Mechanics of Fluids - selected short answer questions from AMIE exams

Displacement thickness and momentum thickness

Displacement thickness. It is defined as the distance by which the external potential flow is displaced outwards due to the decrease in velocity in the boundary layer.
 

Momentum thickness. It is a measure of the boundary layer thickness. Momentum thickness is defined as the distance by which the boundary should be displaced to compensate for the reduction in momentum of the flowing fluid on account of boundary layer formation.

Couette flow and Poiseuille flow

Couette flow is the flow of a viscous fluid in the space between     two surfaces, one of which is moving tangentially relative to the other. The configuration often takes the form of two parallel plates or the gap between two concentric cylinders. The flow is driven by virtue of viscous drag force acting on the     fluid, but may additionally be motivated by an applied pressure gradient in the flow     direction. The Couette configuration models certain practical problems, like flow in lightly loaded journal bearings, and is often employed in viscometry.

 

Poiseuille flow is pressure-induced flow (Channel Flow) in a long duct, usually a pipe. It is distinguished from drag-induced flow, such as Couette Flow. Specifically, it is assumed that there is Laminar Flow of an incompressible Newtonian Fluid of viscosity η) induced by a constant positive pressure difference or pressure drop Δp in a pipe of length L and radius R << L.

Nozzles and diffusers

Nozzle.  A nozzle is a device of uniformly varying cross-sectional duct in which     velocity of fluid increases on the expense of Pressure energy (below image is an example of application of a nozzle).

 

Diffuser.  A diffuser is a device opposite to a nozzle, in which pressure energy increases on the expense of kinetic energy of fluid. 

Boundary layer control

Boundary layer control refers to methods of controlling the behaviour of fluid flow boundary layers. It may be desirable to reduce flow separation on fast vehicles to reduce the size of the wake (streamlining), which may reduce drag. Boundary layer separation is generally undesirable in aircraft high lift coefficient systems and jet engine intakes. Laminar flow produces less skin friction than turbulent, but a turbulent boundary layer transfers heat better. Turbulent boundary layers are more resistant to separation. The energy in a boundary layer may need to be increased to keep it attached to its surface. Fresh air can be introduced through slots or mixed in from above. The low momentum layer at the surface can be sucked away through a perforated surface or bled away when it is in a high pressure duct. It can be scooped off completely by a diverter or internal bleed ducting. Its energy can be increased above that of the free stream by introducing high velocity air.

Viscous flow through pipes

The viscous flow of a fluid in a pipe may be laminar flow, or it may be turbulent flow.
In fluid dynamics, laminar flow (or streamline flow) occurs when a fluid flows in parallel layers, with no disruption between the layers. At low velocities, the fluid tends to flow without lateral mixing, and adjacent layers slide past one another like playing cards. There are no cross-currents perpendicular to the direction of flow, nor eddies or swirls of fluids. In laminar flow, the motion of the particles of the fluid is very orderly, with particles close to a solid surface moving in straight lines parallel to that surface. Laminar flow is a flow regime characterized by high momentum diffusion and low momentum convection.
 

Turbulent Flow.  Turbulent flow is a type of fluid (gas or liquid) flow in which the fluid undergoes irregular fluctuations, or mixing, in contrast to laminar flow, in which the fluid moves in smooth paths or layers. In turbulent flow, the speed of the fluid at a point is continuously undergoing changes in both magnitude and direction. The flow of wind and rivers is generally turbulent in this sense, even if the currents are gentle. The air or water swirls and eddies while its overall bulk moves along a specific     direction.
Most kinds of fluid flow are turbulent, except for laminar flow at the leading edge of solids moving relative to fluids or extremely close to solid surfaces, such as the inside wall of a pipe, or in cases of fluids of high viscosity (relatively great sluggishness) flowing slowly through small channels. Common examples of turbulent flow are blood flow in arteries, oil transport in pipelines, lava flow, atmosphere and ocean     currents, the flow through pumps and turbines, and the flow in boat wakes and around     aircraft-wing tips.

Hot wire anemometer

The Hot-Wire Anemometer is the most well known thermal anemometer, and measures a fluid velocity by noting the heat convected away by the fluid. The core of the anemometer is an exposed hot wire, either heated up by a constant current or maintained at a constant temperature (refer to the schematic below). In either case, the heat lost to fluid convection is a function of the fluid velocity. By measuring the change in wire temperature under constant current or the current required to maintain a constant wire temperature, the heat lost can be obtained. The heat lost can then be converted into a fluid velocity in accordance with convective theory.

Venturi meter

Venturi meters are flow measurement instruments which use a converging section of pipe to give an increase in the flow velocity and a corresponding pressure drop, from which the flow rate can be deduced. They have been in common use for many years, especially in the water supply industry.

Boundary layer and boundary layer separation

All solid objects travelling through a fluid (or alternatively a stationary object exposed to a moving fluid) acquire a boundary layer of fluid around them, where viscous forces occur in the layer of fluid close to the solid surface. Boundary layers can be either laminar or turbulent. A reasonable assessment of whether the boundary layer will be laminar or turbulent can be made by calculating the Reynolds number of the     local flow conditions.
 

Flow separation occurs when the boundary layer travels far enough against an adverse pressure gradient that the speed of the boundary layer relative to the object falls almost to zero. The fluid flow becomes detached from the surface of the object, and instead takes the forms of eddies and vortices.

Intensity of turbulence

The turbulence intensity, also often referred to as turbulence level, is defined as u'/U, where u' is the root-mean-square of the turbulent velocity fluctuations and U is the mean velocity (Reynolds averaged).

Hydraulic gradient line and total energy line

The total energy available in a flow, at a specific position, noted can be written as follows :

 

H = pressure head + potential head + kinetic head

 

The Total Energy Line, also commonly referred as the Energy Grade Line (EGL) is a graphical representation of the aforementioned total head H.

 

Now consider a flow standing still. Which is not moving at all. In that case, the     kinetic head becomes zero. The remaining head is somehow referred as "static head". It is just the total energy head minus the velocity head.

 

The Hydraulic Grade Line (HGL) is just a graphical representation of this static     head.

Pascal's law

Pascal's law states that when there is an increase in pressure at any point in a confined fluid, there is an equal increase at every other point in the container.

Pilot tube

Pitot tubes can be used to indicate fluid flow velocities by measuring the difference between the static and the dynamic pressures in fluids. A pitot tube can be used to measure fluid flow velocity by converting the kinetic energy in a fluid flow to potential energy.

Darcy- Weisbach formula for friction head loss.

In fluid dynamics, the Darcy–Weisbach equation is a phenomenological equation, which relates the head loss, or pressure loss, due to friction along a given length of pipe to the average velocity of the fluid flow for an incompressible fluid. 

 

          
where , 

ρ = the density of the fluid (kg/m³); 

D = hydraulic diameter of the pipe (for a pipe of circular section, this equals the internal diameter of the pipe) (m); 

v = mean flow velocity, experimentally measured as the volumetric flow rate Q per unit cross-sectional wetted area (m/s); 

f_D, the Darcy friction factor.

Venturi meter

A venturi meter is a device used for measuring the rate of flow of a fluid flowing through a pipe.
 

The main parts of a venturi meter are 

• A short, converging part: It is that portion of the venturi where the fluid gets to converge. 
• Throat: It is the portion that lies in between the converging and diverging part of the venturi. The cross-section of the throat is much less than the cross-section of the converging and diverging parts. As the fluid enters the throat, its velocity increases and pressure decreases. 
• Diverging part: It is the portion of the venturi meter (venturi) where the fluid gets to diverge.

The working of venturi meter is based on the principle of Bernoulli’s equation.

Potential flows

Potential flow refers to the flow outside the boundary layer that obeys the laws of potential flow like electric and magnetic fields. This is sometimes called the inviscid flow region meaning that transverse velocity gradients (aka shear) are minimal and viscous effects are small to none. By contrast, the boundary layer, at least in laminar flow, is dominated by viscous effects and does not follow the rules of potential flow.

Turbine flow meter

Turbine flowmeters use the mechanical energy of the fluid to rotate a “pinwheel” (rotor) in the flow stream. Blades on the rotor are angled to transform energy from the flow stream into rotational energy.  Shaft rotation can be sensed mechanically or by detecting the movement of the blades. When the fluid moves faster, more pulses are generated. The transmitter processes the pulse signal to determine the flow of the fluid. 

Notches and weirs

Notches are openings which is used to measure discharge through it. However a Weir is a notch but in a very large scale.
 

A Notch is used to measure relatively smaller discharge (examples include discharge in a flume, water lining etc) while a weir is used to measure larger discharge (examples are discharge in a stream or river, storm discharge etc).
 

Rota meter

A Rotameter is a device that measures the flow rate of fluid in a closed tube. It belongs to a class of meters called variable area meters, which measure flow rate by allowing the cross-sectional area the fluid travels through, to vary, causing a measurable effect.

Atmospheric pressure, gauge pressure, vacuum pressure and absolute pressure

• Absolute pressure is zero-referenced against a perfect vacuum, so it is equal to gauge pressure plus atmospheric pressure.
• Gauge pressure is zero-referenced against ambient air pressure, so it is equal to absolute pressure minus atmospheric pressure.
• Vacuum pressure.  Pressures below atmospheric pressure are called vacuum pressures and are measured by vacuum gages that indicate the difference between the     atmospheric pressure and the absolute pressure.
• Atmospheric pressure.  The atmospheric pressure is the pressure that an area experiences due to the force exerted by the atmosphere.

Types of equilibrium of floating bodies

There are three conditions of equilibrium for floating bodies.

• Stable Equilibrium.  If a floating body is given a small angular displacement (disturbing moment) and after the removal of that Force or moment, body comes back to its original position. It is called as Stable Equilibrium.
• Unstable Equilibrium.  If a floating body is given a small angular displacement (disturbing moment) and after the removal of that Force or moment, body does not come back to its original position. It is called as Unstable Equilibrium.
• Neutral Equilibrium.  If a body in water or any liquid is given a slight angular displacement, it will neither rotates nor goes to the original position but attains a new position. This type of Equilibrium is known as Neutral Equilibrium.

Stagnation pressure in compressible fluid

Limitation of Bernoulli's Equation:

• The Velocity of Liquid particle in the centre of a pipe is maximum and gradually decreases towards the walls of the pipe due to friction. Thus while using Bernoulli's Equation, only the Mean Velocity of the Liquid should be taken into account because the Velocity of Liquid particles is not uniform. As per assumption it is not practical.
• There are always some external Forces acting on the Liquid, which affects the Flow of Liquid. Thus while using Bernoulli's Equation, all such external forces are neglected which is not happened in actual practise. If some Energy is supplied to or extracted from the Flow, same should also taken into account.
• In Turbulent Flow some Kinetic Energy is converted into Heat Energy and in a Viscous Flow some Energy is lost due to Shear Forces. Thus while using Bernoulli's Equation all such losses should be neglected, which is not happened in actual practise.
• If the Liquid is Flowing through curved path, the Energy due to Centrifugal Forces should also be taken into account.

Bulk modulus and compressibility

All materials, whether solids, liquids or gases, are compressible, i.e. the volume V of a given mass will be reduced to V - dV when a force is exerted uniformly all over its surface. If the force per unit area of surface increases from p to p + dp, the relationship between change of pressure and change of volume depends on the bulk modulus of the material.
 

Bulk modulus (K) = (change in pressure) / (volumetric strain)
 

The concept of the bulk modulus is mainly applied to liquids, since for gases the compressibility is so great that the value of K is not a constant.
 

The terms compressibility and incompressibility describe the ability of molecules in a fluid to be compacted or compressed (made more dense) and their ability to bounce back to their original density, in other words, their "springiness." An incompressible fluid cannot be compressed and has relatively constant density throughout. Liquid is an incompressible fluid. A gaseous fluid such as air, on the other hand, can be either compressible or incompressible. 

Falling sphere-type viscometer

A number of methods are used to measure the viscosity of fluids. These are typically based on one of three phenomena—a moving surface in contact with a fluid, an object     moving through a fluid, and fluid flowing through a resistive component. These phenomena utilize three major viscometers in the industry, i.e., a rotating viscometer, a falling-ball viscometer, and a capillary viscometer. The falling ball viscometer typically measures the viscosity of Newtonian liquids and gases.

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