Basic mechanical thermodynamics concept

The field of thermodynamics deals with systems that are able to transfer thermal energy into at least one other form of energy (mechanical, electrical, etc.) or into work. The laws of thermodynamics were developed over the years as some of the most fundamental rules which are followed when a thermodynamic system goes through some sort of energy change.
What is Thermodynamics?:
Thermodynamics is the field of physics that deals with the relationship between heat and other properties (such as pressure, density, temperature, etc.) in a substance. Specifically, thermodynamics focuses largely on how a heat transfer is related to various energy changes within a physical system undergoing a thermodynamic process. Such processes usually result in work being done by the system and are guided by the laws of thermodynamics.
Laws of Thermodynamics
Heat transfer is guided by some basic principles which have become known as the laws of thermodynamics, which define how heat transfer relates to work done by a system and place some limitations on what it is possible for a system to achieve.

Thermodynamic Processes:

A system undergoes a thermodynamic process when there is some sort of energetic change within the system, generally associated with changes in pressure, volume, internal energy (i.e. temperature), or any sort of heat transfer.
There are several specific types of thermodynamic processes that have special properties:
Adiabatic process - a process with no heat transfer into or out of the system.
Isochoric process - a process with no change in volume, in which case the system does no work.
Isobaric process - a process with no change in pressure.
Isothermal process - a process with no change in temperature.
States of Matter:
The 5 states of matter
gas
liquid
solid
plasma
superfluid (such as a Bose-Einstein Condensate)
Phase Transitions
condensation - gas to liquid
freezing - liquid to solid
melting - solid to liquid
sublimation - solid to gas
vaporization - liquid or solid to gas
Heat Capacity:

The heat capacity, C, of an object is the ratio of change in heat (energy change - denoted by delta-Q) to change in temperature (delta-T).
C = delta-Q / delta-T

The heat capacity of a substance indicates the ease with which a substance heats up. A good thermal conductor would have a low heat capacity, indicating that a small amount of energy causes a large temperature change. A good thermal insulator would have a large heat capacity, indicating that much energy transfer is needed for a temperature change.
Ideal Gas Equations:

There are various ideal gas equations which relate temperature (T1), pressure (P1), and volume (V1). These values after a thermodynamic change is indicated by (T2), (P2), and (V2). For a given amount of a substance, n (measured in moles), the following relationships hold:
Boyle's Law (T is constant):P1V1 = P2V2
Charles/Gay-Lussac Law (P is constant):V1/T1 = V2/T2
Ideal Gas Law:P1V1/T1 = P2V2/T2 = nRR is the ideal gas constant, R = 8.3145 J/mol*K. For a given amount of matter, therefore, nR is constant, which gives the Ideal Gas Law.
Laws of Thermodynamics:
Zeroeth Law of Thermodynamics - Two systems each in thermal equilibrium with a third system are in thermal equilibrium to each other.
First Law of Thermodynamics - The change in the energy of a system is the amount of energy added to the system minus the energy spent doing work.
Second Law of Thermodynamics - It is impossible for a process to have as its sole result the transfer of heat from a cooler body to a hotter one.
Third Law of Thermodynamics - It is impossible to reduce any system to absolute zero in a finite series of operations. This means that a perfectly efficient heat engine cannot be created.
The Second Law & Entropy:

The Second Law of Thermodynamics can be restated to talk about entropy, which is a quantitative measurement of the disorder in a system. The change in heat divided by the absolute temperature is the entropy change of the process. Defined this way, the Second Law can be restated as:
In any closed system, the entropy of the system will either remain constant or increase.

By "closed system" it means that every part of the process is included when calculating the entropy of the system.

strength of materials basic mechanical questions

1.Define stress and strain. Write down the S.I. and M.K.S. units
of stress and strain.
2. Explain clearly the different types of stresses and strains.
3. Define the terms: Elasticity, elasticlimit, Young'smodulusandModulus of rigidity.
4. State Hooke's law.
5. Three sections of a bar are having different lengths and different
Diameters. The bar is subjected to an axial load p. Determine the total change
in length of the bar. Take Young's'modul of different sections same.
6. Distinguish between the following, giving due explanation:
(1) Stress and strain,
(2) Force and stress, and
(3) Tensile stress and compressive stress.
7. Prove that the total extension of a uniformly tapering rod of
Diameters D1 and D2, whenthe rod issubjectedto an axial load P is given by 4PL dL .Ceded
Where L=Total length of the rod
8. Define a composite bar. How will you find the stresses and load Carried by each member of a composite bar?
9, Define modular ratio, thermal stresses, thermal strains and Poisson’s ratio.
10. A rod whose ends are fixed to rigid supports, is heated so that
Rise in temperature is rc. Prove that the thermal strain and stresses
Setup in the rod are given by, Thermal strain=a. T and Thermal stress=a.T.E.
Where a=Co-efficient of linear expansion.
11. What is the procedure of finding thermal stresses in a composite Bar?
12 what do you mean by 'a bar of uniform strength’?
13 Find an expression for the total elongation of a bar due to its Own weight, when the bar is fixed at its upper end and hanging freely at the lower end.
14 Find an expression for the total elongation of a uniformly
Tapering rectangular bar when it is subjected to an axial load P.
15.Define and explain the following terms:
Shear force, bending moment, shear force diagram and bending
Moment diagram.
16.What are the different types of beams? Differentiate between
a cantilever and a simply supported beam.
17.What are the different types of loads acting on a beam?
18.Differentiate between a point load and a uniformly distributed load.
19.What are the. Sign conventions for shear force and bending
Moment in general? '
20.Draw the S.F. and, B.M. diagrams for a cantilever of length L
Carrying a point load W at the free end.
21.Draw the S.F. and B.M. diagrams for a cantilever of length L
Carrying uniformly distributed load of w per m length over its entire length.
22.Draw the S.F. and, B.M. diagrams for a cantilever of length L
Carrying a gradually varying load from zero at the free end to w per unit
Length at the fixed end.
23.Draw the S.F. and B.M. diagrams for a simply supported beam
of length L carrying a point loads Wat its middle point.
24.Draw the S.F. and B.M. diagrams for a simply supported beam
Carrying a uniformly distributed load of w per unit length over the entire
Span. Also calculate the maximum B.M.
25.Draw the S.F. and B.M. diagrams for a simply supported beam
Carrying a uniformly varying load from zero at each end to w per unit length
at the centre. '
26.What do you mean by point of contra flexure? Is the point of
Contra flexure and point of inflexion different?
27. How many points of contra flexure you will have for simply
Supported beam overhanging at one end only?
28.How will you draw the S.F. and B.M. diagrams for a beam?
29.Which is subjected to inclined loads?
30.What do you mean by thrust diagram?
31.Draw the S.F. and B.M.diagramsfor a simply supported beam of length L which is subjected to a clockwise couple 11at the centre of the Beam.
32.Define the terms: bending stress in a beam. neutral axis and
section modulus.
33.What do you mean by 'simple bending' or 'pure bending’?
34.What are the assumptions made in the theory of simple bending?
35.Derive an expression for bending stress at a layer in a beam.
36.What do you understand by neutral axis and ", moment of
Resistance?
37.Prove the relation,
M=L=~
I y R'
l=M.O.I.
where M=Bending moment,
y=Distance from N.A.
f=Bending stress,
R=Radius of curvature.
E=Young's modulus, and
(Bangalore University, Jan. 1990)
38.What do you mean by section modulus? Find an expression
for section modulus for a rectangular, circular and hollow circular sections.
39.How would you find the bending stress in unsymmetrical
section?
40.What is the meaning of 'Strength of a section’?
41.Define and explain the terms: modular ratio, fletched beams
and equivalent section.
42.What is the procedure of finding bending stresses in case of
fletched beams when it is of (i) a symmetrical section and (ii) an
unsymmetrical section?
43.Explain the terms: Neutral axis, section modulus, and moment
of resistance. (Bangalore University, July 1988)
44.Show that for a beam subjected to pure bending, neutral axis
coincides with the centroid of the cross-section.
(Bangalore University, March 1989)
45.Prove that the bending stress in any fiber is proportional to the distance
of that fiber from neutrally in beam. (BhavnagarUniversity, 1992)
46.Define the terms: Torsion, torsion rigidity and polar moment
of inertia.
47.Derive an expression for the shear stress produced in a circular
shaft which is subject to torsion. What are the assumptions made in the
derivation?
48.Find an expression for the torque transmitted by a hollow
Circular shaft of external diameter=Do and internal diameter=Dj.
49.Define the term 'Polar modulus'. Find the expressions for polar
Modulus for a solid shaft and for a hollow shaft
50.What do you mean by 'strength of a shaft' 1
51.Define torsional rigidity of a shaft. Prove that the torsional
rigidity is the torque required to produce a twist of one radian in a unit
length of the shaft.
52.Find an expression for strain energy stored in a body which due
to torsion or Prove that the strain energy stored in a body due to torsion is given
By, 2 U=.Lxv. 4C
where q=Shear stress on the surface of the shaft,
C=Modulus of rigidity, and
V=Volume of the body.
53.A hollow shaft of external diameter D and internal diameter d
is subjected to torsion, prove that the strain energy stored is given by,2
U=~ (D2+cf) xV4CD
where V=Volume of the hollow shaft and
q=Shear stress on the surface of the shaft.
54.What is a spring? Name the two important types of spring.

Basic mechanical`s thermodynamic basic questions

BASIC CONCEPTS OF THERMODYNAMICS

1. Define the term thermodynamic.
2 Explain the thermodynamic system, surroundings and universe.
3. Distinguish between closed, open and isolated system with examples.
4. Differentiate between homogeneous and heterogeneous systems.
S. What do you mean by phase of a system?
6. What do you mean by thermodynamic equilibrium?..
9. Explain the terms: state, phase, process and cyclic process
10 What do you understand by reversible and irreversible process? Give examples.
11. Explain cyclic and quasi - static process.
12. Explain the term "Energy". Discuss its various forms.
13. Define work. Show that work is a path function.
14. Define the term heat.
15. Choose the open or closed system from the following:
Water pump, pressure cooker, automobile engine, air compressor, steam turbine, boiler
System.
16. State the number of phases in the following:
- Alcohol mixture, coffee, water - oil mixture, aqua - ammonia, mildPure water, water
Steel, at room temperature.
17. Explain the concept of temperature.
18. State zeroth law of thermodynamics
19.State first law of thermodynamics.
20.What is PMM-1?
21.Show that energy of an isolated system remains unchanged.
22.Write the steady flow energy equation.
23.Write the relationship between specific heats.
24.What is adiabatic index? Give its usual value.
25.What is a steady flow process?
26.What conditions are fulfilled by a steady flow process? '

27.Determine an expansion for the heat transfer in a closed system isochoric process.
28.Explain the concept of a closed isobaric process and determine an expansion for its heat Transfer.
29.Determine an expansion for the work done in a closed isothermal process.
30.What is an isentropic process? Determine an expansion for the work done in a non-flow
Isentropic process.
31.Determine an expansion for the heat transfer and work done in a non-flow Polytrophic
Process. I
32,What is a free expansion process? What are its characteristics?
33.What is a throttling process? State its characteristics?
34.What is a steady
35.Flow process? Determine the work done in such an isochoric process.
36.Determine an expansion for the work done in a steady flow adiabatic process.
37.Compare the work done in a non-flow and flow type polytrophic process.
38.State the limitations of First law of thermodynamics.
39.State Kelvin-Planck statement for second law of thermodynamics.
40.State Clausius statement for the second law of thermodynamic.
41.What is a PMM2?
42.Are Kelvin-Planck and Clausius statements equivalent?
43.Differentiate between a heat engine and a heat sink.
44.What is a thermal reservoir?
45.Differentiate between a heat source and a heat sink.
46.Describe the working of a Carnot cycle.
47.What are the limitations of Carnot cycle?
48.Define thermal efficiency of a heat engine.
49.Differentiate between a heat pump and a refrigerator.
50.Define COP of a heat pump and a refrigerator.
51.State Carnot theorem.
52.What is Clausius inequality?
53.State Carnot's theorem.
54.Define the term 'Entropy'.
55.Show that the entropy is a property of the system.
56.The entropy of the universe tends to be maximum. Comment.
57.What are the characteristics of entropy?
58.Draw the Carnot cycle on T-S diagram.
59.State Third law of thermodynamics.
60.What is the importance of third law of thermodynamics?

Basic mechanical engineering :fluid mechanics

FLUID PROPERTIES
Define fluid.
A Fluid is a substance that deforms continuously when subjected to a shear stress no matter how small that shear stress may be.
Differentiate solid and fluid.
Fluid
The fluid deforms continuously when subjected to a shear stress.
When the shear stress disappears the fluid never regain in to original shape. .
Solid

The Solid deforms a definite amount when subjected to a shear stress
When the shear stress disappears solids gain fully or partly their original shape.
Define density.
Density is defined as the mass of a substance per unit volume.
If a fluid element enclosing a point P has a volume dV and dm , then the density is given by r = lim dV - 0 (dm / dV) = (dm / dV) The unit of density is kg/m3 .
Define specific volume,.
Specific volume is defined as the reciprocal of density that is volume capacity per unit mass of fluid
Vs = ( 1 / r) = ( dV / dm ) The unit of sp. Volume is m3/kg
Define specific weight.
Specific weight is the weight of the fluid per unit volume.
g = ( weight / volume) = ( m g / v) = r g The unit of specific weight is N/m3.
Define specific gravity (SG).
Specific gravity is the ratio of mass density (or) weight density of the fluid to the mass density (or) weight density of the standard fluid. For liquids, water at 4oc is considered as standard fluid.
A liquid has a specific gravity of 1.527

what are the values of specific weight and specific volume ?
Specific gravity of a liquid (SG) = Sp. Weight (or) weight density of liquid / Sp. Weight (or) weight density of std liquid The standard liquid is water and its specific weight = r g = 1000 x 9.81 = 9810 N/m3
The specific weight of the liquid = 9810 x 1.527 = 14979.8 N/m3.
Density of the liquid ( r ) = 14979.8 / 9.81 = 1527 kg/ m3.
Specific volume of liquid = 1 /r = 1 / 1527 = 6.54 x 10 –4 m3/kg.
Define viscosity.
The viscosity can be defined as the property of fluid which resist relative motion of its adjacent layers. It is the measure of internal fluid friction due to which there is resistance to flow, The unit of viscosity is Ns/m2.
State Newton’s law of viscosity. (AU-MQP)
The shear stress on a fluid element layer is directly proportional to the rate of strain (or) velocity gradient, the constant of proportionality being called the coefficient of viscosity.
t a (du / dy) shear stress ( t ) = m (du / dy)
what is real fluid ? Give examples. (AU-M03).
The fluids in reality have viscosity m > 0 hence they are termed as real fluids and their motion is known as viscous flow. (ex) Air , water, kerosene, blood, milk
Why are some fluids are classified as Newtonian fluid ? Give examples of Newtonian fluids. (AU-N02).
The fluids, which obey Newton’s law of viscosity are known as Newtonian fluids. For these fluids, there is a linear relationship between shear stress and velocity gradient. (ex) Air, water, kerosene.
What is a Tthyxotropic fluid ? (AU- N 03)
If the viscosity increases with time the fluid is said to be a Thyxotropic fluid. (ex) Lipstick, paints enamels, crude oil.
What is a Rheopectic fluid ?
If the viscosity decreases with time the fluid is said to be Rheopectic fluid. (ex) gypsum suspension, bentonite clay solution.
What is effect of temperature on viscosity of water and air ?
*The viscosity of water decreases with increase in temperature.
*The viscosity of air increases with increase in temperature.
Define kinematic viscosity and gives its uint.
Kinematic viscosity is defined as the ratio of dynamic viscosity to density.
n = m / r The unit of kinematic viscosity is m2/s
What is compressibility of fluid ?
Compressibility of substance is the measure of its change in volume under the action of external forces, namely, the normal compressive forces. The measure of compressibility of the fluid is the bulk modulus of elasticity (K)
K = lim DV - 0 (- DP) / (DV/V) The unit of compressibility is N/m2
Assuming the bulk modulus of elasticity of water is 2.07 x 106 kN/m2 at standard atmospheric condition. Determine the increase of pressure necessary to produce one percent reduction in volume at same temperature. (AU-N02)
Bulk modulus of elasticity K = 2.07 x 106 kN/m2 - (dV/V) = 1% = 0.01
K = - dP / (dV/V) \ Increase in pressure dP = -(dV/V) x K
= 0.01 x 2.07 x 106 = 20700 kN/m2.
What is meant by vapor pressure of a liquid ?
Liquids evaporate because of molecule s escaping from the liquid surface. These vapor molecules exert a partial pressure on the surface of the liquid known as vapour pressure.
What is cavitation ?
In flowing fluid, if the pressure is equal to or less than the saturated vapor pressure, the liquid boil locally and produce vapor bubbles. These bubbles collapse in the high pressure region causing a partial vaccum. This phenomenon in known as cavitation.
Define surface tension and mention its unit.
A free surface of the liquid is always under stretched condition implying the existence of tensile force on the surface. The magnitude of this force per unit length of an imaginary line drawn along the liquid surface is known as surface tension. The unit of surface tension is N/m.
Define capillarity. (AU-M04)
Capillary implies the raise or depression of liquid in a capillary tube where it is held vertically or inclined in the liquid.
Define the pressure and mention its unit.
If the fluid is stationary, then the force (dF) exerted by the fluid on the area is normal to the surface (dA). This normal force per unit area is called pressure..
P = ( dF / dA) The unit of pressure is N/m2.
What should be the depth of oil of specific gravity 0.8, if it has exerted a pressure of 480N/m2 ?
Specific gravity (SG) = 0.8 \ density = 800 kg/m3
The pressure = r g z depth z = P/(r g) = 480 x 103 / (800 x 9.81) = 61.16 m
Express 3m of water head in cm of mercury.
rm gm Hm = rw gw Hw 13600 x Hm = 1000 x 3 Hm = 0.22 m of Hg
Differentiate between absolute and gauge pressure.
Absolute pressure is measured as a pressure above absolute zero
Gauge pressure is measured as a pressure below atmospheric pressure
Gauge pressure = Absolute pressure - Atmospheric pressure
What do you mean by vacuum pressure ?
If the pressure is less than the local atmospheric pressure it is called as vacuum pressure.
Vacuum pressure = Atmospheric pressure - Absolute pressure
What is a manometer ? Name the common fluids used in it.
A manometer is a transparent tube containing a liquid of known density used for the purpose of measuring the fluid pressure. The common fluids used are mercury, alcohol.
Differentiate between simple manometer and differential manometer.
Simple manometer
In simple manometer, one end is connected to the point at which the pressure is to be measured and the other end is open to atmosphere.

Differential manometer
In differential manometer, two ends are connected to the points whose ‘difference of pressure’ is to be measured.
29. What is micro-manometer ? Where is it used ?
In this manometer a large difference in meniscus levels are obtained for very small pressure difference. This manometer is useful for precise measurement of pressure difference.

Fluid Kinematics : - Lines of flow , velocity field and acceleration, Continuity Equation. (1D, 3D),
Stream function and velocity potential function
Fluid Dynamics : - Bernoulli’s equation, Venturimeter, Orifice meter, Pitot tube.
What do you mean by dimension of flow?
A fluid flow is said to be one, two or three dimensional depending upon the number of independent space coordinates.
When is a flow considered steady?
A flow is considered steady when the dependent fluid variables at any point do not change with time.
When is the flow regarded as unsteady? Give an example for unsteady flow (AU MO3).
When the fluid is regarded as unsteady if the dependent variable change with time at a position in the flow.
The example for unsteady flow is flow at varying rates through a duct.
Differentiate uniform and non uniform flow.
When velocity of fluid at any instant of time do not change from point to point in a flow field, the flow is said to be uniform.
What is the difference between laminar and turbulent flow.
In the laminar flow the fluid particles move along smooth paths in laminar (or) layers with one layer gliding smoothly over the adjacent layer.
In turbulent flow the fluid particles move in a very irregular path causing an exchange of momentum from one portion of the fluid to the another. The turbulence setup greater shear stress throughout the fluid and causes more irreversibility and losses.
Differentiate compressible and incompressible flow.
Compressible flow is that type of flow in which the density of the fluid change from point to point. Incompressible flow is that type of flow in which the density is constant for the fluid flow. r = constant.
Distinguish rotational and irrotational flow.
Rotational flow is that type of flow in which the fluid particles while flowing along stream lines also rotate about their axis. If the fluid particles while flowing along stream lines, do not rotate about their own axis that type of flow is called irrotational flow.
What are streamlines?
A stream line at any instant can be defined as an stationary curve in the flow field so that at any point represents the direction of the instantaneous velocity at that point. The streamlines are defined by
What are path lines?
A path line is the actual path traversed by given fluid particle with the passage of timefrom initial time to final time. The path lines are defined by
What are streak lines?
A streak line at any instant of time is the locus of the temporary location of all particles that have passed through a fixed point in the flow field.
Define convective and local acceleration.
Convective acceleration is the instantaneous space rate of change of velocity, Local acceleration is the local time rate change of velocity.
Write the one dimensional continuity equation for compressible fluid flow.
Continuity equation for compressible fluid flow is mo = r1A1 u1 = r2A2 u2
r1, r2 - density at section 1 & 2
A1, A2 – area at the section 1 & 2, u1, u2 - velocity at section 1 & 2.
Define stream function.
It is defined as the scalar function of space and time, such that its partial derivative with respect to any direction gives the velocity component at right angles to that direction.
State the properties of stream function.
i) If stream function exists , it is a possible case of fluid flow.
ii) If stream function satisfies the laplace equation is a possible case of irrotational flow.
Define velocity potential function.
It is defined as a scalar function of time and space such that its negative derivative with respect to any direction gives the fluid velocity in that direction.
State the properties of velocity potential function.
*If the velocity potential function exists , it is a possible case of irrotational flow.
*Lines of constant velocity potential function and lines of constant stream function are mutually orthogonal.
What is a flow net?
A mesh or net work of stream lines and equipotential lines is called a flow net.
Write the applications and limitation of flow net?
*It is used to determine the direction of flow and velocity at any point in the closed system
*To determine the pressure distribution for given boundaries of flow.
Define circulation.
Circulation is defined as the flow along a closed curve. Mathematically circulation is obtained if the product of the velocity component at any point and the length of small element containing that point is integrated around the curve.
State Bernoulli’s theorem.
Bernoulli’s theorem states that in a steady flow of ideal incompressible fluid, the sum of pressure head, velocity head and potential head is constant along a stream line provided no energy is added or taken out by external source.
What are all the assumptions taken when deriving the Bernoulli’s equation. Write the Bernoulli’s equation and explain the terms.
i. Fluid is ideal and incompressible.
ii. flow is steady
iii. Flow is along the stream line ie. One dimensional.
iv. The velocity is uniform over the section and is equal to mean velocity.
v. The only forces acting on the fluid are the gravity forces and pressure forces.
Write the Bernoulli’s equation and explain the terms.
Bernoulli’s equation is (p/density*g)+(U2/2g)+Z=constant
The first term is the flow energy per unit weight (or) pressure head .The second term is the kinetic energy per unit weight (or) kinetic head. The third term Z is the potential energy per unit weight (or) potential head. The sum of these terms is known as total head.
Water if flowing through a pipe of 10 cm diameter under a pressure of 19.62 N/cm2 with mean velocity of 3m/s. Find the total head of water at a cross section, which is 8m above the datum line.
The pressure (p) = 19.62 N/cm2 = 19.62 x 104 N/m2 ; velocity U = 3m/s
Datum head Z = 8 m density of water r = 1000 kg /m3
Total head = (p/rg) + (U2/2g) + Z = [(19.62x104)/(100x9.81)] + [32/(2x9.81)] + 8 = 28.46 m of water.
Write few applications of Bernoulli’s equation.
*flow through venturimeter
* flow through orifice meter
*flow through orfices & mouth pieces
*flow over notches & weirs
What is venturimeter and name the parts of venturimeter?
A venturimeter is a device used for measuring the rate of a flow of fluid through a pipe. It consists of three parts i) short converging part ii) throat iii) Diverging part. It is based on the principle of Bernoulli’s theorem.
What is a pitot tube and write its principle.
Pitot tube is a glass tube bent at right angle . When it is placed in a flow, the liquid raises up in the tube due to conversion of kinetic energy into pressure energy. This raise is used to measure the velocity of flow at a point in the pipe or channel.

Dimensional analysis, Models & Similitude
Give the dimensions of the following quantities, a) Pressure b) Surface tension c) dynamic viscosity d) kinematic viscosity.
a) Pressure – M L-1 T-2 b) surface tension – M T-2
c) dynamic viscosity– M L-1 T-1 d) Kinematic viscosity– L2 T-1
State the Buckingham’s-p theorem.
Buckingham’s-p theorem states n quantities with in base dimensions can generally be arranged to provide only (n-m) independent dimensionless parameters also referred as p terms.
what do you mean by repeating variables? How are the repeating variables selected for dimensional analysis ?
In dimensional analysis, it is necessary to recognize the common variables for grouping. These common variables are known as repeating variables. The repeating variables should be chosen in such a way that one variable contain geometric property, other variable contains flow property and third contains fluid property. Normally the characteristic length (L), the velocity (u) and the density are chosen.
Show that the ratio of inertia force to viscous force gives Reynolds number,
Inertia force = mass x acceleration = r L3 u /t = r L2 (ut) u /t
= r L2 u2
Viscous force = shear stress x surface area = m (u/L) L2
= m uL
ratio = (r L2 u2) / (m uL) = r u L / m = Reynolds Number.
What is a Mach number? Mention its field of use.
The Mach number is the square root of ratio of inertia force to the elastic force
For surface tension and capillarity studies which dimensionless number is used?
The surface tension forces are associated with Weber number
Weber Number = inertia force/surface tention force
So for surface tension and capillarity studies Weber number is used.
Mention any two applications of Euler’s number.
i) flow through hydraulic turbines and pumps
ii) flow over submerged bodies iii) flow through penstocks.
Name the three types of similarity.
a) geometric similarity b) Kinematic similarity c) Dynamic similarity.
What is geometric similarity?
Geometric similarity concerns the length dimensions. A model and prototype are geometrically similar if and only if all body dimensions in all three coordinates have the same linear scale ratio. scale ratio = Lm/Lp
In fluid flow , what does dynamic similarity mean ?
Dynamic similarity exists when the model and prototype have the same length scale ratio, time scale ratio and force scale ratio. So the forces at homogeneous points are related through a constant called the force ratio.
Estimate the speed of rotation of a 3m diameter propeller to cruise at 10m/s if a 1/16 scale model provided the following results.
U = 5m/s N = 750rpm
The dynamic similitude requires (Nd)/U to e equated for model and the prototype
The speed of rotation = Np = (150 x 10 )/(5 x 10) = 150 rpm.

Laminar flow through circular conduits, flow through pipes , Boundary Layer theory

What is the difference between a laminar flow and turbulent flow?
In the laminar flow the fluid particles move along smooth paths in laminas (or) layers with one layer gliding over the adjacent layer .
In turbulent flow the fluid particles move in a very irregular path causing an exchange of momentum from one portion of the fluid to the other. The turbulence setup greater shear stress throughout the fluid and causes more irreversibility and losses.
In laminar flow through a pipe the maximum velocity at the pipe axis is 0.2m/s. Find the average velocity.
The average velocity Uavg = Umax /2 = 0.2/2 = 0.1m/s
Write the relationship between shear stress and pressure gradient in a laminar flow through pipe.
The shear stress at any point t = - (dp/dx) (r/2) Where (dp/dx) is the pressure gradient and -ve sign shows that pressure decreases in the direction of flow.
What is a boundary layer?
For fluids having relatively small viscosity, the effect of internal friction in a fluid is appreciable only in a harrow region surrounding the boundaries, where the velocity gradients are large and also larger shear stress. This region is known as boundary layer.
Why does the boundary layer increase with distance from the upstream edge ?
At the upstream edge, the free stream velocity is retarded by the solid surface causing a steep velocity gradient form the boundary to the flow. The velocity gradient sets up boundary shear forces that reduce the flow relative to the boundary. As the layer moves along the body the continual action of shear stress tends to slow down causing the thickness of boundary layer to increase.
Define boundary layer thickness.
The boundary layer thickness is defined as the distance from the boundary in which the velocity reaches 99% of main stream velocity and usually denoted by d.
Define displacement thickness.
The distance perpendicular to the boundary , by which the stream velocity is displaced due to the formation of boundary layer. It is denoted by d*.
Define momentum thickness.
Momentum thickness is defined as the distance, measured perpendicular to the boundary of the solid body, by which the boundary should be displaced to compensate for the reduction in momentum of the flowing fluid on account of boundary layer formation. It is denoted by q.
Define Energy thickness .
Energy thickness is defined as the distance, measured perpendicular to the boundary of the solid body, by which the boundary should be displaced to compensate for the reduction in kinetic energy of the fluid flowing on account of boundary layer formation.
What is the purpose of moody diagram ?
The Moody diagram shows the variation of friction factor with the governing parameters namely Reynolds number and relative roughness. This diagram is employed for predicting the values of friction factor in turbulent flow.
What do you understand by energy losses in a pipe ?
When a fluid flowing through a pipe the fluid experiences some resistance due to which some of the energy of the fluid is lost. This loss of energy is classified as
Major losses ---- This is due to friction
Minor losses ---- This due to enlargement , contractions, bents, valve fittings, entrance & exit present in the pipe system.
Give the Darcy-Weisbach equation for frictional head loss in pipe flow.
The frictional head loss hf = f L U2 / (2 g D) D - diameter of the pipe
f - Friction factor L – length of the pipe U – mean velocity of the pipe
The diameter of water pipe is suddenly enlarges from 350mm to 700mm. The rate of flow through it is 0.25m3 /s. Calculate the loss of head in enlargement.
The diameter of the smaller pipe D1 = 350mm = 0.35 m
The diameter of the larger pipe D2 = 700mm = 0.7 m
The rate of flow Q = 0.25 m3/s
The velocity through the pipe U1 = Q/A1 = (0.25 x 4 ) / ( p x 352) = 2.60 m/s
The loss of head in enlargement henl = (U12/2g) ( 1 - (A1/A2) )2 = (U12/2g) ( 1 - (D1/D2)2 )2
= (2.62/2x 9,81) ( 1 - (0.35/0.7)2 )2 = 0.1938 m of H2O
A horizontal pipe carries water at the rate of 0.04 m3/s. Its diameter reduces abruptly from 300mm to 150mm. Calculate the head loss across the contraction. Take the coefficient of contraction as 0.62.
Diameter of the pipe D1 = 0.3m Diameter of the contraction D2 = 0.3m Discharge Q = 0.04 m3/s
The loss of head in enlargement hcont = (U12/2g) ( (1/Cc) - 1 )2
= (2.262/2x 9,81) ( (1/0.62) - 1 )2 = 0.0978 m of H2O
The velocity at the contraction U2 = Q/A2 = (0.04 x 4 ) / ( p x 0.152) = 2.26 m/s
What are energy lines ?
The energy line is a longitudinal display of the total head at all salient sections of the pipe. The energy line therefore represents the degradation of energy along the flow due to friction, minor losses etc as well as additional input or output by means of pumps and turbines.
What are hydraulic gradient lines ?
A hydraulic gradient line is a longitudinal display of the pressure and datum head ie., piezometric head at all salient sections of the pipe line.
What is a compound pipe ?
A compound pipe is one in which a number of pipes of different diameters, different lengths and different friction factors are connected in series
What is an equivalent pipe ?
The equivalent pipe is the pipe of uniform diameter having 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 diameters.
Two pipes of lengths 800mm and 400mm of diameters 50cm and 30cm respectively are connected in series. These pipes are replaced by a single pipe of length 1000m. Find the diameter of single pipe.
Length of pipe –1 L1 = 800m Length of pipe –2 L2 = 400m
Length of equivalent pipe L = 1000m Diameter of pipe-1 D1 = 0.5m
Diameter of pipe-2 D2 = 0.3m
(L/D5) = (L1 /D15 ) +(L1 /D15 ) = (800/0.555 ) +(400 /0.35 )
` = 25600 + 164609 = 190209
D5 = (1000 / 190209) D = 0.416m
Explain the term pipes in parallel.
If two pipes are connected between two given points of a flow system it is called a parallel pipe system.

Fluid Machines - Pumps and Turbines
What is a fluid Machine ?
A fluid machine is a device which converts the energy stored by a fluid in to mechanical energy or work.
What are positive displacement machines ?
The machine functioning depend essentially on the change of volume of a certain amount of fluid within the machine. There is a physical displacement of the boundary of certain fluid hence it is called positive displacement machine.
Based on the direction of fluid flow how are the fluid machines classified ?
According to the flow direction of fluid, the fluid machines are classified as
Axial flow machines - The main flow direction is parallel to the axis of the machine.
Radial flow machines - The main flow direction is perpendicular to the axis of the machine ie. in radial direction
Mixed flow machines - The fluid enters radially and leaves axially or vice-versa.
What is a turbine ?
A turbine converts the energy of the fluid in to mechanical energy which is then utilized in running a generator of a power plant.
State the difference between impulse and reaction turbines ?
At the inlet of the turbine the energy available is only kinetic energy, the turbine is known as impulse turbine. If the inlet of the turbine, possesses kinetic energy and pressure energy, the turbine known as reaction turbine.
What are Homologous units ?
In utilizing scale models in designing turbo machines, geometric simililitude is necessary as well as geometrically similar velocity diagrams at entrance and exit from impellers. Two geometrically similar units having similar vector diagrams are called homologous units.
Define specific speed based on power.
The specific speed (Ns ) of turbine is defined as the speed of some unit of series of such size that it produces unit power with unit head. .
Define specific speed based on discharge.
The specific speed ( Ns ) of the pump is defined as the speed of some unit of the series of such size that it delivers unit discharge at unit speed
What is the significance of specific speed ?
The specific speed inversely proportional to the head across the machine. So low specific speed corresponds to high head across it and vice-versa.
The specific speed is directly proportional to the discharge through the machine or power produced by the machine. So low specific speed therefore refers to low discharge or low power machine and vice-versa.
Name the main parts of a radial flow reaction turbine ?
i) Casing ii) Guide vane iii) Runner iv) Draft tube.
What is the purpose of the guide vanes in radial flow reaction turbine ?
The purpose of the guide vane is to convert a part of pressure energy of the fluid at its entrance to the kinetic energy and then direct the fluid on to the number of blades.
What is a draft tube ? In which turbine it is mostly used.
The draft tube is a conduit which connects the runner exit to the trail race, when water is being finally discharged from the turbine. In reaction turbine , the draft tube is mostly used.
What is the primary function of a draft tube ?
The primary function of the draft tube is to reduce the velocity of the discharged water to minimize the loss of kinetic energy at the outlet.
Name the main parts of Kaplan turbine.
i). Scroll casing ii). Guide vanes iii). Hub with vanes iv). draft tube
Name the main parts of pelton wheel .
i) Nozzle ii) Runner with buckets iii) Casing.
An inward flow reaction turbine running at 250rpm has D1 = 1m, b1 = 0.2m, D2 = 0.5m and b3 = 0.3m. If the water enters the wheel radially at 3.5m/s velocity, determine the discharge and velocity of the flow at the outlet. Assume vane thickness at the extremities to be negligible.
Q = p D1 b1 Uf1 = p D2 b2 Uf2 = p x 1 x 0.2 x 3.5 = 2.199 m3/s
Uf2 = 2.99/ (p x 0.5 x 0.3) = 4.666 m/s
What are the different performance characteristic curves ?
i) Variable speed curves (or) main characteristics
ii) Constant seed curves (or) operating characteristics
iii) Constant efficiency curves (or) Muschel characteristics
Give an example for a low head turbine , a medium head turbine and a high head turbine.
Low head turbine - Kaplan turbine
Medium head turbine - Francis turbine
High head turbine - Pelton wheel.
what are the purposes of casing of a centrifugal pump
i) To provide water to and from the impeller
ii) To partially convert the kinetic energy in to pressure energy
What are the different types of casing in centrifugal pump ?
i) Volute casing ii) Turbine casing (or) casing with guide blades
What is a positive displacement pump ?
In the case of positive displacement pumps, the fluid is physically pushed from an enclosed space. The positive displacement pumps can be either reciprocating type or rotary type.
Where is the reciprocating pump well suited ?>
The reciprocating pump is well suited for relatively small capacities and high heads.
what are the main components of a reciprocating pump ?
) cylinder 2) Piston 3) suction valve 4) Delivery valve 5) Suction pipe 6) delivery pipe 7) crank shaft and connecting rod mechanism.
Define coefficient of discharge of reciprocating pump.
The ratio between the actual discharge and theoretical discharge is known as coefficient of discharge. Cd = Qact / Qthe.
Define slip of the reciprocating pump. When does the negative slip occurs ?
The difference between theoretical discharge and actual discharge is called the slip of the pump.
Slip = Qthe. - Qact , % of slip = (Qthe. - Qact ) x 100 / Qthe.
Negative slip occurs when delivery pipe is short suction pipe is long and pump is running at high speed.
Differentiate between single acting and double acting reciprocating reciprocating pump.
In single acting pump, there is one suction valve and one delivery valve. On the backward stroke of the piston, the suction valve opens and water enters into the cylinder space. On the forward stroke, the suction valve closes and delivery valve opens, the water is forced through the delivery pipe.
In the double acting pump, there are two suction valves and two delivery vales one in the front and one in the rear. When the piston moves backward, the suction valve in the front opens and delivery valve in the rear opens and water is forced through it. When the piston moves forward, the suction valve in the rear opens and delivery valve in the front opens and water is forced through it.
What is an indicator diagram of a reciprocating pump ?
The indicator diagram of a reciprocating pump is the diagram which shows the pressure head in the cylinder corresponding to any position during the suction and delivery strokes.
A single acting single cylinder reciprocating pump has the following characteristics.
Discharge = 6 lps, suction head = 4m, Delivery head = 20m, Find the energy required to drive the pump.
Energy required = r g Q ( Hs + Hd ) Watts = (1000 x9.81 x 6x10-3 x (4 + 20) / 1000
= 1.409 kW.
What is an air vessel and what is its purpose ?
An air vessel is a closed chamber connected on the suction or delivery or both sides of the reciprocating pump to obtain a more uniform flow.
Name some rotary positive displacement pumps.
a. Gear pumps.
b. Vane Pumps.
c. Piston pumps.
d. Screw pumps.

Basic mechanical`s introduction to finite element analysis

STUDY OF FINITE ELEMENT ANALYSIS AND SOFTWARE PACKAGES
History of FEA
Basic ideas of the finite element analysis were developed by aircraft engineers in the early 1940’s.These were primarily the matrix methods of analysis.
The modern development of the finite element method began in the year of 1945 in the field of structural engineering with the work by Hrennikoff. The term finite element was first introduced by Clough in 1960 in the plane stress analysis and he used both triangular and rectangular element in that analysis.
Introduction of FEA
The finite element method (FEM) is the dominant discretization technique in structural mechanics. The basic concept in the physical interpretation of the FEM is the sub division of the mathematical model into disjoint (non-overlapping) components of simple geometry called finite elements or elements for short. The response of each element is expressed in terms of a finite number of degrees of freedom characterized as the value of an unknown function or functions, at a set of nodal points.
Objectives of FEAthe analyst need certain requirements while designing and assembling the parts of the prodiuct those requirements are mentioned below.
To calculate,
Displacement of certain points.
Stress distribution.
Natural frequencies.
Critical buckling loads.
Vibrations.
Pressure, velocity and temperature distribution.
Crack growth, residual strength and fatigue life.


FEA Procedure
The following two general methods are associated with the finite element analysis. They are
Force method.
Displacement or Stiffness method.
Step 1
Discretization of Structure.
The art of subdividing a structure into a convenient number of smaller elements is known as discretization.
Some elements are classified as follow:
One dimensional element.
Two dimensional elements.
Three dimensional elements.
Axisymmetric elements.
Step 2
Numbering of nodes and elements.
The nodes and elements should be numbered after discretization process. The numbering process is most important since it decides the size of the stiffness matrix and it leads the reduction memory requirement. While numbering the nodes, the following condition should be satisfied.
Step 3
Selection of a displacement function or interpolation function.
The polynomial type of interpolation functions are mostly used due to the following reasons.
It is easy to formulate and computerize the finite element equations.
It is easy to perform differentiation or integration.
The accuracy of the results can be improved by increasing the order of the polynomial.
Case1
Linear polynomial
One dimensional problem Φ(x)=a0 +a1 x.
Two dimensional problem Φ(x,y)=a0+a1x+a2y.
Three dimensional problem Φ(x,y,z)=a0+a1x+a2y+a3z.
Case2
Quadratic polynomial
One dimensional problem Φ(x)=a0+a1x+a2x2.
Two dimensional problem Φ(x,y)=a0+a1x+a2y+a3x2+a4y2+a5xy.
Three dimensional problem Φ(x,y,z) =a0+a1x+a2y+a3z+a4x2+a5y2+a6z2+a7xy+a8yz+a9xz.
Step 4
Define the material behavior by using strain-displacement and stress-strain relationship.
In caser of our dimensional deformation, the strain-displacement relationship is given by
e=du/dx.
Where, u=displacement field variable along y direction.
e=strain.
Stress-strain relationship is given by
σ =Ee.
Where , σ = stress in x direction.
E = modulus of elasticity or young’s modulus.
Step 5
Derivation of element stiffness matrix and equations.
The finite element equation is in matrix form as,
f1 k11 k12 k13 … k1n u1
f2 = k21 k22 k23 ... k2n u2
f3 k31 k32 k33 … k3n u3
fu k41 k42 k43 … k4n un
Equation
{Fe} = [ke] {ue}
Step 6
Assemble the element equations to obtain the global or total equations.
{ F} =[k] {u}
Where, {F] = global force vector.
[k] = global stiffness matrix.
{u} = global displacement vector.
Step 7
Interpret the results (post processing)
Analysis and evaluation of the solution results is referred to as post-processing.
Post processor computer programs help the user to interpret the results by displaying them in graphical form.
Advantages
*One of the major advantages of the FEM over other approximate methods is the fact that FEM can handle irregular geometry in a convenient manner.
*Non-homogeneous materials can be handled easily.
*All the various types of boundary conditions are handled.
*Dynamic effects are included.
*Higher order elements may be implemented.
*It handles general load conditions without conditions.
*Vary the size of the elements to make it possible for using small elements where necessary.
Disadvantages FEM
*It requires a digital computer and fairly extensive software.
*It requires longer execution time compared with finite difference method.
*Output result will vary considerably, when the body is modeled with fine mesh when compared to body modeled with course mesh.
*In finite difference method, the governing differential equation of the phenomenon must be known whereas finite element method does not require to express fully.
Application
Structural; analysis is probably the most common application of finite element method. The term structural implies not only civil engineering structures such as bride and buildings, but also naval, aeronautical; and mechanical structures such as ship hulls, aircraft bodies, and machine housings, as well as mechanical components such as pistons, machine parts and tools.
Types of structural analysis
Static analysis.
Modal analysis.
Harmonic analysis.
Transient dynamic analysis.
Spectrum analysis.
Buckling analysis.
Explicit dynamic analysis.
Thermal analysis
A thermal analysis calculates the temperature distribution and related thermal quantities in a system component. Typical thermal quantities of interest are
Temperature distributions.
The amount of heat lost or gained.
Thermal gradients.
Thermal fluxes.
Thermal simulations play an important role in the design of many engineering applications including internal combustion engines, turbines, heat exchangers, piping systems and electronic components.

Loads
The term loads in Ansys includes boundary conditions & externally or internally applied forcing functions. The term loads in different disciplines are.
Structural: Displacements, forces, pressures, gravity temperatures[ for thermal strain].
Thermal: Temperatures, hear flow rates, convections, internal heat generation, infinite surface.
Magnetic: Magnetic potentials, magnetic flux, magnetic current segments, source current density, infinite surface.
Electric: Electric potential (voltage), electric current charge densities, infinite surfaces.
Fluid: Velocities, pressures.
Types of loads
Degree of freedom.
Force
Surface load.
Body load.
Inertia load.
Coupled field loads, etc.
Degree of freedom (DOF)
A DOF constraint fixes a degree of freedom to a known value. ex. of constraints are specified displacements and symmetry boundary conditions in a structural analysis, prescribed temperature in thermal analysis.
Force
A force is a concentrated load applied at a node in the model. Ex. Forces and movements in a structural analysis, heat flow rate in a thermal analysis and current segment in magnetic field analysis.

Surface Load
A surface load is a distributed applied load over a surface. Ex. Pressure in structural analysis, convection and heat flux in thermal analysis.
Body load
A body load is a volumetric (or) Field load. Ex. Temperatures & fluencies in structural analysis, heat generation rate in thermal analysis & current densities in a magnetic field analysis
Inertia loads
Inertia loads are those attributes to the inertia[mass matrix] of a body such as gravitational acceleration, angular velocity, angular acceleration.
Coupler field loads
It is a special case of one of the above loads, where results from one analysis are used as loads in another analysis. For Example: Magnetic forces calculated in a magnetic field analysis as force in a structural analysis.
Related Software of FEA
ANSYS
ANSYS has a substantial commitment to continual improvement of its solver technologies. Improvements in the distributed ANSYS product allow us to run solutions efficiently in parallel across multiple CPU’s Enhanced capability of solver performance directly impacts the return on investment of managing turbine field life and ANSYS has demonstrated and commitment to begin first to market with new solver features

CONCLUSION

Finite element analysis has become a solution to the task of predicting failure due to unknown stresses by showing problem areas in a material and allowing designers to see all of the theoretical stresses within the model. This method of product design and testing is for superior to the manufacturing cost which would occur if each sample was actually built and tested.

Basic mechanical engineering - properties

MECHANICAL PROPERTIES
Strength, hardness, toughness, elasticity, plasticity, brittleness, and ductility and malleability are mechanical properties used as measurements of how metals behave under a load. These properties are described in terms of the types of force or stress that the metal must withstand and how these are resisted.

Strength Strength is the property that enables a metal to resist deformation under load. The ultimate strength is the maximum strain a material can withstand. Tensile strength is a measurement of the resistance to being pulled apart when placed in a tension load.

Fatigue strength is the ability of material to resist various kinds of rapidly changing stresses and is ex­pressed by the magnitude of alternating stress for a specified number of cycles.
Impact strength is the ability of a metal to resist suddenly applied loads and is measured in foot-pounds of force.

Hardness Hardness is the property of a material to resist permanent indentation. Because there are several meth­ods of measuring hardness, the hardness of a material is always specified in terms of the particular test that was used to measure this property. Rockwell, Vickers, or Brinell are some of the methods of testing. Of these tests, Rockwell is the one most frequently used. The basic principle used in the Rockwell testis that a hard material can penetrate a softer one. We then measure the amount of penetration and compare it to a scale. For ferrous metals, which are usually harder than nonferrous metals, a diamond tip is used and the hardness is indicated by a Rockwell "C" number. On nonferrous metals, that are softer, a metal ball is used and the hardness is indicated by a Rockwell "B" number. To get an idea of the property of hardness, compare lead and steel. Lead can be scratched with a pointed wooden stick but steel cannot because it is harder than lead.
A full explanation of the various methods used to determine the hardness of a material is available in commercial books or books located in your base library.

Toughness Toughness is the property that enables a material to withstand shock and to be deformed without rupturing. Toughness may be considered as a combination of strength and plasticity.

Elasticity When a material has a load applied to it, the load causes the material to deform. Elasticity is the ability of a material to return to its original shape after the load is removed. Theoretically, the elastic limit of a material is the limit to which a material can be loaded and still recover its original shape after the load is removed.

Plasticity Plasticity is the ability of a material to deform permanently without breaking or rupturing. This prop­erty is the opposite of strength. By careful alloying of metals, the combination of plasticity and strength is used to manufacture large structural members. For example, should a member of a bridge structure become over­loaded, plasticity allows the overloaded member to flow allowing the distribution of the load to other parts of the bridge structure.

Brittleness Brittleness is the opposite of the property of plastic­ity. A brittle metal is one that breaks or shatters before it deforms. White cast iron and glass are good examples of brittle material. Generally, brittle metals are high in compressive strength but low in tensile strength. As an example, you would not choose cast iron for fabricating support beams in a bridge.

Ductility and Malleability Ductility is the property that enables a material to stretch, bend, or twist without cracking or breaking. This property makes it possible for a material to be drawn out into a thin wire. In comparison, malleability is the property that enables a material to deform by compres­sive forces without developing defects. A malleable material is one that can be stamped, hammered, forged, pressed, or rolled into thin sheets.

Basic mechanical engineering : derived units

QUANTITY.............UNITS..............(symblo)units

Area.....................squaremeter.............. m2

Volume...............cubic meter................. m3

Frequency .......Hertz,cycles per second.. Hz 1/s

Density........... kilogram per cubic meter.. kg/m3

Velocity ...........meter/sec .......................m/s

Angular velocity.... radian/sec ..............rad/s

Acceleration....... meter/second squared ...m/s2

Angular

acceleration.....radians per second square.. rad/s2

Volumetric flow rate.. cubic meter per second... m3/s

Mass flow rate .......kg per second ...........kg/s

Force ...............Newton (N).............. kg-m/s2

Surface Tension... (N/m)................ kg/s2

Pressure, stress .....Pa (N/m2) .........kg/m-s2

Dynamic viscosity.. N-s/m2 ............kg/m-s2

Kinematic viscosity.......................... m2/s

Work, energy .. J, N-m, W-s ........kg-m2/s2

Powe............W, J/s ...................kg-m2/s3

Specific heat,

gas constant..........J/kg-K ...........m2/s2-K

Enthalpy................ J/kg ................m2/s2

Entropy.............J/kg-K ................m2/s2-K

Thermal conductivity...W/m-K .....kg-m/s3-K

Diffusion coefficient ........................... m2/s

Electrical charge .......C.................... A-s

Electromotive force....... V........... kg-m2/A-s3

Electric field strength....V/m...... kg-m/A-s3

Electric resistance......ohm...... kg-m2/A2-s3

Electric Conductivity....A/V-m. .A2-s3/kg-m3

Electric capacitance.......F.........A2-s4/kg-m2

magnetic flux ...........Wb.............kg-m2/s2-A

Inductance........H.....................kg-m2/s2-A2

Magnetic flux density....T ...............kg/s2-A

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Basic mechanical engineering : si units

BASIC UNITS DIMENSION UNIT SYMBOL
Length ------------------meter --------------m
Mass --------------------kilogram ----------kg
Time--------------------- second ------------s
Electric current --------ampere ------------A
Temperature ----------- kelvin------------- K
Amount of matter ------mole ------------mol
Angle-------------------- radian---------- rad
Solid angle-------------- steradian------- sr
Luminous intensity----- candela --------cd