Ideal Fluid Flows & Complex Analysis Course | Prof. Amit Gupta IIT Delhi

Course Details

Master the Art of Modeling Fluid Flows with Complex Analysis

Welcome to an advanced exploration of fluid mechanics where classical mathematics meets engineering design. The course Ideal Fluid Flows using Complex Analysis, instructed by Prof. Amit Gupta of IIT Delhi, offers a deep dive into a powerful analytical technique for solving real-world engineering problems. Over four intensive weeks, this postgraduate-level course demystifies the application of complex variables to model inviscid, incompressible flows—a cornerstone of aerodynamic and hydrodynamic design.

Course Overview & Instructor Profile

This course is meticulously designed to impart competence in modeling engineering challenges using the principles of ideal or potential fluid flows. The primary objective is to equip students with the ability to obtain elegant analytical solutions and deduce critical design parameters, emphasizing complex analysis as a more efficient alternative to traditional methods.

The course is led by Prof. Amit Gupta, a distinguished expert holding the NTPC Chair in the Department of Mechanical Engineering at IIT Delhi. With a robust academic background including a Ph.D. from the University of Central Florida and post-doctoral research at the University of Michigan, Ann Arbor, Prof. Gupta brings invaluable research insights from energy storage, microfluidics, and flapping wing aerodynamics directly to the classroom.

Who Should Enroll?

This course is ideally suited for:

• Senior undergraduate students in Mechanical, Aerospace, or Civil Engineering seeking advanced electives.
• Postgraduate students (M.Tech., M.S., Ph.D.) specializing in fluid dynamics, aerodynamics, or applied mathematics.
• Research scholars and professionals looking to strengthen their analytical toolkit in continuum mechanics.

Prerequisites: A solid foundation in Fluid Mechanics and Calculus is essential to fully engage with the course material.

Detailed 4-Week Course Layout

The curriculum is structured to build knowledge progressively, from fundamental concepts to advanced applications.

Week 1: Foundations of Potential Flow & Complex Variables

The journey begins with the core concepts of ideal flows, introducing the velocity potential and stream function. You will then bridge into the world of complex variables, exploring analytic functions and their direct connection to fluid flow through the powerful concept of the complex potential and complex velocity.

Week 2: Elementary Flows and Superposition

This week focuses on constructing basic flow elements using complex potentials. You will master the representation of:

• Uniform flow
• Source, sink, and vortex flow
• Flow in a sector and around a sharp edge

The principle of superposition is introduced, culminating in the derivation of flow due to a doublet.

Week 3: Superposition for Engineering Applications

Here, theory meets application. You will apply superposition to solve classic problems:

• Flow around a circular cylinder (without and with circulation)
• Combination of source and uniform flow
• Calculation of forces on a circular cylinder with circulation, setting the stage for aerodynamic force prediction.

Week 4: Advanced Theorems and Transformations

The course culminates with advanced tools for force calculation and flow transformation:

• Generalized derivation for forces on a 2D body
• The powerful First Theorem of Blasius
• The foundational Kutta-Zhukhovsky Lift Law
• Introduction to Conformal Transformations, a method to map complex flows to simpler geometries.

Key Learning Outcomes

Upon completion, participants will be able to:

• Formulate engineering fluid flow problems using potential flow theory.
• Employ complex analysis as a streamlined method for obtaining analytical solutions.
• Construct complex flows through the superposition of elementary solutions.
• Calculate forces like lift and drag on two-dimensional bodies using Blasius theorems.
• Understand the mathematical basis of conformal mapping in fluid mechanics.

Recommended Textbooks

This course is more than an academic exercise; it's training in a classical yet supremely relevant analytical approach. By harnessing the power of complex analysis, you will learn to see fluid flows through a different lens—one that simplifies complexity and reveals elegant solutions to challenging engineering problems. Enroll to master a fundamental skill set that bridges advanced mathematics with practical mechanical and aerospace engineering design.

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