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  1. Differentiate dynamic and kinematic viscosity.

Sr. No.

Dynamic viscosity

Kinematic viscosity

It is resistance to fluid flow. It gives an idea about the thickness of fluid.
If the fluid is thin like water, it has less viscosity. If the thickness of the fluid
is more like honey, its viscosity is more.
It is the ratio of the fluid’s viscous force to the inertial force.
Its symbol is ‘µ’.
Its symbol is’ υ‘.=µ /ρ
Its unit is N-s/m2.
Its units is m2/s.
Dynamic viscosity is absolute viscosity or just viscosity.
Kinematic viscosity is momentum diffusivity.
  1.  List practical applications of dynamic viscosity.

It is ratio of dynamic viscosity to density of the fluid. Its symbol is ʋ (nu). Units of dynamic viscosity is m2/s. Mathematically, it is ʋ = μ /ρ.
It represents fast momentum transfer between different layers of the fluid. Dynamic viscosity is resistance to flow between various layers of the fluid. Then how do we say about fast momentum transfer for kinematic viscosity? This change of nature is due to density as denominator. Lower is the density, lower will be the inertia force and faster will be the momentum transfer between various layers. Higher is the density, more will be the inertia force and slow will be the momentum transfer between various layers. Hence kinematic viscosity is also momentum diffusivity. It is very much similar to thermal diffusivity in heat transfer. Kinematic viscosity is used in Naiver Stokes equations governing the fluid motion.


Effect of Temperature
Viscosity of liquids decrease with the increase of temperature and vice versa.
Viscosity of gases increase with the increase of temperature and vice versa.
Effect of Pressure 
NO effect on liquids and gases viscosity.

What is Newton’s Law of Viscosity?

τ= μ du/dy
τ is shear stress between two adjacent layers of a moving fluid
du change in velocity in x direction (direction of motion)
dy is the distance (perpendicular to du) between the two layers in y direction
NOTE du is in x direction and dy is in y direction
du/dy becomes shear strain or velocity gradient in y direction
μ is constant of proportionality & is  Dynamic viscosity.
μ = τ/ (du/dy)
τ =N/m2
du = m/s
dy = m
Therefore, Units of viscosity are Ns/m2.
  1. State the basic principle used in discharge measurement in Venturimeter and Orifice meter?

 Bernoulli’s Theorem deals with conservation of energy. Pressure head changes into kinetic head. Use pressure difference the measurement of discharge in the Venturimeter and Orifice meter.

Q. What are the advantages of Venturimeter over orifice meter  in a flow measurement?

The comparison of Venturimeter and an Orifice meter is as flows:

Sr. No.


Orifice meter

Coefficient of discharge
is Cd =0.98.
Coefficient of discharge
is Cd =0.60 to 0.65
Rate of flow will be higher with the same diameter
Rate of flow will be lesser with the same diameter
It is very accurate.
It is less accurate.
It is costly.
It is cheap.
Requires more space.
Requires less space.
Energy losses are high.
Energy losses are low.
  1. What is Vena Contracta?

The Vena Contracta is the smallest cross-section of a fluid jet. The jet comes out from a circular small hole (aperture) from a pressurized reservoir.
When fluid comes out from a hole in a tank, the cross section of the flowing fluid decreases. It becomes minimum at some distance from the tank. Vena Contracta is the minimum area of flow. Up to the Vena Contracta flow lines are parallel and straight and are perpendicular to the plane of the orifice. It is only after the Vena Contracta; flow deflects downward due to gravity. Example of Vena Contracta is fluid coming out as jet from a nozzle. Use concept of Vena Contracta in design to obtain maximum flow.

Q. State the differences between triangular and rectangular notches.

Triangular notch or V-notch gives more accurate measurement at low flow rates. In this, the height will be more to measure it accurately.  Whereas in case of a rectangular notch, the height is so small in the measured gap. Thus it gives erroneous results.

Q. Difference between lower and upper Critical Reynolds numbers.

Table: Values of Lower and Upper critical Reynolds Number
Flow in a pipe                                            Flow over a flat plate
Laminar Flow
Turbulent Flow
Laminar Flow
         Turbulent Flow
Lower critical 2100
Upper critical
Lower critical
Upper critical


  1. What are limitations and characteristics of a flow net?

  • Limitations of a flow net

  1. Flow net is applicable only for a 2 dimensional flow.
  2. Due to viscous effects, It does not apply near the boundary.
  3. This is not applicable to a diverging flow.
  4. Flow net analysis is not applicable to separation of flow and eddies formation.
Characteristics of a flow net
  1. Flow net is applicable only for a 2 dimensional flow.
  2. This analysis applies to seepage problems in soil and structures.

22. What is difference between Darcy and Fanning equations for the pressure drop in a fluid flow?

Darcy friction factor is four times the Fanning friction factor. Darcy friction factor is also called as Moody friction factor or Blasius friction factor.

  •  laminar flow, Darcy friction factor = fD= 64/Re

Where Re is Reynolds number

  •  turbulent flow,

Darcy friction factor = fD= 0.06 to 0.006

Fanning friction factor (ff) is one fourth of Darcy friction factor.

For a laminar flow

ff = 16/Re = ζ /ρu2/2


ff is the local Fanning friction factor

ζ is the local shear stress

u is the local flow velocity

ρ is the density of the fluid

Δhff = 2ff u2L/gD

For turbulent flow, Colebrook equation is used to find Fanning friction factor

1/ ( ff)0.5 = -4.0 log10 ((ε/d) / 3.7 + 1.256/ ff)

Where ε, roughness of the inner surface of the pipe (dimension of length);

     d, inner pipe diameter;

ff appears on both sides of the equation and its solution can be found only by hit and trial.

Darcy–Welsbach factor, fD is more commonly used by civil and mechanical engineers, and the Fanning factor, f, by chemical engineers, but one must be careful to determine correctly the friction factor for the equation used. Fanning equation is used by chemical engineers.

23. What is Bernoulli equation?

Bernoulli equation is the mathematical form for the law of conservation of energy for a flowing liquid.
p1/ ρ+ ρ v12/2 + z1 = p2/ ρ   + ρ  v22/2 + z2
Flow work + kinetic energy + Potential energy = constant
(in a flowing liquid with no addition or no withdrawal of energy in between two points under consideration)
Bernoulli equation comes from Euler equation by integration.

 (a) Give the assumptions of Bernoulli Equation?

Assumptions used in the derivation of Bernoulli’s theorem are

  1. Fluid is ideal i.e. there are no losses of any kind in the flow of an ideal fluid.

  2. Flow is steady i.e. No changes in the flow velocity with respect to time.

  3. Fluid is incompressible i.e. It is only for liquids i.e. although pressure changes are there but volume and hence density remains constant during the flow.

  4. Flow is one dimensional.

  5. Fluid is continuous i.e. there are no vapors in it or there are no impurities in it.

  6. Only gravitational and pressure forces are acting on the fluid i.e. fluid is non viscous.

(vi) Flow is non-viscous ( no shear stresses or viscosity is zero)

(vii) There is no energy transfer in between the two sections.

   (b) To which fluids is the Bernoulli equation applicable?

Bernoulli equation is applicable only to LIQUIDS.


Bernoulli and energy equations are derivable from first law of thermodynamics.


The energy equation allows for

(i) friction

(ii) heat transfer,

(iii) shaft work

(iv) viscous work (another frictional effect)

 Bernoulli equation does not consider anyone.

25. Explain Bernoulli’s effect. Fluid velocity affects the fluid pressure. If velocity increases, pressure decreases.

26. Calculate the pressure in a horizontal pipe whose absolute pressure is 2 x 105 N/m2 after the speed of the water in the pipe increases from 2.0 m/s to 20.0 m/s. Fluid is non viscous. Take the fluid density as 103 kg/m3.


Density of the fluid, ρ = 103 kg/m3

Velocity of the fluid at point 1, v1 = 2.00 m/s

Velocity of the fluid at point 2, v2 = 20.0 m/s

Pressure at point 2, p2 = 2 x 105 N/m

From Bernoulli’s principle

Substituting the values, we get


p1=2 x 105 + 1.98 x 105

p1= 3.98 x 105 N/m2

27. What is the Pascal’s law?

This is a law of pressure of a fluid AT A CERTAIN POINT.
“It states that pressure at a point is same in all directions”.
Bernoulli’s equation is applicable to only to liquids at rest.
However it is not applicable to moving fluids.

28. What is an ‘ideal fluid’. What will be value of Reynolds number for an ideal fluid?

Ideal fluid is a hypothetical fluid. It is non viscous, non-rotational and in-compressible. In reality, there is no ideal fluid.
Reynolds number = v d /µ
Since viscosity is zero for an ideal fluid,
Re = infinity for an ideal fluid

29. What is a Newtonian fluid? Give few examples.

A fluid which obeys the Newton’s law of viscosity is a Newtonian fluid.
Newton Law of Viscosity
ζ = µ du/dy
ζ is the shear stress
µ is the dynamic viscosity
du/dy is the velocity gradient in a perpendicular direction to the flow direction i.e. Flow is in x direction whereas velocity gradient is in the ‘y’ direction. Examples of the Newtonian fluids are Air, Water and Kerosene.

30. State Pascal’s Law.

Pressure at any point in a static fluid is same in all the directions. If there is an increase/decrease in pressure at any point in a confined fluid, there is an equal increase/decrease of pressure at every other point in the container.

31. What is a Froude’s number? What is its significance?

Froude’s number (We) is a square root of the ratio of inertia force to the gravitational force. It is a dimensionless number. Mathematically

Fr = V/ (Dg)0.5

V is the velocity in m/s, assuming full pipe flow
D is the pipe inner diameter in m
g is the gravity constant in m/s²

Experimentally it has been found that Froude number should be less than 0.3 to avoid air entrainment and ensure undisturbed flow without pulsations.

The Froude number compares the resistance to wave making between bodies of various sizes and shapes. In free surface flow, it has been found that

  1. When Froude Number = 1, flow is critical.

  2. If Froude Number > 1, flow is super-critical.

  3. When Froude Number < 1, flow is sub-critical.

In appearance, it has similarity with Mach number. Froude’s number is used in a fluid flow around marines, over spillways or flow over the weirs in open channels.


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