Similitude involved in Model Analysis

List the similitude involved in the model analysis.

* Geometric similarity
* Kinematic similarity
* Dynamic similarity

For the prototype and model to be geometrically similar, the ratio of all corresponding linear dimensions in the model and the prototype should be equal.

Kinematic similarity refers to the similarity of motion between model and prototype.

Dynamic similarity corresponds to the similarity of forces between model and prototype.

Meta Centre Definition

Define Meta Centre

Metacentre is defined as the point about which a body starts oscillating when the body is tilted by a small angle.

Condition needed for the submerged body to be remaining in stable equilibrium
Centre of Gravity (G) is below the Centre of Buoyancy (B).

Laminar sub layer

Define laminar sub layer

For a turbulent boundary layer, if the boundary is smooth, the roughness projections are covered by a very thin layer, which remains laminar. This thin layer is called laminar sub layer.

Bernoulli’s equation

Bernoulli’s equation states that in a steady, irrotational flow of an incompressible fluid, the total energy per unit weight of the fluid remains constant.

p/w + V²/2g + Z = constant

Assumptions involved in Bernoulli’s equation:

1. The fluid is ideal
2. The flow is steady
3. The flow is irrotational
4. The flow is incompressible

Why is it necessary to assume that the flow is steady before integrating Euler’s equation to derive Bernoulli’s equation?

In steady flow, a fluid particle will move along a streamline. Thus, in describing the motion of a fluid particle, the distance along a streamline can be used in writing the equations of motion.

What is Dimensional Homogenity?

Dimensional Homogenity

An equation is said to be dimensionally homogenous if the dimensions of the terms on its left hand side are same as the dimensions of the terms on its right hand side.

Dimensions of some of the physical quantities are given below for your use:

(a) Pressure - ML^-1T^-2
(b) Surface tension - MT^-2
(c) Dynamic viscosity - ML^-1T^-1
(d) Kinematic viscosity - L²T^-1