A rheometer (figure 1) is commonly found laboratory device, that measures the flows of liquids, suspension and slurries in response to an applied force. A rheometer is mainly used for fluids that cannot be defined by a single value of viscosity and need other constraints to be set and then measured.

What Are Rheometers Used For?

Rheometers are used in many diverse industries, production facilities, paper, mining, textiles etc. For example, a paper manufacturer might use a rheometer to monitor the flow of pulp during various stages of the production process (paper making).

Typically, rheometers are used in the paint, adhesives, ink, rubber and coating materials industries to monitor production processes. Those production processes may include PVA’s, printing inks, topcoat paints and rubber compounds etc. Reasons for using a rheometer in production are:

• To improve the quality of the resultant product
• To monitor production performance
• To isolate the key processes that contribute to the performance of the end product
• To carry out regression analysis to determine the quantity of the production factor or process needed to achieve optimum product performance

Why Are Rheometers Used In Production?

As is the case with many of the chemical processes in the industry, the performance of the product can only be maximized by controlling all the physical processes of production at the same time. This requires a means of monitoring the different parameters present during the production process so that adjustments to the process can be made when required.

Rheometers are an excellent tool for this purpose because they have the ability to measure the process variables associated with the process as a whole. These include the type of fluid, temperature conditions, stirring conditions, packaging conditions etc.

Some typical Rheometers and their uses:

Viscosity Rheometers

Viscosity rheometers are used to measure the viscosity of fluids for which a numerical value is required. A viscometer measures the viscosity of a fluid by applying a force to the fluid and measuring the time it takes for the fluid to travel a defined distance. A rheometer is the next stage up as the rheometer actually measures the force needed to apply to the fluid. Typically, viscosity rheometers are used in the cosmetics, food, ink and paint industries to monitor production process variables associated with viscosity. A rheometer is also used to compare the performance of products of different manufacturers

Viscosity rheometers have a simple operating principle. They are based on applying a known force to a control cylinder and measuring the force required to move the cylinder over a specific period of time. The material to be measured is positioned between the control and measuring cylinders and the force needed for it to flow is recorded.

Three-Point-Bucket Rheometers

Three-point-bucket rheometers are used to measure the viscosity and rheological behaviour of particulate materials over a long period of time. The three-point-bucket rheometer has three major components:

• A funnel, which enables the material to enter the rheometer
• A sample cell, in which the material is positioned
• A control cylinder, responsible for measuring the speed and force

The speed at which the material flows through the rheometer is dependent on the viscosity and the particle size of the material. The funnel opens as the material enters the rheometer, allowing the material to flow in a controlled flow similar to the flow of material through a pipe. The material flows into the sample cell, where it is regulated by a computer control mechanism.

The sample cell is shaped like a bucket, with the walls being so shaped that the material can fill as much of its capacity as possible without being channelled into a narrow stream. This is achieved by using a set of paddles behind the walls of the sample cell.

The rheometer is designed to account for the change in viscosity of the material as a function of time. The speed of the measuring cylinder is continuously adjusted to maintain a constant shear rate.

Double-Cone Spindle Rheometers (DCR)

A DCR rheometer is used to measure the viscosity and shear rate for liquids, suspensions and slurries. The basis of the DCR rheometer is the double-cone spindle and takes into account the attributes of the force-displacement curve. The sample is placed in a sample tube and control spindle which is then rotated at a constant velocity, proportional to that of the spindle that is recording the velocities. The spindle is able to move by the application of a voltage, which is proportional to the voltage applied to the spindle in pace with the speed of the rotation. Both rotations are synchronized so that the direction of rotation of the spindle and spindle is the same and the viscometer is able to measure precisely the molecular structure of the sample.

Two-Phase Rheometers (TPR)

Two-phase rheometers (TPR) are used to measure the viscosity and shear rate for polymer melts, molten metals, plastisol, carbon-carbon and urethane, and polyurethane matrices. Two-phase rheometers make it possible for both phases to flow at the same time, making it possible for the relationship between the two phases to be examined.

For two-phase systems, the polymer melts or liquid material is placed between two-solid rotating discs, and these discs are rotated at a constant velocity, and voltage is applied to the discs. The material will rotate faster with a progressively decreasing voltage.

Rheometers used for slurry measurement are available in various configurations. Some are designed to supply a slurry directly into a motor-driven spindle, while others require the slurry to be pumped into a reduction chamber, which then provides the slurry to the machine.

Other Types Of Rheometers And Their Uses

Hassan Ahmed

Hassan graduated with a Master’s degree in Chemical Engineering from the University of Chester (UK). He currently works as a design engineering consultant for one of the largest engineering firms in the world along with being an associate member of the Institute of Chemical Engineers (IChemE).

The post A Breakdown | What Is A Rheometer? appeared first on Engineeringness.

To name a few in civil engineering, hydrostatics is vital for designing dams, aqueducts, and flood control systems. It influences how these structures are constructed, ensuring they can withstand the pressures exerted by static fluids. In mechanical engineering hydrostatics principles are employed in the design of hydraulic systems like pumps and pistons, which are essential in machines and vehicles.

What Are Plane Surfaces? 

Plane surfaces in the context of hydrostatics are flat, two-dimensional surfaces. These surfaces are characterised by having the same angle with respect to the horizontal in all points, meaning they do not curve or bend.

What Equation Is Used for Calculating Hydrostatic Forces for Plane Surfaces:

The key equation for calculating the hydrostatic force  exerted by a fluid on a plane surface is given by:

Here:

• γ – is the specific weight of the fluid, which is the weight per unit volume (often expressed in units like N/m³ or lb/ft³).
• h – is the depth of the fluid, or the vertical distance from the surface to the fluid’s free surface level.
• A – is the area of the submerged surface upon which the force is acting.

This equation assumes that the fluid is incompressible and that the depth (h) remains constant across the entire surface area. For surfaces that are not horizontal, the calculation of the hydrostatic force can be more complex and may require integration to account for the variation of pressure over the surface.

What Are Curved Plane Surfaces and How Do We Calculate Their Hydrostatic Forces?

Curved surfaces are significant because the pressure exerted by a fluid at rest varies at each point due to changes in depth. Since hydrostatic pressure increases with depth, the pressure is not uniformly distributed across a curved surface.

The relevance of plane curved surfaces in hydrostatic calculations lies in the need to accurately determine the resultant force and its point of action on the surface. This involves integrating the varying pressure over the entire surface to find the total hydrostatic force. Additionally, engineers must locate the centre of pressure, which is the single point where the total hydrostatic force can be considered to act, causing the same moment as the actual pressure distribution.

Worked Example of Calculating Hydrostatic Forces on a Curved Plane Surface:

Let’s consider the example of a curved plane surface in the form of an arc of a circle submerged in water. This arc forms part of a cylindrical tank’s wall. To calculate the hydrostatic force on this curved surface, we’ll need to integrate the pressure across the surface.

Assume the following:

• The radius of the cylindrical tank is 3 meters.
• The width of the arc (into the page) is 1 meter.
• The arc is fully submerged and centered vertically in the water.

We will need to do the following steps : 

1. Pressure Formula: Pressure at a depth  is given by p = γh, where γ is the specific weight of water.
2. Differential Force: The force on a small horizontal strip of the arc at depth  is dF = p x dA, where dA = w x dh is the area of the strip.
3. Force Expression: Substituting the expressions for p and dA into dF, we get dF = γhwdh
4. Integration: The total hydrostatic force  exerted on the arc is found by integrating  from the top depth  to the bottom depth  of the arc. The integration is performed over the height of the arc, which in this example ranges from the water surface (0 meters) to twice the radius of the tank (6 meters).
5. Calculation: The integral of γhwdh from 0  to 6 meters is evaluated. For water γ = 9810 N/M3 and w =1m .

Result: The integration yields the total force , which calculates to approximately 176,580 N.

This calculation provides the hydrostatic force exerted by the water on the curved surface of the arc, taking into account the increasing pressure with depth.

What Are Layered Fluids

Layered fluids in hydrostatics refer to a scenario where multiple immiscible fluids (fluids that do not mix) with different densities are layered one above the other in a container. The concept is particularly relevant in natural settings (like oceans with layers of varying salinity or temperature) and in industrial applications (such as oil over water in a storage tank).

In hydrostatic calculations, the presence of layered fluids significantly impacts how the total pressure at a given depth is computed, as each fluid layer contributes differently to the pressure based on its density and depth. 

Example of Calculation of Hydrostatic Force on a Surface for a Layered Fluid:

Let’s consider an example where we calculate the hydrostatic force on a vertical wall in a tank that contains two immiscible fluids layered on top of each other, such as oil over water.

Given:

Water layer height = 4 meters

Oil layer height = 2 meters

Wall width = 5 meters

Specific weight of water = 9810 N/m³

Specific weight of oil = 8500 N/m³

To calculate the hydrostatic force of water: 

To calculate the hydrostatic force of oil :

Adding these 2 and you get the answer of 817400 

Application of Hydrostatics in Mechanical Engineering:

hydrostatics principles are employed in the design of hydraulic systems like pumps and pistons, which are essential in machines and vehicles. Understanding the transmission of force through fluids enables the creation of complex machinery that can perform heavy lifting and precise movements with hydraulic actuators.

Application of Hydrostatics in Environmental Engineering:

Environmental engineering too relies heavily on hydrostatics, particularly in the management of water resources, wastewater treatment, and the containment of hazardous materials. Calculating the forces exerted by stationary fluids helps in designing tanks and barriers to prevent leaks and spills, which is crucial for protecting the environment.

Applications of Hydrostatics in Naval Architecture:

The fundamentals of hydrostatics also extend into naval architecture and marine engineering, where the buoyancy and stability of vessels are paramount. Engineers must calculate the forces acting on ship hulls to design vessels that can float and move efficiently through water. In aerospace engineering, hydrostatic principles find a place in designing fuel tanks for rockets, where fluid behavior in low-gravity environments is a critical consideration.

Energy Harvesting Systems an Innovations Using Hydrostatics:

There’s ongoing research in using hydrostatic pressure differences in natural water bodies to generate renewable energy, which could open new avenues for sustainable energy resources.

The concept of generating energy from hydrostatic pressure differences is based on exploiting the potential energy available due to varying water depths. In simple terms, the greater the depth, the higher the hydrostatic pressure. This pressure difference can be harnessed to produce energy, similar to how hydroelectric power utilizes gravitational potential energy.

It involves 2 Technologies:

Pressure Retarded Osmosis (PRO):

This method involves using semipermeable membranes that allow water to pass through but block salt. When freshwater from a river meets seawater in an estuary, the osmotic pressure difference can be used to generate power.

Reverse ElectroDialysis (RED): 

RED uses membranes that allow ions to pass but not water. By alternating membranes that selectively allow positive and negative ions to pass, a potential difference is created that can be used to generate electricity.

Adrian Michaels

Adrian graduated with a Masters Degree (1st Class Honours) in Chemical Engineering from Chester University along with Harris. His master’s research aimed to develop a standardadised clean water oxygenation transfer procedure to test bubble diffusers that are currently used in the wastewater industry commercial market. He has also undergone placments in both US and China primarely focused within the R&D department and is an associate member of the Institute of Chemical Engineers (IChemE).

The post Hydrostatic Forces Decoded: An Advanced Insight appeared first on Engineeringness.

Internal flow is the transport of fluids in pipes, ducts and conduits (flow sections). There are different flow regimes for the flow of fluids: laminar flow, transitional flow, and turbulent flow. Flow regimes mainly depend on the ratio of inertial forces to viscous forces, with the ratio being called the Reynolds number. 

For non-circular pipes, the Reynolds number is based on the hydraulic diameter D_h.

Flow Regimes

For the different flow regimes in circular pipes, the Reynolds number is different (Figure 1): 

• Laminar flow, Re < 2300 – characterised by smooth streamlines and highly ordered motion. 

• Transitional flow, 2300 < Re < 4000 – flow switches between laminar and turbulent randomly.

• Turbulent flow, Re > 4000– characterised by velocity fluctuations and highly disordered motion.  

Entrance of Pipe Flow

The boundary layer is a region where the viscous shearing forces caused by fluid viscosity are felt. At the boundary layers hypothetical surface divides the flow into two areas (Figure 2) (Course hero, 2020): 

• The boundary layer region – a region of flow in which viscous effects and velocity changes are significant.
• Irrotational (core) flow region – frictional forces are negligible, and velocity remains constant in the radial direction. 

When the temperature profile is constant, the flow is fully developed, with hydrodynamically developed flow equivalent to fully developed flow.

For laminar flow, the velocity profile in the fully developed region is parabolic and somewhat flatter in the turbulent area (Figure 3). 

The hydrodynamic entry length is the distance from the pipe entrance to where the wall shear stress (and thus the friction factor) reaches within about 2% of the fully developed value (TEXSTAN, 2021). For laminar flow, the hydrodynamic entry length is given approximately when the temperature profile is unchanging (Figure 4). 

During turbulent flow, due to the intense mixing, random fluctuations dominate the effects of molecular diffusion. Thus, the hydrodynamic entry length is approximated: 

References

Course hero. (2020). MEC554 FLUID LAB 2 FLOW PAST CYLINDER. Retrieved from Course hero: https://www.coursehero.com/file/47519253/MEC554-FLUID-LAB-2-FLOW-PAST-CYLINDER-COMPILEpdf/

jaimeirastorza. (2017). transition laminar turbulent flow. Retrieved from jaimeirastorza: https://jaimeirastorza.wordpress.com/2017/03/17/elegance-in-flight-book-review/transition-laminar-turbulent-flow/

slidetodoc. (2020). Viscous flow in ducts Circular and noncircular ducts. Retrieved from slidetodoc: https://slidetodoc.com/viscous-flow-in-ducts-circular-and-noncircular-ducts/

TEXSTAN. (2021). TEXSTAN Glossary of Terms – definitions and explanations. Retrieved from TEXSTAN: http://texstan.com/glossary.php

Dr. Adam Zaidi

Dr. Adam Zaidi, PhD, is a researcher at The University of Manchester (UK). His doctoral research focuses on reducing carbon dioxide emissions in hydrogen production processes. Adam’s expertise includes process scale-up and material development.’

The post A Breakdown | Internal Flow Part I appeared first on Engineeringness.

In part 1 the tutorial goes over pressure drop in pipelines. Just to recap pressure drop arises due to skin friction and forms friction. Non-separated boundary layers causes skin friction (the roughness of the pipe causing shear within the boundary layer of the fluid) whereas separated boundary layers cause form friction (geometrical characteristics of the piping system are piled up causing localised losses).

Simply put, pipe pressure drop is due to skin friction. But in a pipeline with valves and fittings pressure drop is mainly due to form friction. The pipelines may be connected to equipment and again pressure drop occur due to the specific piece of equipment. This tutorial is focused on pressure drop in valves and fittings only.

In order to account for pressure drop due to valves and fittings, various methods are used The most common among them is:

1. K values or Head Loss Coefficient.
2. Equivalent length method.

1. K values or Head Loss Coefficient Method

Depending upon the type of valves and fittings, various K values are available, which can be seen in the table below:

K values that are subject to change, then the pipe diameter can be calculated as follows:

The Km, Ki, and Kd values corresponding to the type of fittings and valves that are given in the table below.

Once determining the appropriate K value for your pipe, it can be substituted back into the first equation to determine the pressure drop or headloss

2. Equivalent Length Method.

Where:

f = Darcy’s Friction Factor

D = Internal Diameter of the pipe

Another method that is widely used in calculating pressure drop is the equivalent length method. For every valve and fitting particular L/D, equivalent length value is available in the previous table. To find the equivalent length, multiply the L/D value with the diameter and insert this value in the given formula, in place of Leq.

Similarly, for contraction and expansion losses you need to consider the k value as per the following formula.

Hassan Ahmed

Hassan graduated with a Master’s degree in Chemical Engineering from the University of Chester (UK). He currently works as a design engineering consultant for one of the largest engineering firms in the world along with being an associate member of the Institute of Chemical Engineers (IChemE).

The post Pressure Drop In Pipe Lines And Fittings | Part 2 appeared first on Engineeringness.

What Pressure Is Involved In Driving Fluid Through Pipes And Fittings?

Pressure is force acted per unit area

Pressure in a pipeline may be due to pumping, vaporization, compression, etc. The fluid should travel the entire pipeline without losing its pressure otherwise we need to spend extra for pumping the fluid to compromise for the loss in pressure.

Why Is Pressure Lost Through Pipes?

The reason is due to friction, wake formation, separation of the boundary layer by fittings, pipe roughness, etc. In order for the pump to work efficiently, the pump will be designed to accommodate any extra pressure that is required.

Pressure drop due to unseparated boundary layers (Skin friction) can be calculated by the following classical formula,

Pressure drop varies with length and diameter of the pipe, velocity, and density of the fluid, and Fanning friction factor. Don’t confuse this fanning friction factor with Darcy’s friction factor.

The Fanning friction factor varies with the nature of the flow. So if we know the nature of flow i.e., laminar or turbulent we can calculate the ‘f ‘ value accordingly.

If the flow is laminar the fanning friction varies with Reynolds number as follows,

If the flow is turbulent a lot of equations are in practice and you can use any of those equations at the expense of accuracy. the equations are mentioned as follows.

• Colebrook equation (1938)

• Swamee and Jain equation (1976)

• Haaland equation. (1983)

The ‘ ε ‘ symbol corresponds to the roughness factor which depends on the material of the construction of the pipe, whereas D and Re have their usual meaning.

After calculating the friction factor, we can find the pressure drop due to skin friction in a pipeline by substituting the ‘ f ‘ value into the pressure drop formula stated earlier.

In the Second Part pressure drop due to fittings will be covered.

Hassan Ahmed

Hassan graduated with a Master’s degree in Chemical Engineering from the University of Chester (UK). He currently works as a design engineering consultant for one of the largest engineering firms in the world along with being an associate member of the Institute of Chemical Engineers (IChemE).

The post Pressure Drop In Pipe Lines And Fittings | Part 1 appeared first on Engineeringness.

Energy can exist in numerous forms;

• Thermal, 
• Mechanical, 
• Kinetic, 
• Heat,
• Potential, 
• Electrical, 
• Magnetic, 
• Chemical, 
• Nuclear. 

The sum of these energy is the total energy and the sum of all microscopic forms is called the internal energy of a system. 

Heat is a form of energy (sometimes called heat energy), that can be transferred between systems when there is a temperature difference. Heat transfer occurs from a higher temperature region to a lower temperature region, with heat transfer stopping when there is no longer a temperature difference. 

There are three types of basic model that describe heat transfer, these are; 

• Conduction 

• Convection 

• Thermal Radiation 

Conduction

Conduction involves the transfer of heat from more energetic particles of a substance to less energetic particles, due to the interaction between the two particles (Figure 1). In solids conduction occurs due to vibrations of molecules and the energy transport by free electrons. For gases and liquids conduction occurs due to collisions and diffusion of molecules during their random motion. 

The rate of heat conduction through a plane is proportional to the temperature difference across the layer and the heat transfer area, and is inversely proportional to the layer thickness: 

Rate of heat conduction ∝ (area x temperature difference) / thickness

Q_cond = kA x (ΔT/Δs)

k – thermal conductivity a measure of a materials ability to conduct heat

A – Area of the material

The heat transfer area is the thermal conductivity multiped by the material area. A high thermal conductivity means that the material is a good heat conductor, and low thermal conductivity shows that the material is a bad conductor or an insulator. Heat is conducted from the higher temperature regions to lower temperature regions, with the temperature gradient becomes negative when temperature decreases with increasing thickness. 

Convection 

Convection involves heat transfer between a solids surface and a moving liquid or gas, and involves both conduction and fluid motion, with the greater fluid motion the greater the convection heat transfer (figure 2). If there is no fluid motion, then heat transfer would be purely by conduction. 

There are two types of convection, forced convection and natural convection (figure 3). 

• Forced convection – forcing a fluid to flow over a solid surface,

• Natural convection – fluid motion is due to the buoyancy force that are induced by density differences due to temperatures variations in the liquid or gas. 

Furthermore, a change in phase of a fluid is classified as convection as the fluids are in motion such as vapour bubbles during boiling or liquid droplets during condensation. 

The equations for convection involved the surface area and convection heat transfer coefficient: 

q_conv = hA(Ts-Tf)

h – convection heat transfer coefficient (W/(m2-K))

A – surface area convection is taking place (m2)

Ts – surface temperature (K)

Tf – temperature of fluid away from the surface (K).

Thermal Radiation 

Heat transfer by thermal radiation is done by electrometric waves and doesn’t require any medium and can pass through a vacuum (figure 4). Thermal radiation is caused by the random movement of atoms and molecules, with the movement of the charged protons and electrons results in the emission of electromagnetic radiation.

The hotter an object the greater the thermal radiation, with the temperature of an object affecting the wavelength and frequency of the radiated waves. As temperatures increase the wavelengths of the emitted spectra decrease, resulting in a short wavelength high-frequency radiation. 

The Stefan-Boltzmann law is used to calculate thermal radiation:

P = e · σ · A · (Tr4 – Tc4)

• P = net radiated power; 
• A = radiating area; 
• Tr = temperature of the radiator; 
• Tc = temperature of surroundings; 
• e = emissivity; 
• σ = Stefan’s constant.

Emissivity is as object’s effectiveness in emitting energy as thermal radiation and is a ratio, at a given temperature, of the thermal radiation from a surface to the radiation from an ideal black surface as determined by the Stefan-Boltzmann law (machinedesign, 2015). Stefan’s constant is determined by constants of nature: 

σ = (2 · π5 · k4)/(15 · c2 · h3) = 5.670373 × 10^–8 W · m^–2 · K^–4

k = Boltzmann’s constant; 

h = Planck’s constants; 

c = speed of light in a vacuum.

Common materials have lower emissivity values than an ideal radiator which has a value of 1.

References 

claesjohnson. (2011). claesjohnson. Retrieved from Radiative Heat Transfer: Theory: http://claesjohnson.blogspot.com/2011/10/radiative-heat-transfer-theory.html

Engineering ToolBox. (2020). Conductive Heat Transfer. Retrieved from Engineering ToolBox: https://www.engineeringtoolbox.com/conductive-heat-transfer-d_428.html

machinedesign. (2015). What’s the Difference Between Conduction, Convection, and Radiation? Retrieved from machinedesign: https://www.machinedesign.com/learning-resources/whats-the-difference-between/document/21834474/whats-the-difference-between-conduction-convection-and-radiation

McGraw-Hill Higher Education . (2020). Convection Heat Transfer. Retrieved from McGraw-Hill Higher Education : http://www.mhhe.com/engcs/mech/cengel/notes/ConvectionHeatTransfer.html

Dr. Adam Zaidi

Dr. Adam Zaidi, PhD, is a researcher at The University of Manchester (UK). His doctoral research focuses on reducing carbon dioxide emissions in hydrogen production processes. Adam’s expertise includes process scale-up and material development.’

The post A Breakdown | Heat Transfer Mechanism appeared first on Engineeringness.

Flow rate is the volume of fluid that flows through a pipe or other enclosed region each second. Suppose we would want to describe the flow rate a fluid flows through a pipe:

• Mass flow rate – Mass of a substance which flows per unit of time, units kg/s
• Volumetric flow rate – Volume of a substance which flows per unit of time, units m³/s

The relationship that relates to the mass flow rate and the volumetric flow rate is the density:

m˙ – Mass flow rate, Q – Volumetric flow rate

The units of density are kg/m3 which are derived from the standard density equation (1.1). Thus, having the units of time will cancel and the units of density will be the same.

Flow Rate Examples

1. The mass flow rate of a fluid is 6 g/s with a density of 2 kg/cm³. What is the volumetric flow rate in m³/s?
2. If a fluid is flowing through a cone-shaped pipe

a. what is the difference between the inlet and outlet mass flow rates? Show your workings.

b. If the density is constant will the volumetric flow rate be the same at the inlet and outlet? Show your workings.

Show Answer

Mean Velocity

 If the size of the pipe is known and the flow rate is known we can find the mean velocity. Velocity is the rate of change of the position of an object with respect to a frame of reference and time and mean velocity is the average velocity of a fluid in motion.

Figure 1: Cylindrical pipe with fluid flowing through

The area of the cross-section of the pipe at point z is A and at this point the mean velocity is u_mean. In a period fluid will pass point z with a length of u_meant as (distance = speed x time).

Using the mean velocity, we can develop an expression for the volumetric flow rate:

Using the previous equations (1.3 and 1.7), we express the mass flow rate using the mean velocity along a cylindrical pipe:

Both expressions (1.7 and 1.8) are true for any shape of duct, as long as the condition of the cross-sectional area being perpendicular to the velocity is meet.

Dr. Adam Zaidi

Dr. Adam Zaidi, PhD, is a researcher at The University of Manchester (UK). His doctoral research focuses on reducing carbon dioxide emissions in hydrogen production processes. Adam’s expertise includes process scale-up and material development.’

The post A Brief Introduction To Fluid Flow Within Pipes appeared first on Engineeringness.