# Fluid Mechanics

A substance which can flow is known as fluid. Hence, the term includes both **liquids and gases**. The study of fluids at rest is called **fluid statics**.

Solids are incapable of flow because the intermolecular forces are very strong. Hence, solids possess a definite shape and volume. The intermolecular forces are weak in liquids. Hence, liquids do not possess a definite shape but take the shape of the container. In the case of gases, the intermolecular forces are practically non-existent. Therefore, gases possess neither a definite shape nor a definite volume.

**Density** of a homogeneous substance is defined as the ratio of its mass to its volume. In other words density is the mass per unit volume.

**Specific gravity** of a material is defined as the ratio of its density to that of water at 4°C. It is a mere number and has no units. It is also known as **relative density**.

**Pressure** is defined as the ratio of the normal force acting on the area on which the force acts.

P = F/A

S.I. unit of pressure is pascal (Pa). Pressure is a scalar quantity.

### Pascal's Law

When ever pressure is applied on any part of a fluid contained in a vessel, it is transmitted undiminished and equally in all directions.

The Bramah’s press works on the principle of Pascal’s law. It is used to compress cotton bales, extract oil from seeds and drill holes in large metal sheets. If in a hydraulic press (Bramah’s press), the area of the smaller and larger pistons are a and A and a force f is applied on the smaller piston, then the force F developed on the larger piston is given by:

F = fA/a

### Archimedes Principle

When a body is immersed wholly or partially in a fluid at rest, the fluid exerts an upward force on the body equal to the weight of the fluid displaced by the body.

The loss of weight (ΔW) of a solid when immersed in a liquid is given by ΔW = vdg where v = volume of the displaced liquid, d = density of the liquid and g = acceleration due to gravity.

The upward force is called the **buoyant force** or force of buoyancy. Buoyant force depends on the volume of the displaced liquid and not on the volume of the body. Buoyant force depends on the density of the liquid and not on the density of the body.