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Lecture# Dimensional Analysis & Modelling

Description

This lecture covers the concept of dimensional analysis, focusing on the Buckingham Pi-theorem and the determination of dimensionless pi-terms. It also explores examples such as drag on a sphere, flow in an inclined open channel, and pressure drop across a constriction. The importance of modeling in predicting physical system behavior is discussed, along with the theory of models and design conditions for similarity requirements. Gravitational effects in open channel flow are highlighted, emphasizing the need for Froude number similarity. The lecture concludes with practical examples and considerations for experimental model experiments.

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Related concepts (33)

Related lectures (35)

BIOENG-312: Fluid mechanics (for SV)

This introductory course on fluids mechanics presents the basics concepts in fluids statics, dynamics and kinematics.

Gravitational acceleration

In physics, gravitational acceleration is the acceleration of an object in free fall within a vacuum (and thus without experiencing drag). This is the steady gain in speed caused exclusively by the force of gravitational attraction. All bodies accelerate in vacuum at the same rate, regardless of the masses or compositions of the bodies; the measurement and analysis of these rates is known as gravimetry. At a fixed point on the surface, the magnitude of Earth's gravity results from combined effect of gravitation and the centrifugal force from Earth's rotation.

Design of experiments

The design of experiments (DOE or DOX), also known as experiment design or experimental design, is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation. The term is generally associated with experiments in which the design introduces conditions that directly affect the variation, but may also refer to the design of quasi-experiments, in which natural conditions that influence the variation are selected for observation.

Experiment

An experiment is a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. Experiments provide insight into cause-and-effect by demonstrating what outcome occurs when a particular factor is manipulated. Experiments vary greatly in goal and scale but always rely on repeatable procedure and logical analysis of the results. There also exist natural experimental studies.

Buckingham π theorem

In engineering, applied mathematics, and physics, the Buckingham pi theorem is a key theorem in dimensional analysis. It is a formalization of Rayleigh's method of dimensional analysis. Loosely, the theorem states that if there is a physically meaningful equation involving a certain number n of physical variables, then the original equation can be rewritten in terms of a set of p = n − k dimensionless parameters pi1, pi2, ..., pip constructed from the original variables, where k is the number of physical dimensions involved; it is obtained as the rank of a particular matrix.

Potential flow

In fluid dynamics, potential flow (or ideal flow) describes the velocity field as the gradient of a scalar function: the velocity potential. As a result, a potential flow is characterized by an irrotational velocity field, which is a valid approximation for several applications. The irrotationality of a potential flow is due to the curl of the gradient of a scalar always being equal to zero. In the case of an incompressible flow the velocity potential satisfies Laplace's equation, and potential theory is applicable.

Covers the analysis of drag on a sphere in Newtonian fluid mechanics, focusing on key parameters and the significance of Reynolds number.

Explores turbulence characteristics, simulation methods, and modeling challenges, providing guidelines for choosing and validating turbulence models.

Explores boundary layer concepts, viscosity impact, drag and lift forces, and dimensional pipe flow analysis.

Explores friction forces, Newton's laws applications, and momentum calculation on various surfaces.

Covers the importance of boundary layers, viscosity effects on drag and lift.