280.272 Notes

1

Can apply stress prior to

static conditions

Problem 1.1

Fluid Statics

Fluids are liquids or gases

Fluid mechanics consists of fluid statics (stationary fluids) and fluid dynamics (moving fluids)

The characteristic property of a fluid is that it is unable to

support a shear stress in static equilibrium

Stress

Defined as force per unit area and is measured in Pa

The force can be applied

in many directions

Static Pressure

In static equilibrium there is no shear stress so therefore there is only hydrostatic pressure

stress, which is a scalar.

Hydrostatic Pressure follows Pascal’s Law: Pressure is transmitted without loss through the

fluid system

Pressure at the Base:

Consequences of

The static pressure will only be dependent upon the height. Therefore if the liquids are the

same density then the pressure will be the same at any horizontal line.

The pressure also increases in direct proportion to the depth. i.e. the deeper down the

liquid the higher the pressure.

Shear stress is two forces

moving relative to

another

280.272 Notes

2

Problem 1.2

Problem 1.3

Problem 1.4

Gauge Pressure

Defined as the difference between measured pressure and the instrument pressure

NB: in problems this normally relates to setting

Bourdon Tube: when pressure is applied he tube

straightens but the deformation is small so that there is

no permanent damage

It measures the difference in pressure between inside

and outside

NB: There needs to be clarity between absolute and gauge pressure. Gauge pressures

should always be followed by (gauge) or (g)

If the object is in static equilibrium then

Following the derivation laid out on Fluid Static Slides Slide 8,

the following equation arrises for the pressure at points 1 and

2

This is because the density is constant with the height

and can be pulled out of the height.

If the density changes with height (i.e. the fluid is very deep) then the pressure must

be calculated from the integral

Piezometer: Tube that comes off to determine pressure at a particular height. A difference

of height between the tube and the vessel may be different due to the vessel being

closed

280.272 Notes

3

Problem 1.5

Problem 1.6

Manometer: Uses a U-tube which determines the difference in height which can be directly

related to the differences in pressure between the ends of the manometer.

The pressure range of a manometer depends on fluid densities

- Air over water gives better sensitivity as there is a small density difference

- Mercury is better at measuring high range because of the greater density difference

An Orfice Plate is sometimes added to know the

pressure drop for particular flow rates. These types

of manometers are called Differential

Manometers

Assuming the pipe diameter is much smaller

incomparison to

Pressure Forces on Submerged Surfaces

The Pressure increases with depth

The centroid is the centred

of gravity on the surface

The pressure centre is the

location of the nett force

Calculating Centroid (Ẋ)

Look up in tables for formulas

Examples:

Rectangle:

Triangle:

NB: a centroid will always lie on a line of symmetry if there is one

𝜌𝑖 = density of indicator

= height between indicator and liquid

More force below

centroid than above

Dot above x (Ẋ) should be

replaced by dash

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