Fluid mechanics

Course Objectives:

-Students who take this class can expect to Develop an appreciation for the properties of Newtonian fluids.

-Study analytical solutions to variety of simplified problems.

-Understand the dynamics of fluid flows and the governing non-dimensional parameters.

-Apply concepts of mass, momentum and energy conservation to flows.

-Grasp the basic ideas of turbulence.

Course Outcomes: At the end of the course, the student will be able to:

• Apply conservation laws to derive governing equations of fluid flows.
• Compute hydrostatic and hydrodynamic forces.
• Analyze and design simple pipe systems.
• Apply principles of dimensional analysis to design experiments.
• Compute drag and lift coefficients.

UNIT - I

Introduction: Dimensions and units – Physical properties of fluids specific gravity, viscosity, surface tension, vapor pressure and their influences on fluid motion pressure at a point, Pascal’s law, Hydrostatic law - atmospheric, gauge and vacuum pressure- measurement of pressure. Pressure gauges, Manometers: differential and Micro Manometers. Hydrostatic forces on submerged plane, Horizontal, Vertical, inclined and curved surfaces – Center of pressure. Derivations and problems.

UNTI – II

Buoyancy and floatation: stability of bodies, meta centre, liquids in relative equilibrium.

Fluid Kinematics: Description of fluid flow, Stream line, path line and streak lines and stream tube. Classification of flows : Steady, unsteady, uniform, non uniform, laminar, turbulent, rotational and irrotational flows – Equation of continuity for one, two , three dimensional flows – stream and velocity potential functions, circulation and vorticity, flownet analysis.

UNIT – III

Fluid Dynamics and Measurement of Flow: Surface and body forces – Euler’s and Bernoulli’s equations for flow along a stream line for 3-D flow, (Navier – stokes equations (Explanationary) Momentum equation and its application – forces on pipe bend. Pitot tube, Venturi meter, and orifice meter – classification of orifices, flow over rectangular, triangular and trapezoidal and Stepped notches - –Broad crested weirs.

UNIT - IV

Closed Conduit Flow: Reynold’s experiment – Characteristics of Laminar & Turbulent flows. Laws of Fluid friction – Darcy’s equation, ,variation of friction factor with Reynold’s number – Moody’s Chart, Minor losses – pipes in series – pipes in parallel – Total energy line and hydraulic gradient line. Pipe network problems Flow between parallel plates, Flow through long tubes, flow through inclined tubes, water hammer.

UNIT – V

Boundary Layer Theory: Approximate Solutions of Navier Stokes Equations – Boundary layer – concepts, Prandtl contribution, Characteristics of boundary layer along a thin flat plate, Vonkarmen momentum integral equation, laminar and turbulent Boundary layers (no derivations) BL in transition, separation of BL, control of BL, flow around submerged objects-Drag and Lift- Magnus effect.