Relationship between a model and Similitude

Relationship between a model and Similitude
For a model, similitude is achieved when testing conditions are created such that the test results are applicable to the real design.
There are some criteria that are required to achieve similitude;
1. Geometric similarity – The model is the same shape as the application (they are usually scaled).
2. Kinematic similarity – Fluid flow of both the model and real application must undergo similar time rates of change motions. (Fluid streamlines are similar).
3. Dynamic similarity – Ratios of all forces acting on corresponding fluid particles and boundary surfaces in the two systems are constant.
BEFORE THAT!! The application is analyzed in order to satisfy the conditions;
1. All parameters required to describe the system are identified using principles from continuum mechanics.
2. Dimensional analysis is used to express the system with as few independent variables and as many dimensionless parameters as possible.
3. The values of the dimensionless parameters are held to be the same for both the scale model and application. This can be done because they are dimensionless and will ensure dynamic similitude between the model and the application. The resulting equations are used to derive scaling laws which dictate model testing conditions.
However, it is often impossible to achieve strict similitude during a model test. The greater the departure from the application's operating conditions, the more difficult achieving similitude is.
Similitude is a term used widely in fracture mechanics relating to the strain life approach. Under given loading conditions the fatigue damage in an un-notched specimen is comparable to that of a notched specimen. Similitude suggests that the component fatigue life of the two objects will also be similar.

One example that we can give here is the ‘PIPE FRICTION APPARATUS’.
Pipe friction apparatus has been designed for students to measure pipe friction losses for laminar and turbulent flows. For laminar flow study, an elevated head tank is used for water supply, whilst for turbulent flow; the supply is from the Hydraulics Bench using hoses with rapid action hose coupling. Students may control the flow rate of water by adjusting the flow regulator valve. The test section is connected to manometers via pressure tappings.

The purpose (objectives) doing this experiment are;
• Measurement of the pressure loss for laminar flow
• Measurement of the pressure loss for turbulent flow
• Determination of the critical Reynolds’ number
• Measurements using a tube manometer
• Measurements using a mercury U tube manometer
Reynolds number in pipe friction

Pressure drops seen for fully developed flow of fluids through pipes can be predicted using the Moody diagram which plots the Darcy–Weisbach friction factor f against Reynolds number Re and relative roughness. The diagram clearly shows the laminar, transition, and turbulent flow regimes as Reynolds number increases. The nature of pipe flow is strongly dependent on whether the flow is laminar or turbulent.

Reynolds number in pipe friction

Pressure drops seen for fully developed flow of fluids through pipes can be predicted using the Moody diagram which plots the Darcy–Weisbach friction factor f against Reynolds number Re and relative roughness . The diagram clearly shows the laminar, transition, and turbulent flow regimes as Reynolds number increases. The nature of pipe flow is strongly dependent on whether the flow is laminar or turbulent.