EGB101 | Fundamentals of Engineering Science

Vector

A quantity defined by both magnitude and direction

Scalar

A quantity defined only by its magnitude with no direction

Displacement

The straight linear change in position from the starting point to the ending point

Distance

The total length of the path travelled

Speed

How fast an object is moving

Velocity

The rate of change of displacement in a specific direction

Average Velocity

The total displacement over the total time taken; informs you the speed and in what direction an object moves over a time interval

Instantaneous Velocity

The velocity at a specific moment in time; the limit of average velocity as the time interval approaches zero

Fluid

A material that continually deforms (flows) under an applied shear stress (or an external force). If at rest, forces on it are balanced.

Gas (fluids)

A fluid that is easily compressed, able to fill any vessel containing it.

Liquid (fluids)

A fluid which is hard to compress. Given a mass, it will occupy a fixed volume, irrespective of the size of the container.

Free Surface (fluids)

Formed as a boundary between liquid and a gas above it.

Newton’s First Law

A body remain at rest/continues at a constant speed in a straight line unless acted upon by a force.

The Properties of Fluids

• density

• viscosity

• vapour pressure

Density

$\rho$ [rho] mass (m) per unit volume (V) of substance

$$\rho=\frac{m}{V}$$

Specific Weight (unit weight)

$\gamma$ [gamma] (Force Weight) excreted by a unit volume of substance in earth’s gravity.

$$\gamma=\rho g$$

Relative Density (specific gravity)

The ratio of density of a substance to that of water at standard temperature and pressure

$$s=\frac{\rho}{\rho_{w}}$$

Newton’s Law of Viscosity

For a moving fluid, the shear stress is directly proportional to the rate of shear strain.

Pressure

Normal stress acting inward to a surface, force per unit area (Pa or N/m squared)

Pascal’s Law

Pressure at a point in a fluid (at rest or in motion) has the same magnitude in all directions and is called isotropic.

In a fluid confined by a solid boundary, pressure acts perpendicular to the boundary; pressure is a distributed normal force.

$$P=\frac{force}{area}=\frac{N}{m^2}=Pa$$

Absolute Pressure

Measure above perfect vacuum

$$\int dp=\int pgdz$$

$$p=pgz+p_{o}$$

z : depth from free surface