Question

1. Discuss the significance of Reynold number for the classification of the type of fluid flow. [4]
2. Explain the terms Hydraulic Grade Line and Total Energy Line. Compare the total energy line and hydraulic grade lines for the pipe sections if there is sudden enlargement in the pipe section or sudden contraction in the pipe with the help of sketches. [8]
3. Describe the term most economical section of a channel. Explain the condition for most economical rectangular section for an open channel flow. [6]
4. Differentiate between the terms kinematic similarity and dynamic similarity. Give suitable examples to support your answer. [8]
5. Discuss the advantages of dimensional and model analysis. [4]

Answer 1

5

1)
Reynolds number is used where viscosity has significant effect like laminar flow
A high Reynolds number usually indicates turbulent flow conditions
For pipe: Re<2000 , laminar flow
Re>2000, turbulent flow
For parallel plate: Re<1000 ,laminar flow
: Re>2000 , turbulent flow
In between , transition flow
: Reynolds number depend on the density, viscosity and velocity of fluid in motion with respect to surface
At low Reynolds number, viscous force is comparable to inertial effect and flow is laminar
: At high Reynolds number, viscous force is insignificant compared to inertial force and turbulent flow

2)
Hydraulic gradient line is the sum of pressure head and datum head of flowing fluid

And total energy line is the sum of pressure head, velocity head and datum head
Hydraulic grade line lies one velocity head below the energy grade line
In case of constant cross section along the streamline and the flow is steady , discharge remain constant and so velocity, therefore velocity head remain same and in case HGL is remain parallel to EGL
Due to sudden contractions or expansion there is loss due to and hydraulic grade line fall and consequently energy grade line fall too

3)
A section is said to be economical when its construction cost is minimum for a given discharge
Or for given cross section area,the discharge carrying capacity is maximum
.the perimeter is kept minimum ,the cost of lining will be minimum and it will be most economical section

For most rectangular section,
Depth of flow(y) is half of width of rectangular section and hydraulic radius is half of depth of flow
Most effective section is circular

4)
for complete similarity to exist between model and prototype,it is necessary that they must be geometrically, kinematically and dynamically similar
Kinematic similarity: kinematic parameters are velocity, acceleration , discharge
Such similarity can be attained if flownets for model and prototype are geometrically same
And for dynamic similarity: identical type of forces(viscous, pressure, elastic) must be parallel and must bear same ratio at all corresponding sets of points

For kinematic similarity , geometrically similarity must exist
And for dynamic similarity, geometrically similarity must exist and kinematic similarity must exist
For example ship model is partially submerged body ,both Reynolds and froude law should be satisfied
Submarine model etc

5)
Dimensional homogeneity means the dimension in each equation on both sides equal
Dimensional analysis is a mathematical technique for solving engg. Problems ,it makes use of dimensions of variables on which the problem depends
A physical phenomena can be expressed by sn equation giving relationship between different quantities
Such quantities are dimensional and non dimensional
Dimensional analysis helps in determining a systematic arrangements of variables in physical relationship , combining dimensional variables to form non dimensional parameters
An important tool for analysing fluid flow problem
Fundamentals quantities are mass, length,time, temperature
2 methods of dimensional analysis
1) Rayleigh method (maximum no. Of variables are 3 or 4 only)
2) Buckingham pi method (no. Of variables is large)