Fluid Mechanics and Machines (Short Answer Questions from BTech Exams)

Basic Concepts and Definitions

What are the different properties of liquid? (RTU 2023)

Capillary action, Cohesive and adhesive forces, Surface tension, vapour pressure, Viscosity etc.

Define ideal fluid. What will be Viscosity, Shear stress. Surface tension. Bulk modulus of elasticity for ideal fluid and real fluid. (RTU 2020)

A fluid is said to be ideal when it cannot be compressed and the viscosity doesn’t fall in the category of an ideal fluid. It is an imaginary fluid which doesn’t exist in reality.

Ideal fluid

Non-viscous, frictionless, and incompressible.
Does not offer shear resistance against the flow.
Bulk modulus is infinite.
Used in mathematical analysis and flow problems.
No such fluid exists in a practical situation.
For an ideal fluid, the surface tension is zero

Real fluid

Posses the properties such as viscosity, surface tension, and compressibility.
Offers resistance against the flow.

What do you mean by Newtonian and non-Newtonian fluids? (AKTU 2022, RTU 2022)

Newtonian fluid. When the fluid obeys Newton’s law of viscosity, it is known as a Newtonian fluid.
Non-Newtonian fluid. When the fluid doesn’t obey Newton’s law of viscosity, it is known as Non-Newtonian fluid.

Distinguish between compressible and incompressible fluids. (PTU 2021)

Compressible fluids, like gases, alter their volume drastically based on changes in pressure and temperature, while incompressible fluids display an insignificant change in volume even when pressure or temperature fluctuates.

Define ideal fluid. (AKTU 202)

A fluid is said to be ideal when it cannot be compressed and the viscosity doesn’t fall in the category of an ideal fluid. It is an imaginary fluid which doesn’t exist in reality.

What is the difference between an ideal and a real fluid? (HPTU 2021, RGPV 2023)

An ideal fluid (also called Perfect Fluid) is one that is incompressible and has no viscosity. Ideal fluids do not actually exist, but sometimes it is useful to consider what would happen to an ideal fluid in a particular fluid flow problem in order to simplify the problem.
Real fluids are fluids with viscosity. These fluids always provide the shear resistance.

Explain capillary action, what are the different forces involved in capillary action. (RTU 2020)

The phenomenon of rising water in the tube of smaller diameter is called the capillary rise.
Capillary action is the movement of a liquid through or along another material against an opposing force, such as gravity.
Capillary action depends on cohesion, the attraction between particles of the same substance, and adhesion, the attraction between particles of different substances.

Describe capillary rise. (AKTU 2022, RTU 2022)

The phenomenon of rising water in the tube of smaller diameter is called the capillary rise.

Write down the expression for capillary fall. (JNTUH 2023)

Consider following figure.

h = height of capillary rise

d = diameter of capillary tube

α = angle of contact of the water surface.

σ = Force of surface tension per unit length of the periphery of the capillary tube.

Then h = 4σcosα/wd = 4σcosα/ρgd

Define viscosity and derive its units and dimensions. (PTU 2023)

The viscosity of a liquid is its property which controls its rate of flow.

Consider a thin layer of a liquid sandwiched between two flat parallel plates as shown in Figure. Now let us apply a force (Ft) on the upper plate which will cause it to move with respect to the lower one.

Let A = area of the plate .

F_t = shear stress ´ Area = t ´ A = μ dv/dy A

So, In S.I. units, the unit of viscosity is N sec/m²

Explain how viscosity varies with temperature. What will be the effect of temperature on the viscosity of the liquid and gas, explain and draw graph between viscosity and temperature. (RTU 2020, AKTU 2022)

In liquids, when temperature increases, the distance between molecules increases and the cohesive force decreases. So, viscosity of liquids decrease when temperature increases.
In the case of gases, the contribution to viscosity is more due to momentum transfer. As temperature increases, more molecules cross over with higher momentum differences. Hence, in the case of gases, viscosity increases with temperature.

The graph between viscosity and temperature is shown below.

Define compressibility and bulk modulus. (JNTUH 2023)

The compressibility of fluid is essentially a criterion of the density modification in the fluid resulting in a specific change which is the pressure. Commonly, gases have high compressibility, while maximum liquids are extremely poor compressible.

The two categories of fluid : liquids and gases, differ in the extent of volume change under an external pressure. The volumetric strain is defined through a "Bulk Modulus" β , as,

Δp = -β(Δv/v₀)

Where, v_o is the initial volume and Δp and Δv are increases of the respective parameters.

Define specific Gravity. (RTU 2022)

The specific gravity of a liquid may be defined as the ratio of its specific weight to that of a standard substance at a standard temperature. For liquids, pure water is taken as a standard substance and at 4⁰C.

Specific gravity = w_liquid/w_water

Differentiate between mass density and specific volume. (AKTU 2022, JNTUH 2023)

The specific volume is the reciprocal of the density of the material, which is the mass per unit volume i.e. r = (1/v) = (m/V). The “Specific Gravity” of a substance is the ratio of its mass to that of an equal volume of water at the same temperature and pressure.

State the Newton’s Law of Viscosity. Compare it with Hook's law. (AU 2023, GTU 2022, HPTU 2021, RTU 2020, 2022)

Hooke's law describes the mechanical behaviour of an ideal solid. Newton's law describes the mechanical behaviour of an ideal viscous fluid.

Mention specific weight and specific volume of a fluid. (BPUT 2020)

The specific weight of liquid may be defined as the weight per unit volume, at the standard temperature and pressure. The variation in the specific weight of water with the variation of pressure and temperature is also so small, that it is generally neglected. It is also known as weight density and is denoted by ‘ω ‘ The specific weight of water is taken as 9.81 kN/m³ in SI units. The specific weight of mercury is taken as 13.33 kN/m³ in SI units.
Specific volume = total volume/mass

What is, the property by which its own molecules are attracted, called? (BPUT 2020)

Cohesion

Give the SI units of the following: kinematic viscosity, Dynamic Viscosity, pressure. (GTU 2022)

Unit of kinematic viscosity is m²/s.

Unit of dynamic viscosity is Ns/m²

Unit of pressure is N/m²or Pascal.

Differentiate dynamic and kinematic viscosity with unit of each. (HPTU 2021, PTU 2021)

Dynamic viscosity

The ratio of shear stress to rate of shear strain is called dynamic viscosity.
It represents viscous forces in fluids.
It is useful when only viscous forces are dominant in the flow.
Its unit is 1 Ns/m² = 10⁴ Poise.

Kinematic viscosity

Ratio of dynamic viscosity to mass density is called kinematic viscosity.
It represents both viscous and inertia forces in fluids.
It is useful when both viscous and inertia forces are pre-dominant.
Its unit is 1 m²/s = 10 Stokes.

Name the characteristics of fluid property to which the following phenomenon are attributable: (i) Rise of shape in tree (ii) Spherical shape of liquid drop (iii) Cavitation (GTU 2022)
Answer:

Rise of shape in tree is due to capillary action.
Surface tension is responsible for the spherical shape of liquid drops. Basically liquid drops take shape of sphere as an effort to reduce surface area.
Cavitation is the phenomenon of formation of vapour bubbles of a flowing liquid in a region where the pressure of the liquid falls below the vapour pressure of the fluid. There is sudden collapsing of these bubbles in the region of higher pressure.

One litre of petrol weighs 7.0 N. Calculate the specific weight, density, specific volume and relative density. (AKTU 2022)

Volume of petrol (v) = 1 L

Weight of petrol (w) = 7 N

Acceleration due to gravity = 9.81 m/s²

Mass of 1 litre of petrol, m = 7/g = 7/9.81 = 0.71 kg

Mass density of petrol = mass of petrol/volume of petrol = m/v = 0.71/(1 x 10^-3) = 710 kg/m³

Specific weight of petrol = mg/V = (m/V)g = 710 x 9.81 = 6.97 kN/m³

Specific volume of petrol = total volume/mass = 1 x 10^-3/0.71 = 1.41 x 10^-3 m³/kg

Specific gravity = petrol density/water density = 710/1000 = 0.710

If the surface tension at the air and water interface is 0.0735 N/m, what is the pressure difference between inside and outside an air bobble of diameter 0.01 mm? (GTU 2023)

d = .01 mm = 0.01 x 10^-3 m

σ = 0.0735 N/m

Δp = 8σ/d = 8 x 0.0735/0.01 x 10^-3

= 58800 Pa = 58.8 kPa

Fluid Statics

What are the types of pressure measurements? (AU 2022)

Atmospheric pressure

The atmospheric air exerts a normal pressure upon all surfaces with which it is in contact, and it is known as atmospheric pressure. The atmospheric pressure is also known as ‘Barometric pressure’. The atmospheric pressure at sea level (above absolute zero) is called ‘Standard atmospheric pressure’.

Gauge pressure

It is the pressure, measured with the help of a pressure measuring instrument, in which the atmospheric pressure is taken as datum. The atmospheric pressure on the scale is marked as zero. Gauges record pressure above or below the local atmospheric pressure, since they measure the difference in pressure of the liquid to which they are connected and that of surrounding air.

If the pressure of the liquid is below the local atmospheric pressure, then the gauge is designated as ‘vacuum gauge’ and the recorded value indicates the amount by which the pressure of the liquid is below local atmospheric pressure, i.e. negative pressure. (Vacuum pressure is defined as the pressure below the atmospheric pressure).

Absolute pressure

It is necessary to establish an absolute pressure scale which is independent of the changes in atmospheric pressure. A pressure of absolute zero can exist only in complete vacuum. Any pressure measured above the absolute zero of pressure is termed as an ‘absolute pressure’.

A schematic diagram showing the gauge pressure, vacuum pressure and the absolute pressure is given in the following figure.

Mathematically,

Absolute pressure = Atmospheric pressure + gauge pressure

Vacuum pressure = Atmospheric pressure – absolute pressure

Differentiate between absolute pressure and gauge pressure. (BPUT 2020, GTU 2022, HPTU 2022)

Described above.

Distinguish between gauge pressure and vacuum pressure. (JNTUH 2023)

Described above.

Describe single column manometer with neat sketch. (GTU 2023)

A simple manometer, in its simplest form, consists of a U-tube, one end of which is attached to the gauge point and the other is open to the atmosphere as shown in Fig.(a) and (b).

For positive pressure,

h = ( s2h2 - s1h1 ) cm of water

For negative pressure,

h = - ( s1h1 + s2h2 ) cm of water

"s" stand for specific gravity.

State the term total pressure and centre of pressure. (BPUT 2020, JNTUH 2023)

Total Pressure refers to the total force exerted by a static fluid (a fluid at rest) on a surface in contact with it.

Center of Pressure (CP), on the other hand, is the point of application of this total pressure force. Imagine the total force acting on the surface concentrated at a single point, that's the centre of pressure.

How do you determine the fluid pressure and its location on a submerged horizontal surface? (PTU 2023)

Consider a plane horizontal surface immersed in a liquid as shown in the figure.

Let w = Specific weight of the liquid,

A = Area of the immersed surface in m2

x̅ = Depth of the horizontal surface from the liquid level in metres

P = Weight of the liquid above the immersed surface

= Specific weight of liquid × volume of liquid

= Specific weight of liquid × area of surface × depth of liquid

= wAx̅

Explain Archimedes principle. (GTU 2023)

It states that when a body is totally or partially immersed in a fluid, it is lifted by a force which is equal to the weight of the fluid displaced by the body. (This force is called Buoyancy).

The buoyancy force shall be experienced by a solid in any fluid, whether gas or liquid, or when the solid spans more than one fluid, one above the other. Similarly, it is not limited to the situation that the solid be fully immersed in a fluid. When immersed partially, the upward force is proportional to the volume of fluid displaced by the extent of immersion.

Buoyant force

FB = ρgv = wv

Where, ρ is the fluid density and `v’ is the volume of the fully submerged body, w is the specific weight of fluid. In other words, `v’ is the volume of the fluid displaced by the body.

Explain the terms metacentre and metacentric height. (RTU 2022)

The location M at which the line of action of buoyant force meets the centroidal axis of the body, when disturbed, is defined as metacentre. The distance of this point from the centroid of the body is called metacentric height. This is illustrated in Figure.

If the metacentre is above the centroid of the body, the floating body will be stable. If it is at the centroid, the floating body will be in neutral equilibrium. If it is below the centroid, the floating body will be unstable.

The larger the metacentric height, the better will be the stability. Referring to the following figure, the centre of gravity G is above the centre of buoyancy B.

After a small clockwise tilt, the centre of buoyancy has moved to B'. The line of action of this force is upward, and it meets the body centre line at the metacentre M which is above G.

In this case, metacentric height is positive, and the body is stable.

It may also be noted that the couple is anticlockwise. If M falls below G, then the couple will be clockwise and the body will be unstable.

Define stable, unstable and neutral equilibrium of a floating body. (GTU 2022, 2023)

Described above.

Define the term buoyancy and centre of buoyancy. (BPUT 2020)

Buoyancy is a force that acts on an object immersed in a fluid (such as water or air), and it is an upward force that counteracts the downward force of gravity. The buoyant force on an object is equal to the weight of the fluid displaced by the object.

The resultant upward pressure or buoyancy of a fluid will act vertically at the centre of gravity of the volume of fluid displaced. This point is known as the centre of buoyancy.

These answers are taken from study material for B. Tech. exams for working professionals by amiestudycircle.com. With our study material which is prepared by IIT, Roorkee faculty (Retd.), no text book study is required.

Fluid Kinematics & Compressible Flow

Define streamline, Streak line and Path line. (AKTU 2023, GTU 2023, HPTU 2021, UTU 2022)

Streamline Flow. A flow, in which the particles have a definite path and the paths of individual particles do not cross each other, is called a stream line flow. It is also called a laminar flow.

Path line is the trace of the path of a single particle over a period of time. Path line shows the direction of the velocity of a particle at successive instants of time. In steady flow path lines and stream lines will be identical.
Streak lines provide an instantaneous picture of the particles, which have passed through a given point like the injection point of a dye in a flow. In steady flow these lines will also coincide with stream lines. Particles P1, P2, P3, P4, starting from point P at successive times pass along path lines shown. At the instant of time considered the positions of the particles are at 1, 2, 3 and 4. A line joining these points is the streak line.

Describe laminar and turbulent flow. (AKTU 2023, GTU 2023)

Laminar flow If the flow is smooth and if the layers in the flow do not mix macroscopically then the flow is called laminar flow. For example a dye injected at a point in laminar flow will travel along a continuous smooth line without generally mixing with the main body of the fluid.
Turbulent flow In turbulent flow fluid layers mix macroscopically and the velocity/temperature/mass concentration at any point is found to vary with reference to a mean value over a time period. A dye injected into such a flow will not flow along a smooth line but will mix with the main stream within a short distance.

The difference between the flows can be distinguished by observing the smoke coming out of an incense stick. The smoke in still air will be found to rise along a vertical line without mixing. This is the laminar region. At a distance which will depend on flow conditions the smoke will be found to mix with the air as the flow becomes turbulent.

Laminar flow will prevail when viscous forces are larger than inertia forces.

Turbulence will begin where inertia forces begin to increase and become higher than viscous forces.

Explain rotational and irrotational flow. (PTU 2021)

Rotational flow

A flow in which the fluid particles also rotate ( i.e. have some angular velocity) about their own axes, while flowing is called a rotational flow. Various rotational components are

\(\begin{array}{l}{w_x} = \frac{1}{2}\left( {\frac{{\partial w}}{{\partial y}} - \frac{{\partial v}}{{\partial z}}} \right)\\{w_y} = \frac{1}{2}\left( {\frac{{\partial u}}{{\partial z}} - \frac{{\partial w}}{{\partial x}}} \right)\\{w_z} = \frac{1}{2}\left( {\frac{{\partial v}}{{\partial x}} - \frac{{\partial u}}{{\partial y}}} \right)\end{array}\)

Irrotational Flow (Potential flow)

A flow in which the fluid particles do not rotate about their do not rotate about their own axes, and retain their original orientations, is called an irrotational flow.

For irrotational flow

\(\begin{array}{l}{w_x} = \frac{1}{2}\left( {\frac{{\partial w}}{{\partial y}} - \frac{{\partial v}}{{\partial z}}} \right) = 0\\{w_y} = \frac{1}{2}\left( {\frac{{\partial u}}{{\partial z}} - \frac{{\partial w}}{{\partial x}}} \right) = 0\\{w_z} = \frac{1}{2}\left( {\frac{{\partial v}}{{\partial x}} - \frac{{\partial u}}{{\partial y}}} \right) = 0\end{array}\)

Define uniform and Non-Uniform flow. (RTU 2022)

Uniform Flow

A flow in which the velocities of liquid particle at all sections of the pipe or channel are equal, is called a uniform flow, this term is generally applied to flow in channels.

∂V/∂T = 0

Non-Uniform Flow

A flow in which the velocities of liquid particles at all sections of the pipe or channel are not equal, is called a non uniform flow.

Differentiate between steady flow and unsteady flow. (AKTU 2023)

Steady Flow

A flow in which the quantity of liquid flowing per second is constant, is called a steady flow. A steady flow may be uniform or non-uniform.

\(\frac{{\partial V}}{{\partial t}} = 0,\frac{{\partial p}}{{\partial t}} = 0,\frac{{\partial \rho }}{{\partial t}} = 0\)

Unsteady Flow

A flow in which the quantity the of liquid flowing per second is not constant i.e. flow parameters changes with time, is called unsteady flow.

∂V/∂T ≠ 0

Define the following: (i) Uniform and Non-Uniform Flow (ii) 1D, 2D, 3D flow (iii) Compressible vs Incompressible flows (AKTU 2023)

Uniform and Non-Uniform Flow. Described above.
One-Dimensional Flow. A flow whose streamline may be represented by a straight line is called one dimensional flow. It is because of the reason that a straight streamline, being a mathematical line, possesses on dimension only; i.e. either x-x, or y-y or z-z direction. 1D flow examples include flow through a pipe or flow along a river.
Two-Dimensional Flow. A flow, whose streamlines may be represented by a curve, is called a two dimensional flow. It is because of the reason that a curved streamline will be along any two mutually perpendicular directions. 2D flow examples include flow over a flat surface or flow over an air foil.
Three-dimensional Flow. A flow, whose streamlines may be represented in space i.e., along three mutually perpendicular directions, is called three dimensional flow. 3D flow examples include flow in a tornado or flow around a three-dimensional object like a car or airplane.
Compressible Flow. A flow in which the volume and thus the density of the flowing fluid changes during the flow, is called a compressible flow. All the gases are generally considered to have compressible flows.
Incompressible Flow. A flow in which the volume and thus the density of the flowing fluid does not change during the flow, is called an incompressible,. All the liquids are, generally, considered to have incompressible flow.

How do you relate stream function and velocity potential function? (BPUT 2020)

Stream function

In a two dimensional flow consider two streamlines S1 and S2. A stream function is so defined that it is constant along a streamline and the difference of for two streamlines is equal to the flow rate between them.

Thus ψB - ψB flow rate between S1 and S2. The flow left to right is taken as positive, in the sign convention. The velocities u and v in x and y directions are given by

u = ∂ψ/∂y

v = -∂ψ/∂x

Velocity potential

In irrotational flows, the velocity can be written as a negative gradient of a scalar function φ called velocity potential.

u = -∂φ/∂x

v = -∂φ/∂y

w = -∂φ/∂z

Write the uses of the Continuity Equation.(AU 2022)

The continuity equations can be used to demonstrate the conservation of a wide range of physical phenomena, including energy, mass, momentum, natural numbers, and electric charge. The continuity equation offers useful knowledge about the flow of fluids and their behaviour as they go through a pipe or hose.

What are the assumption made in continuity equation? (AU 2023)

Following are the assumptions of continuity equation:

The tube is having a single entry and single exit
The fluid flowing in the tube is non-viscous
The flow is incompressible
The fluid flow is steady

Obtain the equation to the streamlines for the velocity field, given as: V = 2x3i - 6x2yj. (GTU 2022)

Given that V = 2x3i - 6x2yj

Here u = 2x3; v = 6x2y

The streamlines in two dimensions are defined by

dx/u = dy/v

dy/dx = v/u = -6x2y/2x3 = -3y/x

Separating the variables

dy/y = -3dx/x

Integrating

ln(y) = -3ln(x) + C1

Or, yx3 = C

Distinguish between subsonic and supersonic flow. (GTU 2022)

According to the magnitude of Mach number M = U/C where U is the velocity of body in a compressible fluid, the flows are classified as follows:

Bernoulli's Equation and its Applications

Write the assumptions made for Euler’s equation of motion. (AKTU 2022)

The fluid is non-viscous (i.e. the frictional losses are aero)
The fluid is homogeneous and incompressible (i.e. = constant)
The flow is continuous, steady and along the streamline.
The velocity of flow is uniform over the section.
No energy or force, except gravity and pressure forces is involved in the flow.

What are the limitations of Bernoulli's equation? (PTU 2021)

The Bernoulli’s theorem has been derived on certain assumptions, which are rarely possible. Thus the Bernoulli’s theorem has the following limitations;

The Bernoulli’s equation has been derived under the assumption that the velocity of every liquid particle, across any cross section of the pipe, is uniform. But in actual practice, it is not so. The velocity of liquid particle in the centre of a pipe is maximum, and gradually decreases towards the walls of the pipe duct to pipe friction. Thus, while using this equation, only the mean velocity of the liquid should be taken into account.
The Bernoulli’s equation has been derived under the assumption, that no external forces, except the gravity force is acting on the liquid. But in actual practice, it is not so. There are always some external forces (such as pipe frictions) acting on the liquid, which affect the flow of the liquid. Thus while using the Bernoulli’s equation, all such external forces should be neglected. But if some energy supplied to, or extracted from the flow, the same should also be taken into account.
The Bernoulli’s equation has been derived, under the assumption, that there is no loss of energy of the liquid particle while flowing. But in actual practice, it is rarely so. In a 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.
If the liquid is flowing in a curved path, the energy due to centrifugal force should also be taken into account.

Write the Bernoulli's equation applied between two sections with losses. (RGPV 2022)

Bernoulli's equation is

\(\frac{{{p_1}}}{\gamma } + {Z_1} + \frac{{{v_1}^2}}{{2g}} = \frac{{{p_2}}}{\gamma } + {Z_2} + \frac{{{v_2}^2}}{{2g}} + {H_f}\)

Where Hf is loss of head.

These losses are:

Major loss

Loss of Head Due to Friction (hf = fLV2/2gD), f is friction factor = 4 x coefficient of friction

Minor losses

Loss of head due to sudden enlargement (hL = (V1 - V2)2/2g)
Loss of head due to sudden contraction (hL = 0.5V22/2g)
Loss of head at entrance in a pipe (hL = 0.5V2/2g)
Loss of head at exit in a pipe (hL = V2/2g)

Define the term “hydraulic gradient line”. (AU 2023, BPUT 2020)

The total energy plotted along the flow to some specified scale gives the energy line. When losses (frictional) are negligible, the energy line will be horizontal or parallel to the flow direction.

For calculating the total energy, kinetic, potential and flow (pressure) energy are considered.

Energy line is the plot of (P/γ) + z + (V2/2g) along the flow. It is constant along the flow when losses are negligible.

The plot of (P/γ) + z along the flow is called the hydraulic gradient line (HGL). When velocity increases this will dip and when velocity decreases this will rise.

An example of plot of these lines for flow from a tank through a venturimeter is shown in following figure.

How is vena contracta defined? (HPTU 2021)

It has been observed that the jet after leaving the orifice, gets contracted. the maximum contraction takes place at a section slightly on the down stream side of the orifice, where the jet is more or less horizontal. Such a section is known as vena contracta as shown by section C-C in given figure.

The distance of vena contracta depends upon the size of orifice and the head of water. generally, this section is at a distance of about d/2 from the plane of orifice, where ‘d’ is the orifice diameter.

Classify orifice based on shape, size and nature of discharge. (GTU 2023)

The Orifices are classified on the basis of their size, shape, nature of discharge and shape of upstream edge.

Based on size

The Orifice are classified as Small Orifice or Large orifice depending upon the size of Orifice and head of liquid from the centre of the Orifice. If the head of liquid from the centre of the Orifice is more than five times the depth of Orifice, the Orifice is called Small Orifice. And if the head of Orifice, the Orifice is called Small Orifice. And if the head of liquids is less than five times the depth of Orifice, it is known as Large Orifice.

Based on shape

The Orifices are classified as

Circular Orifice
Triangular Orifice
Rectangular Orifice
Square Orifice

depending upon their cross-sectional areas.

Based on edge

The Orifices are classified as

Sharp-edged Orifice
Bell-mouthed orifice

depending upon the shape of upstream edge of the Orifices.

Based on nature of discharge

The Orifices are classified as

Free discharging Orifices
Drowned or Submerged Orifices

depending upon the nature of discharge.

The Sub-merged Orifices are further classified as

Fully Sub-merged Orifices
Partially Sub-merged Orifices

What are the advantages of venturimeter over orifice meter? (JNTUH 2023)

The advantage of orificemeter over venturimeter is that its length is short and hence it can be used in a wide variety' of application. Venturimeter has excessive length. The disadvantage of orificemeter is that a sizeable pressure loss is increased because of the flow separation downstream of the plate. In a venturimeter the expanding section keeps boundary layer separation to a minimum, resulting in good pressure recovery across the meter.

Give the difference between an orifice and a mouthpiece. (GTU 2022, HPTU 2022)

Orifice: It is a small opening of any Cross-section (Such as Circular, Triangular ,rectangular etc) on the side or at bottom of a tank, through which a fluid is flowing.

Mouthpiece: A mouthpiece is short length of a pipe which is two to three times its diameter in length fitted in a tank or vessel containing the fluid.

What is Pitot-tube? (HPTU 2022)

A Pitot tube is a simple instrument to determine the velocity of flow at the required point in a pipe or a stream. In its simplest form, a Pitot tube consists of a glass tube bent through 900 as shown in the Figure.

Velocity is calculated from

h = v2/2g

How are the weirs and notches classified? (HPTU 2022)

Notch

A notch may be defined as an opening provided in the side of a tank or vessel such that the liquid surface in the tank is below the top edge of the opening.

There are several types of notches, depending upon their shapes. However, the following are important from subject point of view:

Rectangular notch,
Triangular notch,
Trapezoidal notch, and
Stepped notch.

A weir may be defined as any regular obstruction in an open stream over which the flow takes place. It is made of masonry or concrete.

Weir

There are several types of weirs depending upon their shapes, nature of discharge, width of crest or nature of crest.

The following are important from subject point of view:

According to shape

Rectangular weir, and
Cipoletti weir.

According to nature of discharge

Ordinary weir, and
Submerged or drowned weir.

According to the width of crest

Narrow-crested weir, and
Broad-crested weir.

According to the nature of crest

Sharp-crested weir, and
Ogee weir

Distinguished between notch and weir. (GTU 2023)

Described above.

What are the advantages of triangular notch or weir over rectangular notch or weir. (JNTUH 2023)

For a right angled F'-notch or weir the expression for the computation of discharge is very simple.
For low discharges, a triangular notch gives more accurate results than a rectangular notch.
In a given triangular notch, only one reading, i.e., head (H) is required to be taken for the measurement of discharge.
Ventilation of a triangular notch is not necessary.
The same triangular notch can measure a wide range of flows accurately.

Flow through Pipes and Vortex Motion

Describe major and minor losses in pipes. (AKTU 2022, 2023, JNTUH 2023)

Already explained.

What are minor head losses in pipes? (PTU 2023)

Already explained.

What do you mean by flow through parallel pipes? (AU 2022)

A combination of two or more pipes connected between two points so that the discharge divides at the first junction and rejoin at the next is known as pipes in parallel. See following figure.

Here the head loss between the two junctions (M and N) is same for all the pipes.

Thus the total discharge

Q = Q1 + Q2 + Q3

What is an impulse momentum equation? (HPTU 2021)

This equation states that the vector sum of all external forces acting on a control volume in a fluid flow equals the time rate of change of linear momentum vector of the fluid mass in the control volume.

For a steady flow, in the x-direction,

Fpx + Fsx + Fbx = (Mx)out - (Mx)in = (ρQVx)out - (ρQVx)in

Fpx, Fsx and Fbx represent x-component of pressure force, shear and body force respectively acting on the control volume surface.

Give the mathematical expression for the kinetic energy correction factor to define the same. (GTU 2022, 2023, PTU 2023)

The kinetic energy correction factor is a multiplying factor used with the kinetic energy term of Bernoulli’s equation, while applying the equation for real flow, through a flow passage.

In engineering problems, in order to simplify the process, the kinetic energy at any section is generally prescribed in terms of average velocity V and a factor called kinetic energy correction factor, usually denoted as α, to account for kinetic energy variation.

α = (1/AV3)∫u3dA

Explain vortex motion. (PTU 2023)

Vortex motion is defined as a motion in which the whole fluid mass rotates about an axis. A mass of fluid in rotation about a fixed axis is called vortex,

A vortex motion is characterised by a flow pattern wherein the stream lines are curved. When fluid flows between curved stream lines, centrifugal forces are set up and these are counter balanced by the pressure force acting in the radial direction.

The vortex flow is of the following types:

Forced vortex flow; and
Free vortex flow;

Differentiate between free and forced vortex. (AKTU 2022, JNTUH 2021)

Two types of vortices are distinguished in the dynamics of the motion: forced and free vortices. The forced vortex is caused by external forces on the fluid, such as the impeller of a pump, and the free vortex naturally occurs in the flow and can be observed in a drain or in the atmosphere of a tornado.

Laminar, Turbulent & Boundary Layer Thickness

Describe the significance of Reynold’s number. (AKTU 2022, 2023, RTU 2020)

Prof. Reynold found that the value of critical velocity is governed by the relationship between the inertia forces and viscous forces (i.e. viscosity). He derived a ratio of these two forces and found out a dimensionless number known as Reynold’s number i.e.

R = inertial force/viscour force

\( = \frac{{\rho {U^2}}}{{(\mu U/d)}} = \frac{{\rho Ud}}{\mu } = \frac{{Ud}}{\nu }\)

It may be noted that the Reynold’s number is a dimensionless quantity, and gives us the information about the type of flow (i.e., laminar or turbulent).

Prof. Reynold’s after carrying out a series of experiments, found that if the Reynold’s number for a particular flow is less than 2000, the flow is a laminar flow.

But if the Reynold number is between 2000 and 2800, it is neither laminar flow nor turbulent flow.

It may be noted that the value of critical velocity corresponding with R = 2000, is for a lower velocity and that corresponding with R = 2800 is for a higher critical velocity.

Give the expression for the coefficient of friction in viscous flow. (RTU 2022)

It is usual to designate the frictional resistance to flow in a pipe by Darcy-Weisbach equation as

hf = fLU2/2gD

where f is friction factor.

Also, f = 4f’ where f’ is coefficient of friction.

Give the formula for velocity distribution. (RTU 2022)

In pipe flow, the velocity at the wall is zero due to viscosity and the value increases as the centre is approached.

Velocity distribution is given as

\(\frac{u}{{{u_{mean}}}} = 2\left[ {1 - {{\left( {\frac{r}{R}} \right)}^2}} \right]\)

What do you mean by turbulent flow? (AKTU 2023)

As flow proceeds farther along the flat plate, inertia forces begin to prevail and viscous forces are unable to keep the flow in an orderly way. Reynolds number is the ratio of inertia force to viscous force. As inertia force increases, Reynolds number increases and the flow becomes turbulent. When the Reynolds number Re = UD/υ of a pipe flow exceeds a critical value (2000), the flow becomes turbulent.

How does turbulence affects the flow properties? (PTU 2021)

In general terms, in turbulent flow, unsteady vortices appear of many sizes which interact with each other, exchanging energy, as a result drag increases due to friction effects. The level of turbulence has significant impact on the stability of boundary and shear layers.

Describe laminar and turbulent flow. (AKTU 2023)

Laminat flow

It is a flow, in which the viscosity of the fluid is dominating over the inertia forces. It is more or less a theoretical flow, which rarely comes in contact with the engineers and is also known as a viscous flow. A laminar flow takes place at very low velocities.

Turbulent flow

Described above.

Define the term boundary layer and boundary layer thickness. (JNTUH 2022)

Boundary layer

Because of no slip condition, the fluid is always retarded at and near the boundary. For high velocity flows and provided the fluid does not separate away from the boundary (e.g. in converging flows) this retardation of the fluid due to viscosity is limited to a thin layer near the boundary which is commonly known as boundary layer. Formation of boundary layer gives rise to frictional resistance to flow.

Boundary layer thickness

Boundary layer thickness is the distance from the plate where the velocity differs by one percent from the ambient velocity U. In other words at y = δ, u = 0.99U in which δ is the boundary layer thickness.

Define the displacement thickness. (AKTU 2022, JNTUH 2023)

The displacement thickness δ* is defined as the distance the actual boundary would have to be displaced in order that the actual discharge would be the same as that of an ideal fluid past the displaced boundary.

\(\delta * = \int_0^\infty {\left( {1 - \frac{u}{U}} \right)} dy \simeq \int_0^\delta {\left( {1 - \frac{u}{U}} \right)} dy\)

Explain bluff and streamlined body. (AKTU 2022)

Streamlined body

A body whose surface coincides with the stream lines when placed in a flow, is called a streamlined body. In this case, flow separation takes place only at the training edge or rearmost part of the body.

Bluff body

A body whose surface does not coincide with streamlines when placed in a flow, is called a bluff body.

In this case there is extensive boundary layer separation accompanied by a wake with large scale eddies. Due to large wake formation, the resulting pressure drag is very large as compared to the drag due to friction on the body.

What is Drag? Write types of drag. (GTU 2023)

The total drag FD on an immersed body in a relative free stream velocity V0 is expressed as

FD = CDA(ρV02)/2

where CD is total drag coefficient and A is characteristic area of the body.

Types of drag

Deformation drag. The total drag is in fact sum of deformation drag and form drag. The deformation drag exists at very small velocities, or when the length dimensions are small and kinematic viscosity is large. It must be remembered that deformation drag itself consists of friction drag or surface drag at the boundary and the pressure drag due to variation of pressure caused by wide spread deformation. Deformation drag chiefly depends on projected area and not much on the actual shape of the body.
Form drag. At high Reynolds number if the boundary form (shape) is such that separation occurs, a low pressure area is created in the rear portion of the body and this produces form drag. The form drag is therefore due to the pressure difference between the front and the rear of the body

Differentiate Drag and Lift. (GTU 2023)

Drag force and lift force are two different forces that act on an object moving through a fluid. Drag force is a resistance force that opposes the motion of the object and is parallel to the direction of the flow. It is caused by the interaction between the object and the fluid molecules, resulting in a net force that slows down the object's motion. On the other hand, lift force is a perpendicular force to the direction of the flow and is responsible for the upward motion of the object. It is generated due to the pressure difference between the upper and lower surfaces of the object, resulting in an upward force. While drag force always acts in the direction of the flow, lift force acts perpendicular to it.

Explain Magnus effect. (GTU 2023)

Magnus force is the force exerted on a rapidly spinning cylinder or sphere moving through air or another fluid in a direction at an angle to the axis of spin, following the Bernoulli's relation. This force is responsible for the swerving of balls when hit or thrown with spin. This effect is called Magnus effect.

Dimensional & Model Analysis

What do you mean by ‘Dimensional Analysis’? (AKTU 2022, UTU 2023)

Dimensional analysis is a mathematical method of obtaining the equations governing certain natural Phenomena by balancing the fundamental dimensions, mass, length and time, of the problem considered. These equations are DIMENSIONALLY HOMOGENEOUS EQUATIONS among certain variables.

State Buckingham's π theorem. (AU 2023, PTU 2021, RTU 2022)

The theorem states – If there are n variables in a dimensionally homogeneous equation and if these variable contain m fundamental dimensions such as (M, L, T, etc.) they may be grouped into (n – m) non – dimensional independent n – terms.

Let a variable x1 depends upon n variables viz. x2, x3, x4, then we may write

x1 = f (x2, x3, x4, ……………xn)
in which f stands for the expression “ is a function of ” . the above equation may also be written as

x1 = f (x2, x3, x4, ……………xn) = 0

In this equation, there are n variables and if there are n variables and if there are m fundamental dimensions then according to Buckingham’s Pi - theorem.

f1 (π1, π2, π3, …………..πn – m) = 0

Explain Reynolds model law. (PTU 2023)

In flow situations where in addition to inertia, viscous force is the other predominant force, the similarity of flow in the model and its prototype can be established if Reynolds number is same for both the systems. This is known as Reynolds law and according to this law

Remodel = Reprototype

\(\frac{{{\rho _m}{V_m}{L_m}}}{{{\mu _m}}} = \frac{{{\rho _p}{V_p}{L_p}}}{{{\mu _p}}}\)

where,

ρm = Density of fluid in model,

Vm = Velocity of fluid in model,

Lm = Length or linear dimension of the model,

μm = Viscosity of fluid in model,

and ρp, Vp, Lp and μp are the corresponding values of density, velocity, linear dimension and viscosity of fluid in prototype.

What are the different types of similarities that must exist between model and prototype? (AKTU 2023, AU 2022, PTU 2023)

Geometrical Similarity It is the similarity in shape. For this similarity, the ratios of corresponding length dimensions between the model and the prototype must be the same.
Kinematics Similarity It is the similarity in motion. For this similarity, the ratios of corresponding velocity and acceleration between model and prototype must be the same.
Dynamic Similarity It is the similarity in forces. For this similarity, the ratios of corresponding forces (such as viscous, pressure, elastic etc.) between model and prototype must be the same.

Give the name of four important dimensionless numbers in fluid mechanics. (AKTU 2023)

Brinkman number

\(\begin{array}{l}Br = \frac{{\mu {{({v_0}/{l_0})}^2}}}{{k({T_1} - {T_0})/{l_0}^2}}\\ = \frac{{\mu {v_0}^2}}{{k({T_1} - {T_0})}}\\ = \frac{{(M/Lt){{(L/t)}^2}}}{{(ML/{t^3}T)(T)}}\end{array}\)

Biot Number

\(Bi = \left( {\frac{{hL}}{k}} \right) = \frac{{\left( {\frac{M}{{{t^3}T}}} \right)L}}{{\left( {\frac{{ML}}{{{t^3}T}}} \right)}} = 1\)

Prandtl number

\(\Pr = \frac{{{C_p}\mu }}{k} = \frac{{({L^2}/{t^2}T)(M/Lt)}}{{(mL/{t^3}T)}} = 1\)

Grashof number

\(\begin{array}{l}Gr = \frac{{g\beta ({T_1} - {T_0}){l_o}^3}}{{{v^2}}}\\ = \frac{{L{t^{ - 2}}{T^{ - 1}}T{L^3}}}{{{{({L^2}/t)}^2}}}\\ = 1\end{array}\)

Nomenclature

k = thermal conductivity
ν = kinematic viscosity
β = thermal coefficient of volumetric expansion
Cp = heat capacity at constant pressure

What is the requirement for dynamic similarity? (AKTU 2023)

For this similarity, the ratios of corresponding forces (such as viscous, pressure, elastic etc.) between model and prototype must be the same.

Hydraulic Turbines

Mention the classification of turbine according to the type of energy at inlet. (BPUT 2020)

Impulse turbine

In the case of impulse turbine all the potential energy is converted to kinetic energy in the nozzles. The impulse provided by the jets is used to turn the turbine wheel. The pressure inside the turbine is atmospheric. This type is found suitable when the available potential energy is high and the flow available is comparatively low. Some people call this type as tangential flow units. Later discussion will show under what conditions this type is chosen for operation.

Reaction Turbine

In reaction turbines the available potential energy is progressively converted in the turbines rotors and the reaction of the accelerating water causes the turning of the wheel. These are again divided into radial flow, mixed flow and axial flow machines. Radial flow machines are found suitable for moderate levels of potential energy and medium quantities of flow. The axial machines are suitable for low levels of potential energy and large flow rates. The potential energy available is generally denoted as “head available”. With this terminology plants are designated as “high head”, “medium head” and “low head” plants.

Describe the difference between impulse and reaction turbine. (AKTU 2023, AU 2022, GTU 2022, 2023, PTU 2023)

Water Flow

Impulse Turbine: In an impulse turbine, water flows over the blades as a high-velocity jet. The pressure of the water remains constant, and the energy is derived from the kinetic energy of the water.
Reaction Turbine: In a reaction turbine, water flows over the blades in a controlled manner, and both the pressure and velocity of the water change as it passes through the turbine. The energy is derived from both kinetic and potential energy.

Blade Design

Impulse Turbine: The blades of an impulse turbine are designed to efficiently capture the kinetic energy of the water jet. These blades are typically shaped like buckets or cups.
Reaction Turbine: The blades of a reaction turbine are designed to efficiently utilize both the kinetic and potential energy of the water. They are shaped like airfoils or propeller blades.

Pressure Variation

Impulse Turbine: There is no pressure drop in an impulse turbine. The pressure of the water remains constant as it flows over the blades.
Reaction Turbine: In a reaction turbine, there is a pressure drop as water passes through the turbine. The pressure decreases from the inlet to the outlet.

Efficiency

Impulse Turbine: Impulse turbines are generally more efficient at high heads (large water drop) and low flow rates
Reaction Turbine: Reaction turbines are often more efficient at low heads (small water drop) and high flow rates.

Applications

Impulse Turbine: Impulse turbines are commonly used in high head, low flow applications. Examples include Pelton turbines.
Reaction Turbine: Reaction turbines are suitable for low head, high flow applications. Examples include Francis and Kaplan turbines.

What is draft tube? Why it is used in reaction turbine? (AU 2023, BPUT 2020, RTU 2020)

The turbines have to be installed a few meters above the flood water level to avoid inundation. In the case of impulse turbines this does not lead to significant loss of head. In the case of reaction turbines, the loss due to the installation at a higher level from the tailrace will be significant. This loss is reduced by connecting a fully flowing diverging tube from the turbine outlet to be immersed in the tailrace at the tube outlet. This reduces the pressure loss as the pressure at the turbine outlet will be below atmospheric due to the arrangement. The loss in effective head is reduced by this arrangement. Also because of the diverging section of the tube the kinetic energy is converted to pressure energy which adds to the effective head.

The draft tube thus helps

to regain the lost static head due to higher level installation of the turbine and
helps to recover part of the kinetic energy that otherwise may be lost at the turbine outlet.

Name the different types of draft tubes used in the turbines? (PTU 2023)

Straight divergent tube, Moody’s bell mouthed tube, Simple elbow, Elbow having square outlet and circular inlet.

Explain Specific Speed of a turbine. (AKTU 2023, AU 2022, PTU 2023)

The specific speed of a turbine is defined as the speed of a turbine which is identical in shape, geometrical dimensions, blade angles, gate opening, etc. which would develop unit power when working under a unit head.

Ns = N√P/H5/4

where P is in kW and H is in metres.

Define hydraulic efficiency. (AU 2022)

It is defined as the ratio of the power produced by the turbine runner and the power supplied by the water at the turbine inlet.

ηH = power produced by runner/ρQgH

where Q is the volume flow rate and H is the net or effective head. Power produced by the
runner is calculated by the Euler turbine equation P = Qρ [u1Vu1 – u2Vu2]. This reflects the runner design effectiveness.

Centrifugal and Positive Displacement Pumps

Define a pump. (AKTU 2022)

A pump moves fluid by creating a pressure difference between the inlet and outlet of the device. The movement of the piston, impeller, or other mechanisms in the pump creates this pressure difference and drives the fluid through the pump. Different types of pumps use different mechanisms to create the pressure difference and move the fluid, such as the movement of a piston, the spinning of an impeller, or the rotation of blades in an axial flow pump.

Explain the difference between Turbine and Pump. (AKTU 2023, GTU 2022, 2023, PTU 2023)

Turbine: turbine is defined as a hydraulic machine which converts hydraulic energy to mechanical energy there by mechanical energy to electrical energy by using generators. Examples: Pelton turbine, Francis, Kaplan turbine.
Pump: pumps are hydraulic machines which convert electrical energy to hydraulic energy where hydraulic energy is in the form of pressure energy Examples: centrifugal pump, reciprocating pump, submersible pump etc.

Mention the components of the centrifugal pump. (AU 2022)

Impeller An impeller is a wheel (or rotor) with a series of backward curved vanes (or blades). It is mounted on a shaft which is usually coupled to an electric motor.
Casing The casing is an airtight chamber surrounding the pump impeller. It contains suction and discharge arrangements, supporting for bearings, and facilitates to house the rotor assembly.
Suction pipe The pipe which connects the centre/eye of the impeller to sump from which liquid is to be lifted is known as suction pipe. In
Delivery pipe The pipe which is connected at its lower end to the outlet of the pump and it delivers the liquid to the required height is known as delivery pipe.

\(\sigma = \frac{{{H_a} - {H_s} - {H_v}}}{{{H_{mano}}}} = \frac{{{H_{sv}}}}{{{H_{mano}}}}\)

where

Ha = Atmospheric pressure expressed in metres of water head,

Hv = Vapour pressure expressed in metres of water head

Hs = total suction head =

Hsv = Net positive suction head (NPSH), and

Hmano = Manometric head.

State the working principle of positive displacement pump. (BPUT 2020)

The reciprocating pump is a positive displacement pump as it sucks and raises the liquid by actually displacing it with a piston/plunger that executes a reciprocating motion in a closely fitting cylinder. The amount of liquid pumped is equal to the volume displaced by the piston.

When will you select a reciprocating pump? (AU 2022)

Reciprocating pumps for industrial uses have almost become obsolete owing to their high capital cost as well as maintenance cost as compared to that of centrifugal pumps. However, small hand-operated pumps such as cycle pumps, football pumps, kerosene pumps, village well pumps and pumps used as important parts of hydraulic jack etc. still find wide applications. The reciprocating pump is best suited for relatively small capacities and high heads.

Describe the slip of a reciprocating pump. (AKTU 2022, 2023)

The difference between the theoretical discharge and actual discharge is called the slip of the pump. That is

Slip = Qth - Qact

What is the difference between a fluid coupling and a fluid torque converter? (GTU 2022)

Hydraulic (or fluid) coupling is a device which is employed for transmission of power from one shaft to another through a liquid medium. It has no mechanical connection or face to face contact. The magnitudes of input and output torques are equal.
Hydraulic torque converter is a device used for transmitting increased or decreased power from one shaft to another. A variable torque is impressed on the driven member without the use of a gear train or clutch. The torque at the driven shaft may be increased about five times the torque available at the driving shaft with an efficiency of about 90 percent.

What is priming? Why is it necessary? (BPUT 2020, JNTUH 2022, RTU 2020)

Sometimes pump fails to lift liquid at the time of its starting. This happens because suction pipe is filled with air when liquid flows back to sump due to failure of one-way valve fitted at the entrance of suction pipe. Since air is lighter than liquid, rotation of impeller does not create enough suction head to raise liquid from sump. It is overcome by filling the suction pipe and the space around the impeller with liquid by pouring it through a funnel fixed in delivery pipe or by sucking air from the pump using an extraction pump that also pulls liquid from sump and fills the whole space around impeller. This process is called priming.

Define the terms: Suction head, delivery head and manometric head. (RTU 2022, PTU 2023, UTU 2023)

Suction head. It is the vertical height of the centre line of the pump shaft above the liquid surface in the sump from which the liquid is being raised), and
Delivery head It is vertical height of the liquid surface in the tank/reservoir to which the liquid is delivered above the centre line of the pump shaft).
Manometric head The head against which a centrifugal pump has to work is known as the manometric head.

What is cavitation in pump? What are its effect? (BPUT 2020, JNTUH 2021)

Cavitation begins to appear in centrifugal pumps when the pressure at the suction falls below the vapour pressure of the liquid. The intensity of cavitation increases with the decrease in value of NPSH.
The cavitation in a pump can be noted by a sudden drop in efficiency, head and power requireme

The cavitation imposes limitation on the flow rate and speed of rotation of pump (since as the speed of rotation and flow rate of discharge increase the velocity of liquid at inlet increases due to which absolute pressure is reduced which facilitates cavitation).

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