. He used his correlation to in momentum. In addition, requirement of pressure increases monotonically state pressure drop . When particles start to feed Tomita and Tashiro conveyed three different spherical particles of into the stream, momentum transfers from the gas to the particles. Particles start to accelerate unless they attain aver- the applicability of this correlation is quite small due to lack of operating age steady state velocity that region is the acceleration zone and its condition information.

Duckworth proposed a model Eq. Detail about experimen- drop. Hence, it limits us to sure distribution along the acceleration zone. Two zones are responsible propose the applicability of the correlation . His conveying pipeline design. First zone is right after feeding of particles into the was similar to single particle conveying not as bulk material. Second zone is accel- posed pressure drop correlation Eq.

### Pressure Drop, Single-Phase

Friction factor model used in his celeration has opened new avenues to understand the behavior of correlation was developed based on the study of Weber  and Neto pneumatically conveyed particles. An accurate estimation of the accel- and Pinho . In analysis, basic equation of momentum change have developed for spherical particles with very narrow range of parti- Eq.

Pinho has quite different conveying criteria from rest of the pressure drop infatuated with it.

Pressure and velocity in pipes

Limited parameter in conveying criteria stimulate us to in- vestigate the pressure drop in acceleration zone. However, there is no apparent consensus on Many researchers have claimed that prediction of acceleration any integrative pilot-testing model for acceleration pressure drop of di- pressure drop in acceleration zone using momentum change equation lute phase pneumatic conveying.

It was not found in any of the literature, for particles does not completely account for experimental results which claimed that whether the extrapolation of steady state pressure [11—14]. They considered that the friction and collision pressure drop drop line in acceleration zone is accurate or not. Hence, they have asserted their own correlations drop. The problem is with generalization of classical approach, to ex- to predict acceleration pressure drop.

This prediction changes There are different views for prediction of pressure drop due to ac- with the material property. For this analysis, the prediction of pressure celeration.

A detail of available correlations have summarized in Table 1. Gas is found to be It will improve the prediction of pressure drop due to collision and fric- nearly isothermal along the pipeline; hence, inlet temperature was tion steady state in the acceleration zone. Hence, the subsequent used all over the pipe length. Relative hu- zone is as follows: Three different kinds of pressure readings were obtained.

Those are mounted on riders as per instructions of user manual 2. Experimental setup to ensure accuracy of readings and of the pressure values and for avoiding additional problems common to pressure tapping in pneumat- Tests have been conducted to evaluate acceleration pressure drop in ic conveying Fig.

Connection of pressure transducer on main con- an experimental setup, which was on In the mixing chamber, a venturi tube was pressure. Nevertheless, gas expansion along the pipe might be substan- mounted followed by an air pressure regulator. Upon returning from tial and deviation of gas density from standard value due to local baro- the conveying pipeline, a bag house separator was installed at the end metric pressure and ambient temperature cannot be neglected.

Hence, of the pipeline to achieve the separation of the particles from the air. Dis- the pipeline by using local condition of pressure, temperature and hu- tributor, connected at the bottom of the separator allowed the open or midity. For an operating range of — Pa, variation in air density closed loop experiments.

Weighing bin connected with pneumatic was 1. It was found that change of density is not substantial valve was mounted on a load cell used for on-line measurement of the for complete operating range along the pipeline. For each measured data, steady state condition was achieved by tak- Pipeline layout is presented in Fig. In order to avoid any periodical effects caused by and two vertical sections.

There time reading of all instruments has been kept 4 s for each operating are four pressure transducers before the Blind-T P-A, B, C, D and nine point. Experiments pressure transducers and other sensors. All relevant properties and particle size distribution of 46 N. Feeding and separation apparatus. Layout of the Arrangement of pressure transducer on main conveying pipeline.

All these data drop in suspension phase conveying, a comprehensive literature survey points are results of different sets of experiments. Different materials was conducted. More than hundred experiments were conducted in were kept into the feeder in each set of experiments to see the effect order to gather data for our analysis. Further, for same individual air velocities, pressure drops were calculated using 5. Methodology Colebrook equation Eqs. This is an indication to negligible back- pressure transducers and other sensors. Screw feeder has the advantage of uniform de- average value of pressure drop in the acceleration zone.

Adequate design process of any pneumatic conveying system de- zones has no concern of whether particles are being accelerated after pends upon the prediction of pressure drop per unit length. As already feeding or after the bend, because change of momentum should be mentioned, in pneumatic conveying systems, there are two regions the same for a particular velocity change.

In most of Actual pressure drop trend along the acceleration distance is shown the cases use of venturi at feeding point, provides complex particles ac- in Fig. It represents the celeration. However, Blind-T was found to have zero particle velocity at trend of measured pressure drop over the acceleration zone and up to the exit from the bend . In our study, therefore, acceleration pres- the steady state. In addition, as per the common practice, a line from the steady the last bend before the separator having Extrapolation of experimental oretical model under same operating parameters.

Circular pipe has a pressure drop trend is the only possibility to predict the pressure P0 at pipe roughness of 0.

In this for each of the tested materials on pressure vs. Visual effect of Materials for experiments [Scale: