FLUID DYNAMICS

INTRODUCTION: - The study of fluids at rest is called hydrostatics. Fluid dynamics deals with fluids in motion. The study of the motion of fluids is relatively complicated. This study can, however, be simplified by making a few assumptions. The analysis is further simplified by the use two important conservation principles, namely, the conservation of mass and the conservation of energy. The law of conservation of mass gives us the Equation of Continuity where as law of conservation of energy gives us Bernoulli’s Theorem. 

VISCOUS DRAG AND STOKES’ LAW: - As we know that there is always some resistance to the flow of a fluid. There is a frictional effect between different layers of the flowing fluid. The numerical value of resistance to the flow of a fluid is called the co-efficient of viscosity of the fluid. Substances that do not flow easily such as engine oil, grease, honey etc. have small coefficient of viscosity.

Since fluids have viscosity an object while moving through a fluid experience a resistive frictional force and is called the viscous drag. The magnitude of the drag depends on the size, shape, orientation and speed of the object as well as the viscosity of the fluid. Swimmers and skydivers change their effective size and orientation of their bodies by bending, twisting or stretching their arms and legs in and out. This allows them to manipulate the drag and consequently to control their speed and direction of motion. Even in the simplest cases the exact values of the drag forces is difficult to calculate. However the viscous drag on spherical objects can be expressed by mathematical formula called stokes’ law.

FLUID FLOW: - Te study of moving fluids is of great practical importance. A large quantity of liquid may have to flow rapidly through a pipe from one location to another. Air entering the inlet of a jet engine may have to be transported to the outlet. In all such cases of mass transport, knowledge of the condition existing oat various points is essential for efficient design.

Basically fluid dynamics is complex subject. The fluid flow can be very smooth or it can be turbulent. We shall restrict our discussion to the simple situation of steady streamline flow. “ The flow is said to be streamline or laminar, if every particle of the fluid that passes a particular point, moves along exactly the same path, as followed by particles which passed that point earlier.