#2 Essay Site on Sitejabber
+44 20 8638 6541
  • 中文 (中国)
  • English GB
  • English AU
  • English US
  • العربية (Arabic)


Student’s name

Course name





1.0 Introduction

Pipeline transit involves the long-distance carriage of gas or liquid oil in the gas and oil sector that occurs in a closed canal. The oil and gas piping criterion remains the most essential component of the contemporary-world energy-delivery unit, hence remaining as among the major prerequisites of oil and gas industries. Considering the fact that pipeline flow in this industry normally occurs in a closed canal, there has been a consequent increase in energy demand thus necessitating the comprehension of the difficulty of pipelining and the bracketing procedures considered in the oil-gas sector (Bansal 2005). Since the oil-gas pipeline flow is integral to the liquid machine plus the hydraulic branch kept within a closed canal, there is no presence of direct atmospheric pressure, however there is sufficient pressure considered in having the fluid pressed down the drain. With the fluid flowing via a 2-different way pipe, the process involves conversion of kinetic gravitational force into kinetic energy, achieved through pipe tilting to decrease the fluid flow (White 2008). The other procedure involves increasing the pressure on one end of the pipeline.

For pipes, pressure difference acts like the pressure of a net, causing the fast flow of the fluid. Bernoulli’s principle may thus be applied to the flow where there is a constant fluid flow and where the fluid is not visible and unobtrusive. The suction power is determined using the pipe size; smooth pipes have increased speeds. Besides, being conversant with the collision impact and fluid flow mass is important in comprehending the flow of fluids (Modi and Seth 2002). Typically, the Naiver-Stokes equation offer the basis for liquid machines. Stokes’ theorem is applicable to diverse sectors of machinery and electromagnetics. Stokes’ theorem is quite important in this field of electromagnetics and machinery, and it is based on the verity that “the surface integral of a vector field curl to the vector field’s line integral equates to the line integral of the surface’s specific vector function” (Modi and Seth 2002, p. 69). The next section offers a review of literature on the existing applications of Navier Stroke analysis and Boundary Layer analysis.

1.1: Review of Literature

In accordance with Sajben et al. (1997), the Navier-Stroke equations indicate momentum conservation, with the continuum equation reflecting mass conservation. The Navier-Strokes theorems oversee the fluids’ motion and are perceived as the second law of Newton for fluid. In view of a compressible Newtonian fluid, the theorem is as follows: Equation 1 …Navier-stroke equation

The Navier-Stroke equations are complementary to the following complementary continuity equation:

Equation 2………………………………………Continuity equation

The two equations are extensive boulders in the contemporary climate change issues. There are huge amounts of money associated with solving such naiver stokes problems and equations. In the analysis of the flow of complex liquids like suspensions, gels, bubbles and liquid crystals, there is the need to create novel methods and new-era mathematical procedures (Bogar et al. 1983). Researchers have attempted to attain a well-adjusted comprehension of turbulent flow like shock waves using the old fluid machines. The significance of the Naiver-Stokes theorems is seen in aiding the regulation of fluid flow in space and time. This equation is indeed a product an equation initially proposed by Euler Leonhard, a Swiss Mathematician. Nonetheless, several equations are accredited to the Swiss mathematician. In accordance with Bogar et al. (1993), the middle 19th century saw the English Mathematician and Philosopher Gabriel Stokes come up with an answer to the fluid flow simplicity on the two sides. These equations give engineers the needed mathematical basis in various mechanical fields.

In terms of understandability, the Naiver-strokes equation is quite comprehensible on matters fluid flow. Boyer and Fabrie (2012) mention the applicability of Naiver-Stokes equation’s Cartesian form in comprehending fluid dynamic flow. The liquid mechanics’ boundary layer denotes the flowing liquid’ or gas’ thin layer inside a pipeline. The liquid inside the boundary line is considered in estimating the shear strength. Provided the fluid is in contact with the surface, the boundary layer is subjected to a number of velocities from upper to lower zone. Should a liquid cross an object, or an object crosses a liquid, the liquid molecules adjacent to the object become disturbed and agitated.

There is always a dynamic energy created between an object and a liquid (Zhuming 2019). In aerodynamics, there is a thin fluid layer near the surface generated at the point where velocity shifts from surface zero (Zero-velocity surface) to a free diffusion distance further than the surface. This is known as boundary layer owing to the fact that it rests on the liquid’s boundary (Zhuming 2019). The significance of this boundary layer flow is seen in dealing with various aerodynamics conditions, such as an object’s skin pulls, wing table, as well as transfer of heat in top-speed airplanes. In 3-D weight savings, velocity change in an intelligent direction results in a variation of velocity among other indicators. According to Brill (2010), an insignificant percentage of velocity in relation to the surface is considered in moving the flow over the surface. Owing to this withdrawal, it becomes easy to define the boundary layer size.

What are the Types of Fluid Flow in Pipe? - The ConstructorDifference between Laminar and Turbulent Flow - YouTube

Laminar and turbulent flow in fluid mechanics (Source, The Constructor, 2021)

For a 2-phase flow, the object’s size and volume is indicated by two discrete phases, with the channel housing a common meeting point. The 2-phase flow has four likely combinations such as (a) solid-gas (where a velocity change carries solid particles in an intelligent direction thus causing velocity change among other indicators; (b)solids-liquids where there is a dispersion of solid particles in a liquid; (c) different flow; and, (d) the four combined. According to the drop data pressure, flow characteristics may be established to lessen, erosion, corrosion or scale formation, where should these occur might lead to excessive friction (Zhuming 2019). The subsequent section defines the aims and objectives of the present report.

2. Report Objectives and Aims

This report seeks to offer an analysis and implementation of various occurrences of fluid mechanics in the day to day professional and daily life, while putting much emphasis on the following specific objectives:

  1. The application of Boundary Layer analysis on a specific occurrence,

  2. The application of Naiver Stroke analysis in identifying Stresses and velocity profile,

  3. The application of knowledge in different flow control strategies,

  4. The application of Two-Phase flow analysis on specified data, and

  5. Extra aerodynamics analysis

3. Methodology

This section offers an analysis of the relevant theorems considered in the assessment of various problems in fluid dynamics. These comprise of:

…….Equation 3

……Equation 4

………….Equation 5

Directly related with fluid dynamics, the above Euler equations comprise of a set of quasilinear hyperbolic equations considered in regulating the inviscid and adiabatic flow (Marchioro and Pulvirenti 1994). These equations are credited to Leonhard Euler, where the conservation form underscores the equations’ interpretation as conservation equations via a control volume fixed in space. The convective type underscores variations to the state in the reference frame moving with the fluid. The equations are representative of continuity and the force and force balance (Naiver-Strokes equation having zero thermal conductivity and viscosity). According to Hassan (2012), Euler’s calculations are arrived at through a comparison with other calculations of direct continuity identical to Maxwell’s equality Naiver-Stroke equations.

U(C1) = β(1+r)U′(C2)…………equation 6

According to Gibbon et al. (2003), a continuity equation defines the transportation of large quantities like gas or liquid. It is possible to maintain continuous balance via weight, strength, pressure, electrical charging as well as natural mass. This is a great illustration of conservation law. According to fluid dynamics theorem, in a given stable condition approach, the frequency of weight leaving the system equates the frequency of the mass entering the system, inclusive of the system’s mass (Gibbon et al. 2003).

A1V1 = A2V2………. Equation 7

4.0 Result

Following conducting the Naiver analysis, and by considering the higher Reynold number, it can be concluded that the pipe flow is turbulent, while the oil velocity is as a result of combined wall velocity and oil velocity, thus totaling up to 44.25m/s(rounded to the next microsecond). A maximum stress is achieved at the top since it is fixed, while the bottom wall experiences minimum stress since it is in motion. The total identified length is 12.5 m while oil’s total flow rate is 0.124m/s and the actual flow rate being 0.125m/s. By employing boundary layer analysis, the following are estimated: displacement thickness, boundary layer thickness, as well as momentum thickness. This is followed by plotting a boundary layer parameter versus various lengths graph. The flow control analysis has been considered in establishing whether or not the fluid at specific data will be feasible. The final task involved identifying the pros and cons of various flow control approaches and especially as pertains the current problem under study.

4.1 Boundary Layer Analysis

For this task, considering a flat plate at y=0, then:

At the surface of the plate, there is zero flow rate, meaning that v = 0 at y = 0

As a result of the viscosity, the plate has a ‘no slip’ condition…this means the following

u = 0 at y = 0

Outside the boundary layer (at infinity), distant from the plate, the following is achieved,

u → U as y → ∞

A zero pressure gradient is assumed for the flow along a flat plate and parallel to the stream velocity U,

Thus, the following equation is as a result of momentum equation for steady motion (towards x direction in boundary layer)

with the necessary boundary conditions being:

solution: provided the necessary data, then:

The first step is to compute for the distance flow to be considered laminar

The R for flat plate is 5×105

from the above computation, it can be deduced that the plate’s flow will remain laminar at all times. This is followed by determining the velocity profile so as to compute for the momentum thickness and displacement thickness:

by aligning the Plate parallel to the flow, then the stream velocity will not be changed

$$frac{text{δμ}}{text{δx}} = 0$$

The first assumption is as follows:

Assuming the fluid being at a steady flow:

Assumption number two:

Assuming the fluids as Newtonian fluid

substituting in (i)

Since there is no change of velocity with x, there is no change in pressure with x

  1. bo ( )


b) ( ∗)

(c) ( )

From the above solutions, everything has been computed with reference to ‘x’; meaning the ability to determine boundary layer thickness at any plate’s distance. This has been portrayed from the following graphical analysis


Figure 2: a figure representing Boundary Layer Parameters vs Length (x)

4.2 Naiver-Stokes Analysis

For this equation,

Deviation: for a 2-D steady case

The assumptions include:

  1. S is Constant (fluid is not compressible)

  2. A x-direction flow (one dimensional)

  1. Steady flow

  2. Independence of the flow of any z-direction variation

  3. The forces of the body/unit mass=0

Thus, by considering continuity equation

Taking into consideration the above assumptions, then equation (i) changes to:


Integrating for the second time


With c1 and c2 being the integration constants:

Boundary conditions become:

moving plate’s velocity

By considering boundary condition

Replacing C1 and C2 in equation (2),

Velocity profile equation

, from the questions, the values given are as follows:

Top wall= fixed

The moving velocity of the bottom wall =

A) Reynold Number is as follows:

b) in computing for the oil velocity (Voil)

Velocity Profile

Schematic velocity profiles of laminar, averaged turbulent flow, and... | Download Scientific Diagram

Source: The Constructor, 2021)

c) Finding shear strength

D) To determine channel length

I , , ℎ

E) To determine flow rate

4.3 Flow control analysis

Energy transfer from the source ton destination becomes successful courtesy of the hydrostatic transmission. Through regulating the total liquid going through the actuator, then any value may be well regulated. As such to control fluid flow in pump-regulated systems entails the regulation of pump movement or its rotational speed. By employing valve-regulated systems, an application of constant migration having a speed pump is considered, while a valve controls this flow. Regulating hydraulic flow may be attained in different ways. In the same way, each technique comes with different pros and cons. These advantages and disadvantages have a close association with the efficacy, complexity, efficiency, as well as the cost of such programs. Valve systems are perceived less complicated, quite affordable, and highly effective compared to delivery systems. Their major setback include power losses as a result of decreased pressure across the valve. As valve-regulated systems, modified asset systems are able to minimize power dissipation. For the inlet metering system, positioning of the valve at the top enables it to minimize the total energy wasted in the valve. Among the setbacks associated with such systems include sound mobility. Nonetheless, hydraulic fluid flow is regulated by closed/open valves for digital systems.

Calculating Two phase Pressure Drop

4.4 Aerodynamic Analysis

In an entertaining French tournament match between Brazil and France in 1997, Roberto Carlos of Brazil lined up to take a free kick, 35m from the goal line. When he went for the spot, Carlos did not have a direct kick through position so he had to apply additional technique. When he finally took the freekick, the ball veered extremely away from the goalposts that the French goalkeeper thought it was going out of the field of play. Then boom, came the goal! This goal seemed to defy physics but it was all physics according to the player’s tactics. With the ball rotating around its own axis, it endured pressure differential on both sides but in a different pressure level, forcing it to curve towards the side with less pressure. This condition is identified as the Magnus effect. Simply put, a ball or cylinder spinning forth or back in an airstream thus producing this Magnus effect.

A spinning ball and the Magnus effect. | Download Scientific Diagram

The Physics of Tennis | Ball Spin In Flight

5. Discussion

All fluid points, at any given point of time, defines direction for vector quantities, thus consecutively giving the fluid speed’s magnitude. The field is normally researched in 3-dimensions through instantaneous simulations, even though two spaces and static conditions are normally employed as models, with increased analogy being read both in applied and pure equation. Dynamic computations and associations may be considered in computing for the temperature and pressure on the basis of the calculated velocity field. Unlike classical mechanics, one is able to compute for different directions. The waterless particle’s direction is determined by the vector field direction, normally as translated as flow velocity. These techniques rely on an area identical to the vector field in offering a visual portrayal of the vector field performance at a specific time.

In view of standard deviation, and as non-linear variables, Naiver Ratings- Stokes are found in virtually all real-world situations. In certain instances, like moving flow (or stokes flow), simplification of the calculations may be obtained through equal measurement. As a result of nonlinearity, there’s dilemma in the standard model through hardening various problems or making them unsolvable. Nonlinearity is as a result of the acceleration due to velocity change on top of the position. Thus, any transmission flow, whether chaotic or not, there will be incompatibility with the other side. In different cases, it is possible to research and comprehend a flow thoroughly.

6. Conclusion

Comprehending the behavior of water/oil flow in pipes is quite important in establishing the level of erosion/corrosion resulting from the level of free water in contact with the pipe. Sooner or later, mixtures of water/oil and liquid/gas systems will be considered in the analysis of the most intricate cases of oil/gas/water mixture.


Batchelor, G. K. 1967. An Introduction to Fluid Dynamics. Cambridge University Press. ISBN 0-521-66396-2. Thompson, Philip A. (1972). Compressible Fluid Flow. New York: McGraw-Hill. ISBN 0-07-064405-5.

Bogar, T., Sajben, M., and Kroutil, J., 1983. Characteristic Frequencies of Transonic Diffuser Flow Oscillations,” AIAA Journal, 21(9), pp.

Boyer, F. and Fabrie, P., 2012. Mathematical Tools for the Study of the Incompressible Navier-Stokes Equations andRelated Models (Vol. 183). Springer Science & Business Media.

Friedlander, S.; Serre, D., eds. 2003. Handbook of Mathematical Fluid Dynamics – Volume 2. Elsevier. p. 298. ISBN 978 0 444 51287

Gibbon, J.D.; Moore, D.R.; Stuart, J.T. (2003). “Exact, infinite energy, blow-up solutions of the threedimensional Euler equations”. Nonlinearity. 16 (5): 1823–1831.

Hasan, A., Foss, B. and Sagatun, S., 2012. Flow control of fluids through porous media. Applied mathematics and computation, 219(7), pp.3323-3335.

Herbert, L. and Hansen, Z., 2016. Restructuring of workflows to minimise errors via stochastic model checking: an automated evolutionary approach. Reliab Eng Syst Saf 145 (3), pp.351–365.

Marchioro, C., and Pulvirenti, M.1994. Mathematical Theory of Incompressible Nonviscous Fluids. Applied Mathematical Sciences. 96. New York: Springer. p. 33. ISBN 0 387 94044 8.

Sajben, M., Kroutil, J., and Chen, C., 1977. A High-Speed Schlieren Investigation of Diffuser Flows with Dynamic Distortion, AIAA Paper 77-875,

Salmon, J., Bogar, T., and Sajben, M., 1983. Laser Doppler Velocimetry in Unsteady, Separated, Transonic Flow, AIAA Journal, 21(12).pp. 1690–1697.

Toro, E.F.1999. Riemann Solvers and Numerical Methods for Fluid Dynamics. Springer-Verlag. ISBN 3-540-65966-8.



How The Order Process Works

Amazing Offers from The Uni Tutor
Sign up to our daily deals and don't miss out!

The Uni Tutor Clients