Define boundary layer

A very thin layer of fluid, in the immediate vicinity of a solid boundary surface, where the velocity of the flowing fluid increases gradually from zero at the boundary surface to the velocity of the main stream is known as boundary layer.

It is to be noted that the higher the Reynolds number (or smaller the viscosity), the thinner is the boundary layer. Within the boundary layer, the flow can either be laminar or turbulent. The concept of boundary layer helps in significantly simplifying the theoretical treatment of flows with high Reynolds number.

Hydraulic Grade Line, Energy Gradient Line

Hydraulic grade line
A line joining the piezometric levels at various points is known as hydraulic grade line or hydraulic gradient line.

Piezometric Head
The sum of the pressure head (p/w) and the potential head (Z) is known as piezometric head.

Total Head
Total head is given by the sum of piezometric head (p/w + Z) and the kinetic head (V²/2g)

Energy Gradient Line
Total energy at various points along the axis of the pipe is plotted and joined by a line, known as Energy Gradient Line.

Forces in Fluid Flow

Name the different forces present in fluid flow.

* Inertia force
* Viscous force
* Gravity force
* Pressure force
* Surface tension force
* Elastic force

Reynolds Number

Physical significance of Reynolds number:
* Reynolds number signifies the relative predominance of the inertia to viscous forces occurring in the flow system.
* Reynolds number is very useful in determining whether the flow is laminar or turbulent.

Moody's Chart
If the value of relative roughness k/D for the pipe and Reynolds number for the flow are known, the friction factor f can be determined using Moody’s chart.

Submarine is tested in the air tunnel. Identify the model law applicable.
Reynolds model law.

Distorted and Undistorted Models

What is meant by undistorted models?
An undistorted model is one that is geometrically similar to its prototype.


Demerits of a distorted model:
* Pressure and velocity distributions are not truly reproduced
* Difficult to extrapolate and interpolate results obtained from distorted models
* The observer experiences an unfavourable psychological effect

Mach Model law

In any fluid system, where the forces resulting from elastic compression alone are significant in addition to inertia force, the dynamic similarity between the model and the prototype may be achieved by equating the Mach numbers.

(M)_model = (M)_prototype

What is a Mach number?
Mach number is defined as the square root of the ratio of the inertia force and elastic force. It is a non-dimensional number.

Mach Number's field of use:
Aerodynamic testing and in phenomena involving velocities exceeding the speed of sound.

Dynamic Similarity in Fluid Flow

In fluid flow, what does dynamic similarity mean?

Dynamic similarity means the similarity of forces between the model and the prototype.


What are the non-dimensional numbers associated with dynamic similarity?

Non-dimensional numbers associated with dynamic similarity:

# Reynolds number
# Froude’s number
# Euler’s number
# Weber number
# Mach number