Download DHANALAKSHMI COLLEGE OF ENGINEERING, CHENNAI

DHANALAKSHMI COLLEGE OF ENGINEERING, CHENNAI
DEPARTMENT OF CIVIL ENGINEERING
QUESTION BANK
Title of the Paper: Mechanics of Fluids
Subject Code: CE6303
PART – A
UNIT I
FLUID PROPERTIES AND FLUID STATICS
1.
Define – Fluid
Fluid is a substance, which is capable of flowing. It will continuously deform under
shear deformations. It may be in gaseous state or liquid state.
2.
Differentiate ideal fluid from real fluid.
Ideal fluid does not offer any resistance to shear deformations. Its viscosity is zero
and it is nonexistent. Whereas, real fluid does exist on the universe and it has
viscosity. Hence, a real fluid offers resistance to shear deformations. All fluids
found on the universe are real fluids. For example air and water are real.
3.
Define – Dimension
In common language, dimension means size referring to the length and breadth. For
example, the dimension of a room is 10 m x 8 m. In technical parlance, it means the
symbolic representation of a physical quantity. For example, M for mass, L for
length, T for time, L T-1 for velocity, L T -2 for acceleration, etc.
4.
Define – Density
Density or mass density is defined as the amount of substance present in unit
volume. It can also be defined mathematically as mass per unit volume. It is
denoted by a Greek Symbol, ρ. Its dimension is M L-3. The unit of measurement can
be either kg/m3 or gm/cm3.
5.
Define – Specific Gravity
Specific gravity is defined as the ratio between the density (or specific weight) of
the substance and the density (or specific weight) of water at 4oC. It is a comparison
of densities (or specific weights), which indicates whether the substance is heavier
or lighter than water. Since it is a comparison, it has no dimension and no unit.
6.
Define – Dynamic Viscosity
According to Newton, the shear stress developed between fluid particles due to
differential movements is directly proportional to the velocity gradient (i.e., change
in velocity divided by the distance between them). This can be made as an equation
by introducing a constant of proportionality, which is termed as dynamic viscosity.
τ α du/dy = μ (du/dy)
where
and
τ is shear stress;
du is change in velocity;
dy is distance between the molecules;
μ is dynamic viscosity.
7.
What is the basis for viscosity?
The basis for viscosity is molecular attraction between fluid molecules. By nature,
every molecule is attracted by every other molecule surrounding it. When
molecules travel in differential speed, shear stress is developed between the layers
of the molecules and hence resistance, which is termed as viscosity.
8.
Define – Surface Tension
Adhesive force depends on the types of the molecules involved. For example
adhesion between water and glass is higher than that between water and air. Also
the cohesion between water molecules is higher than the adhesion between water
and air molecules. Consequently, when water is stored in a glass beaker a thin film
of water will be formed on the surface under the influence of tension acting along
the circumference. This tensile force is termed as surface tension. It is denoted by σ,
which has a dimension of F L-1 and unit as N/m or dyne/cm. Draw a sketch here.
9.
Suggest suitable SI units for the measurement of dynamic viscosity.
Suitable units for the measurement of dynamic viscosity can be either kg(f) s/m2 or
N s/m2 or gm(f) s/cm2 or dyne s/cm2. The unit dyne s/cm2 is termed as 1 poise,
which is named after the scientist Poiseullie
10. State Pascal’s law.
Pascal’s law states that the pressure intensity at a point inside a fluid mass is the
same in every direction
11. Pressure at a point is 25 N/cm2. Express this in m head of water and of Hg.
p = γh
where p is pressure intensity;
γ is specific weight of fluid;
and h is the depth of the point at which the pressure is considered.
Therefore, the pressure head, h = p/γ
p = 25 N/cm2 = 25 x 100 x 100 N/m2
Specific weight of water,
γw = 9810 N/m3
Specific weight of mercury,
γm = 13.6 x 9810 N/m3
Pressure head of water,
hw = p/γw = 25 x 100 x 100/9810 = 25.48 m of
water.
Pressure head of mercury,
hm = p/γm = 25 x 100 x 100/(13.6 x 9810)
= 1.87 m of mercury.
12. Define – Buoyancy
Buoyancy or buoyant force is the net resultant upward hydrostatic force acting on a
floating or submerged object.
13. What is gauge pressure?
Pressure can be measured with respect to the local atmospheric pressure, taken as
zero, as the datum, which may be +ve or -ve. It is termed as gauge pressure if it is
+ve. If it is –ve, it is termed as negative or suction or vacuum pressure.
Absolute pressure = Local atmospheric pressure  gauge pressure
pab = pat  p
14. List out different types of pressure measuring equipments.
Pressure measuring equipments are:
(a)
Pressure gauges; and
(b)
Manometers
(i) Simple manometers; and
(ii) Differential manometers.
15. Define – Differential Manometer
Differential manometer is an instrument used to measure the difference in pressure
heads between two points or sections in a pipe line or between two pipe lines. It has
a U-tube filled with a liquid heavier than the liquid in the pipe or liquids in the
pipelines.
UNIT II
FLUID KINEMATICS AND DYNAMICS
1.
Define – Fluid Kinematics
Study of fluids in motion without giving any considerations for the force causing
the motion is fluid kinematics. It is an applied mathematics, which involves only
fluids.
2.
Define – Streamline
Streamline is an imaginary continuous line. It can be drawn through the fluid mass
in motion. The tangent to the streamline at any point will indicate the direction of
the velocity at that point.
3.
Define – Steady Flow
If there is no change in any of the flow parameters at a point with respect to time,
then the flow is said to be steady.
If V is the velocity at a point (x,y,z), then:
V/t = 0
steady flow
Likewise, there is no change in other flow parameters as well in a steady flow.
4.
Define – Non-uniform Flow
If the flow characteristics at a given time do not remain the same at all points, then
the flow is said to be nonuniform.
V/s  0
nonuniform flow
V/x  0; V/y  0; and V/z  0
The velocity vector is not identical at every point at a given instant of time in a nonuniform flow. It varies from place to place at a given instant of time.
5.
Differentiate rotational flow from irrotational flow.
If the fluid elements undergo rotations during the flow, then the flow is rotational.
The orientations of the fluid elements are changed. If there is no rotation or no
change in the orientation, then the flow is irrotational.
6.
What is the basis of continuity equation?
Conservation of mass is the basis for continuity equation. Mass can neither be
created nor destroyed. In a given control volume, the net mass rate of inflow into
the control volume is equal to the rate of change of mass.
7.
Define – Stream Function
A stream function, ψ, is defined as a function of x and y (and t if the flow is
unsteady) such that when differentiated with respect to y, it yields the velocity
component in the x-direction, u. When differentiated with respect to x, it yields the ve velocity component in the y-direction, v. Hence by definition:
u = /y
and
v = -/x
8.
What is a current meter?
Current meter is an instrument, which is used to measure the velocity of flow at a
point in a cross section of open channels. This instrument works on the basis of
conversion of kinetic energy into mechanical energy. Every current meter has to go
with a chart known as ‘Calibration Chart’.
9.
Which velocity is measured by a float?
There are two types of floats: (i) Surface float; and (ii) Sub-surface float.
Surface float measures the surface velocity (vs) from which the average velocity is
calculated as V = 0.85 vs.
10. What is the basis of Euler’s equation?
Energy is the basis of Euler’s equation. Energy can neither be created nor
destroyed. Euler’s equation is derived by the use of Newton’s second law of
motion.
According to Newton’s second law of motion, the time rate of change of
momentum of a fluid mass in any direction is equal to the sum of all the external
forces in that direction, i.e.,
F = d(M V)/dt
where F is the force, M is the mass and V is the velocity.
11. Write the Bernoulli’s equation and identify the terms.
Bernoulli’s equation is:
p/ + Z + V2/2g = constant
where p is pressure;
γ is specific weight of the fluid;
Z is the vertical distance from a datum line;
V is velocity of flow;
and
g is acceleration due to gravity (9.81 m/s2).
p/ stands for the pressure energy, which is termed as pressure head, Z stands for
the potential energy, which is termed as potential head and V2/2g stands for the
kinetic energy, which is termed as velocity head.
12. State why fire hoses are fitted with nozzles at the end.
The purpose of a fire hose is to reach the water to the place where fire is taking
place. This is possible only when the kinetic energy of the flowing jet of water is
high. Nozzle has the capacity to create a jet of water, which will increase the kinetic
energy by converting the pressure energy. This is the reason why nozzles are fitted
to fire hoses.
13. What is a hydraulic grade line?
If a piezometer tube is introduced at a section in a pipe flow carrying a liquid, the
liquid will rise to a height equivalent to the pressure head at that section. The sum
of pressure head and potential head is termed as hydraulic or piezometric head. The
line joining the points of hydraulic head at various sections is termed as hydraulic
grade line.
14. Define – Ventury Meter and State the Basis of its Working
Venturi meter is a flow measuring equipment used to measure the discharge
flowing through a pipe. It works on the Bernoulli’s principle.
It has a convergent cone reducing the diameter from the mouth to throat followed
by a divergent cone increasing the diameter back to its original diameter. In the
convergent cone the diameter decreases and hence the velocity will increase. This
will increase the kinetic energy. To compensate the increase in kinetic energy, the
pressure energy will decrease. The drop in pressure between the mouth and throat is
measured by a differential manometer, which is then equated to the gain in kinetic
energy and solved with the help of continuity equation.
15. Define – Coefficient of Discharge (Cd) of a Notch/Weir
Flow measuring equipments such as venture meter, notches, weirs, etc. work on the
concept of Bernoulli’s principle. Application of Bernoulli’s equation neglects the
losses. The discharge calculated neglecting the loss, which is termed as the
theoretical discharge, will be greater than the actual discharge flowing through the
pipe. In order to correct this anomaly, a correction factor is introduced. This is
known as the coefficient of discharge, which is the ratio between the actual
discharge (Qa) and the theoretical discharge (Qt).
UNIT III
FLOW THROUGH PIPES
1.
What is a hydraulic grade line?
If a piezometer tube is introduced at a section in a pipe flow carrying a liquid, the
liquid will rise to a height equivalent to the pressure head at that section. The sum
of pressure head and potential head is termed as hydraulic or piezometric head. The
line joining the points of hydraulic head at various sections is termed as hydraulic
grade line.
2.
Define – Major Energy Loss in a Pipe
Major energy loss is caused due to pipe friction. It is called as major energy loss
because of its magnitude and it will be taking place continuously over the length of
the pipe in which the flow is taking place. It is directly proportional to the length of
the pipe.
3.
Write an expression for loss of head due to sudden expansion of the pipe.
Head loss due to sudden expansion is given as:
he = (V1 - V2)2/2g
where he is head loss due to expansion;
V1 is velocity of flow before the pipe expansion;
V2 is velocity of flow after the expansion;
and
g is acceleration due to gravity.
4.
Write the Hagen-Poiseuille equation and identify the terms.
Hagen-Poiseuille equation for the pressure drop in a pipe flow is given as:
p = 32  V L/D2
where p is the decrease in pressure between two sections of length L;
V is the velocity of flow through the pipe;
L is the length of the pipe between the sections;
D is the diameter of the pipe;
and
 is the dynamic viscosity of the fluid flowing through the pipe.
5.
Write the Darcy-Weisbach formula and identify the terms.
Darcy-Weisbach formula for the head loss in a pipe flow is given as:
hf = 4 f LV2/(D 2g)
where hf is the head loss in the pipe;
f is the coefficient of friction as applicable to the pipe;
L is the length of the pipe over which the loss is taking place;
V is the velocity of flow through the pipe;
D is the diameter of the pipe;
and
g is the acceleration due to gravity.
State why energy loss takes place when a fluid flows through a pipe.
6.
There will be resistance to the fluid motion due to viscous effects of the fluid as
well as due to the internal surface roughnous of the pipe. This resistance has to be
overcome for the flow to be sustained and hence there will be energy losses taking
place in a pipe flows.
7.
Classify the energy losses in flow through pipes.
There are two types of energy losses in flow through pipes:
Major energy loss due to frictional resistance offered by the pipe; and
Minor energy losses due to sudden expansion or contraction of the pipe, bend, pipe
fittings, etc. Minor losses are very small in magnitude compared to major losses.
8.
Define – Minor Energy Loss in a Pipe
Minor loss is local in character, which may be caused due to local disturbances such
as sudden expansion of the pipe, sudden contraction of the pipe cross section, bend,
pipe fittings, etc. Minor because its magnitude is very small.
9.
What is the loss of head at the entrance to a pipe?
Head loss at the entrance of a pipe is given as:
hi = 0.5 V2/2g
where hi is head loss at the entrance of the pipe;
V is velocity of flow in the pipe;
and
g is acceleration due to gravity.
10. What is a Moody diagram?
Moody diagram also known as Stanton diagram is a plot of friction factor of a pipe
‘f’ as a function of Reynold’s number of flow in the pipe (f Vs. Re) for various
types of pipes such as smooth and rough as well as for various types of flows such
as laminar, transition and turbulent. The ratio between the roughnous element and
diameter of the pipe, which is termed as the relative roughness, is taken as a
parameter to plot the diagram. Please refer to a standard text book for the
diagram.
11. What is meant by pipes in series?
Pipes in series or compound pipes is defined as the pipes of different lengths and
different diameters connected end to end in series to form a single pipe line. Field
conditions may force to go in for different lengths and different diameters.
12. What is an equivalent pipe?
Equivalent pipe is defined as the pipe of uniform diameter having the loss of head
and discharge equal to the loss of head and discharge of a compound pipe
consisting of several pipes of different lengths and different diameters. The uniform
diameter of the equivalent pipe is called as equivalent size of the pipe. The length of
the equivalent pipe is equal to the sum of lengths of all the pipes connected in
series.
13. When are pipes used in series?
There may be a practical situation that the required length of a required diameter
pipe may not be adequately available. In such a situation, one has to go in for
different diameter and different lengths of pipes to form pipes in series.
14. When are pipes used in parallel?
Total head loss in a pipe and the discharge flowing through are proportional to each
other. This means that for a given head loss the discharge is fixed. If there is a need
to increase the discharge for practical reasons, the pipes can be laid in parallel,
which will increase the discharge as many times as that of the number pipes in
parallel.
15. What is meant by pipe network?
A pipe network is an interconnected system of pipes forming several loops and
circuits. Example of such network of pipes is Municipal water supply distribution
system. In such a system, it is required to determine the distribution of flow through
various pipes along with the pressure under which the flow is taking place to ensure
that the required quantity at the required pressure is supplied at all locations.
UNIT IV
BOUNDARY LAYER
1.
Define – Boundary Layer
The velocity of fluid particles will increase from zero velocity at the boundary to
the uniform stream velocity U in the direction normal to the boundary. This
variation in velocity from zero to U will take place over a short distance in a narrow
region. This narrow region of the fluid flow is called as boundary layer.
2.
Define – Boundary Layer Thickness
The narrow region in which the velocity will increase from zero at the surface to the
free flow stream velocity U is called as Boundary Layer. The depth of this narrow
region is termed as the boundary layer thickness, which is zero at the leading edge
and will increase along the boundary in the direction of flow.
3.
Classify boundary layers.
Boundary layer is classified as: Laminar boundary layer; Transitional boundary
layer; and Turbulent boundary layer.
4.
Define – Laminar Boundary Layer
If the flow within the boundary layer is laminar, then it is known as laminar
boundary layer. The distance from the leading edge over which laminar boundary
layer exists is called as the laminar zone. This distance is determined by the use of
Reynold’s number as defined below:
Reynold’s number,
Rex = U x/υ
where
Rex is the Reynold’s number calculated at a section ‘x’ from the
leading edge;
x
is the distance of the section from the leading edge of the plate;
and
U
υ
is free stream velocity of flow;
is the kinematic viscosity of fluid.
It has been found that laminar flow will exist up to the section where the Reynold’s
number is equal to 5 x 105.
5.
Define – Turbulent Boundary Layer
If the flow within the boundary layer is turbulent, then it is known as turbulent
boundary layer. The distance over which turbulent boundary layer exists is called as
the turbulent zone. This distance is determined by the use of Reynold’s number as
defined below:
Reynold’s number,
Rex = U x/υ
where
Rex is the Reynold’s number calculated at a section ‘x’ from the
leading edge;
x
is the distance of the section from the leading edge of the plate;
U
is free stream velocity of flow;
and
υ
is the kinematic viscosity of fluid.
It has been found that turbulent flow will exist beyond the section where the
Reynold’s number is greater than 5 x 105.
6.
Define – Laminar Sub-layer
Whether the boundary layer is laminar or turbulent, there is a thin layer at the
boundary surface wherein the flow is always laminar because of the influence of the
boundary. This layer is known as laminar sub-layer.
7.
Define – Displacement Thickness of a Boundary Layer
Displacement thickness is defined as the distance, measured normal to the
boundary, by which the boundary has to be displaced to compensate the reduction
in flow rate (or mass rate of flow) due to the formation of boundary layer.
8.
Define – Momentum Thickness of a Boundary Layer
Momentum thickness is defined as the distance, measured normal to the boundary,
by which the boundary should be displaced to compensate for the reduction in
momentum of the flowing stream on account of boundary layer formation
9.
Define – Energy Thickness of a Boundary Layer
Energy thickness is defined as the distance, measured normal to the boundary, by
which the boundary should be displaced to compensate for the reduction in kinetic
energy of the flowing stream on account of boundary layer formation
10. What is the limiting value of Reynolds’s number for laminar boundary layer?
Reynold’s number,
Rex = U x/υ
where
Rex is the Reynold’s number calculated at a section ‘x’ from the
leading edge;
x
is the distance of the section from the leading edge of the plate;
and
U
υ
is free stream velocity of flow;
is the kinematic viscosity of fluid.
It has been found that laminar flow will exist up to the section where the Reynold’s
number is equal to 5 x 105.
11. Define – Reynold’s Number as used in Boundary Layer Theory
Reynold’s number,
Rex = U x/υ
where
Rex is the Reynold’s number calculated at a section ‘x’ from the
leading edge;
x
is the distance of the section from the leading edge of the plate;
U
is free stream velocity of flow;
and
υ
is the kinematic viscosity of fluid.
12. Define – Local Coefficient of Drag
It is defined as ratio of the shear stress τo to the quantity ρU2/2, which is denoted by
CD* as:
CD* = τo/(ρU2/2)
where τo
is shear stress;
ρ
is density of the fluid;
and
U
is main stream velocity.
13. Define – Average Coefficient of Drag CD
This is defined as the ratio of the total drag force to the quantity of ρAU2/2. It is
also called coefficient of drag denoted by CD.
CD = FD /(ρAU2/2)
where FD
is total drag force;
A
is area of the surface where shear stress acts;
ρ
is density of the fluid;
and
U
is main stream velocity.
14. State the boundary conditions for the velocity profiles in a boundary layer.
The following are boundary conditions, which must be satisfied by any velocity
profile whether it is laminar or turbulent boundary layer.
(i)
At y = 0, u = 0 and du/dy has a finite value;
(ii)
At y = δ, u = U; and
(iii)
At y = δ, du/dy = 0
15. State the Von Karman momentum integral equation for a boundary layer.
Von Karman momentum integral equation for boundary layer is stated as:
τo/ ρU2 = 𝜕𝜃/𝜕𝑥
where τo
is shear stress;
ρ
is density of the fluid;
U
is main stream velocity;
and
𝜃
is momentum thickness.
UNIT V
DIMENSIONAL ANALYSIS AND MODEL STUDIES
1.
Classify the types of dimensions.
There are two types, fundamental dimensions and derived dimensions. Fundamental
dimensions are independent of each other, which they don’t depend on others.
Derived dimensions depend on more than one independent dimension.
2.
What are the fundamental dimensions?
There are three fundamental physical quantities, which are Mass, Length and Time.
These are respectively represented symbolically by M, L and T.
3.
Write two examples of physical quantities associated with derived dimensions.
Area, Volume, Velocity, Acceleration, Force, Weight, Viscosity, Kinematic
viscosity, Work, Energy, Power, Moment, Momentum, Torque, etc.
4.
Derive the dimension for force.
By definition:
Force = Mass x Acceleration
= Mass x Change in velocity/Time
= Mass x Distance/Time/Time
Dimension for Force
= Dimension of (Mass x Distance/Time/Time)
= M L/T/T = M L T-2
Dimension for Force is M L T-2
5.
Derive the dimension for dynamic viscosity.
Dynamic viscosity can be derived from Newton’s law of viscosity as:
τ = µ (du/dy)
Therefore, µ = τ x dy/du
Dimension for µ
= Dimension of (τ x dy/du)
= Dimension of (Shear stress x Length/Velocity)
= M L-1 T-2 L/L T-1
= M L-1 T-1
Dimension for µ is M L-1 T-1
6.
Derive the dimension for power.
Power is the rate at which work is done.
Power
= Force x Distance/Time
= Mass x acceleration x Distance/Time
Dimension for power = Dimension of (Mass x acceleration x Distance/Time)
= M L T-2 L/T = M L2 T-3
Dimension for power is M L2 T-3
7.
What is meant by dimensional homogeneity?
All the terms on both sides of an analytically derived equation should have the same
dimension, which is termed as dimensional homogeneity. The powers of
fundamental dimensions, i.e., M, L, T, on both sides of the equation will be the
same in a dimensionally homogeneous equation.
8.
State Buckingham’s π-Theorem.
Buckingham π-theorem states that ‘If there are n variables (both independent and
dependent) involved in a physical phenomenon and if these variables involve m
fundamental dimensions (M, L, T) then the variables can be arranged into (n - m)
dimensionless terms, which are known as π-terms’
9.
Classify the types of similitude.
There are three types of similitudes: Geometric, Kinematic and Dynamic.
10. Define – Reynolds Number
Reynold’s number is defined as the ratio between the inertial forces of the flowing
fluid and the viscous forces of the fluid. Mathematically, it is given as:
Re = Fi/Fv = ρ V L/ µ
11. What is a model?
Model is a miniature size of the prototype dynamically designed for a model study.
If the model is dynamically similar to the prototype, the model results can be
extended to the prototype.
12. State Froude’s model law.
Froude model law is that the Froude numbers are the same between the dynamically
similar model and its prototype. Frp = Frm
13. Define – Distorted Model
Distorted model is one which is not geometrically similar to its prototype. Such a
model uses different Scale Ratios for different dimensions. For example, Lr1 =
Lp/Lm; Lr2 = Bp/Bm; and Lr3 = Hp/Hm.
14. When will you go for a distorted model?
If the linear dimensions of the prototype are disproportionate with each other, use of
single scale ratio will result in an unrealistic model and hence there may be a need
to use different scale ratio for different dimensions leading to a distorted model.
15. Write a practical situation where a hydraulic model study is useful.
Flow measurements in natural rivers are made by the use of weirs constructed
across rivers. The discharge is calculated by a simple weir formula by measuring
the head of water flowing over the weir. However, it requires the coefficient of
discharge, Cd, value as applicable to the weir, which can be obtained through a
model study. Cd is a non-dimensional number and hence it is same for both model
and prototype.