Introduction to Fluid Mechanics

Introduction to Fluid Introduction to Fluid MechanicsMechanics

Benno RahardyanBenno Rahardyan

Definition of a FluidDefinition of a FluidA fluid is a substance that flows under the action of shearing forces. If a fluid is at rest, we know that the forces on it are in balance.

A gas is a fluid that is easily compressed. It fills any vessel in which it is contained.

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

A free surface is formed as a boundary between a liquid and a gas above it.

DensityDensityThe density of a fluid is defined as its mass per unit volume. It is denoted by the Greek symbol, .

=V m3kgm-3

If the density is constant (most liquids), the flow is incompressible.If the density varies significantly (eg some gas flows), the flow is compressible.(Although gases are easy to compress, the flow may be treated as incompressible if there are no large pressure fluctuations)

water= 998 kgm-3

air =1.2kgm-3

kgm

PressurePressurePressure is the force per unit area, where the force is perpendicular to the area.

p=A m2

Nm-2

(Pa)

NF

This is the Absolute pressure, the pressure compared to a vacuum.

pa= 105 Nm-2

1psi =6895Pa

The pressure measured in your tyres is the gauge pressure, p-pa.

PressurePressurePressure in a fluid acts equally in all directions

Pressure in a static liquid increases linearly with depth

p=increase in depth (m)

pressure increase

g h

The pressure at a given depth in a continuous, static body of liquid is constant.

p1 p2

p3 p1 = p2 = p3

Measuring pressure Measuring pressure (1)(1)ManometersManometers

h

p1 p2=pa

liquiddensity

x y

z

p1 = px

px = py

pz= p2 = pa

(negligible pressure change in a gas)

(since they are at the same height)

py - pz = gh

p1 - pa = gh

So a manometer measures gauge pressure.

Measuring Pressure Measuring Pressure (2)(2)BarometersBarometers

A barometer is used to measure the pressure of the atmosphere. The simplest type of barometer consists of a column of fluid.

p1 = 0vacuum

h

p2 = pa

p2 - p1 = gh

pa = gh

exampleswater: h = pa/g =105/(103*9.8) ~10m

mercury: h = pa/g =105/(13.4*103*9.8) ~800mm