Fluid Mechanics Problems And Solutions: Advanced

Advanced Fluid Mechanics: Selected Problems & Solutions

Problem 1: Potential Flow – Flow Over a Rankine Half-Body

Problem:
A uniform stream ( U ) flows in the positive ( x )-direction. A source of strength ( m ) (volume flow rate per unit length) is located at the origin.
(a) Derive the stream function ( \psi ) and velocity potential ( \phi ).
(b) Find the stagnation point location.
(c) Determine the width of the half-body far downstream (i.e., the asymptotic half-width).

) falling through a highly viscous fluid (like honey) at a very low velocity . Calculate the drag force acting on the sphere. Key Concept: At very low Reynolds numbers ( advanced fluid mechanics problems and solutions

7. Modern Computational Approaches: When Exact Solutions Fail

No article on advanced fluid mechanics problems and solutions is complete without addressing computational fluid dynamics (CFD). The most practical solution to realistic problems is numerical. (b) Find the stagnation point location

p open paren x comma t close paren minus p sub a t m end-sub equals integral from x to cap L of the fraction with numerator 6 mu omega and denominator theta cubed x end-fraction space d x equals the fraction with numerator 6 mu omega and denominator theta cubed end-fraction l n open paren the fraction with numerator cap L and denominator x end-fraction close paren Final Answer The pressure distribution under the closing plate is: Calculate the drag force acting on the sphere