Home | | **Mechanics of Fluids** | Mechanics Of Fluids- Dimensional Analysis And Model Studies: Similitude

The three types of similarities are,
1. Geometric similarity
2. Kinematic similarity
3. Dynamic similarity

**Similitude**

The
three types of similarities are,

1. Geometric
similarity

2. Kinematic
similarity

3. Dynamic
similarity

**Scale ratio.**

Scale
ratio is the ratio of linear dimension in the model and prototype which are
equal in a geometric similarity. It is denoted by Lr.

Lr
= Lp/Lm = bp/bm = Dp/Dm

**Dynamic similarity.**

It
means the similarity of forces at corresponding points in the model and
prototype is equal.

**Types of forces in a moving fluid.**

The
types of forces in a moving fluid are,

1. Inertia
force (fi)

2. Viscous
force (fv)

3. Gravity
force (Fg)

4. Pressure
force (Fp)

5. surface
tension (Fs)

6. Elastic
force (Fe)

**Dimensionless numbers.**

Dimensionless numbers are the numbers
obtained by dividing inertia force or gravity force or pressure force or
elastic force or surface tension. They are called as non-dimensional
parameters.

**Surface tension.**

Surface
tension force is defined as the product of surface tension and length of
surface of flowing fluid.

**Pressure force.**

Pressure force is the product of pressure
intensity and cross-sectional area of the flowing fluid in case of pipe flow.

**Elastic force.**

Elastic force is defined as the product of
elastic stress and the area of flowing fluid.

**Types of dimensionless numbers.**

The
types of dimensionless numbers are:

1. Reynold's
number

2. Froude's
number

3. Euler's
number

4. Weber's
number

5. Mach's
number

**Reynold's number. **

Reynold's
number is defined as the ratio of inertia force of flowing fluid and viscous
force of the fluid. It is denoted by (Re)

Re
= V x d / v = ? V d / ?

**Froude's number**

Froude's
number is defined as square root of ratio of inertia force of flowing fluid to gravity. It is denoted as Fe

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