FLUID DYNAMICS

COMPREHENSIVE SUMMARY MEC2404 – Fluid Mechanics 1

Fluid Dynamics Comprehensive Summary

FLUID DYNAMICS COMPREHENSIVE SUMMARY MEC2404 – FLUID MECHANICS 1

1

Contents Fluid properties ................................................................................................................................... 2

Vapour pressure; ................................................................................................................................. 3

Fluid statics / Hydrostatics ...................................................................................................................... 4

Hydrostatic forces ............................................................................................................................... 4

Manometry ......................................................................................................................................... 4

Hydrostatic force on a planar surface ................................................................................................. 5

Curved surface .................................................................................................................................... 5

Buoyancy ............................................................................................................................................. 5

Linear rigid body motion ..................................................................................................................... 5

Rotational rigid body motion .............................................................................................................. 6

Bernoulli equation .................................................................................................................................. 6

Streamlines ......................................................................................................................................... 6

Static, dynamic and total pressure ..................................................................................................... 7

Continuity equation ............................................................................................................................ 7

Fluid kinematics ...................................................................................................................................... 8

Eulerian & langrangian flow descriptions ........................................................................................... 8

Laminar flow ....................................................................................................................................... 8

Turbulent flow..................................................................................................................................... 8

Acceleration field ................................................................................................................................ 9

Control volumes and system representation ..................................................................................... 9

Linear momentum equation ................................................................................................................. 10

Dimensional analysis ......................................................................................................................... 10

Boundary layers .................................................................................................................................... 12

Boundary layer theory ...................................................................................................................... 12

Pressure gradients ............................................................................................................................ 13

Energy equation .................................................................................................................................... 14

Major and minor losses..................................................................................................................... 15

Three types of flow problems ........................................................................................................... 15

Vehicle aerodynamics ........................................................................................................................... 16

Testing vehicle aerodynamics ........................................................................................................... 17

Pumps ................................................................................................................................................... 18

Performance characteristics ............................................................................................................. 19

Mixed and Axial flow pumps ............................................................................................................. 22

Pumps in series and parallel ............................................................................................................. 22

Fluid Dynamics Comprehensive Summary

FLUID DYNAMICS COMPREHENSIVE SUMMARY MEC2404 – FLUID MECHANICS 1

2

Fluid statics; Behaviour of fluids at rest

Fluids dynamics; Behaviour of fluids in motion

Fluid;

- A fluid is a substance that continuously deforms when subjected to a shear stress

- Although solids deform initially, they do not deform continuously

- The term ‘fluid’ generally applies to liquids and gasses

- Generally, do not analyse fluids at the nuclear level

Fluid particles/elements; very small volumes containing larger numbers of molecules

- Assumes average values of important properties over very small volumes is reasonable

- Treat the fluid as a continuum

Fluid properties - Density specific volume, specific gravity

o Measure a fluids mass or weight per unit volume

Density 𝝆 = 𝒎

𝑽

- Dependent on temperature and pressure

- Can be inferred from a hydrometer (which actually measures specific gravity)

- Archmedes principle; buoyancy force = 𝑉𝜌𝑔

o If we know V (volume of a fluid displaced), then 𝜌 can be calculated

Specific volume 𝒗 = 𝑽

𝒎=

𝟏

𝝆

- Volume ‘V’ per unit mass ‘m’

- Reciprocal of density

Specific gravity 𝑺𝑮 = 𝝆

𝝆𝑯𝟐𝑶

- Density relative to density of water at 4°C (1000 kg/m3)

Specific weight 𝜸 = 𝝆𝒈

- Weight per unit volume

Viscosity

- How easily a fluid flows

- Normal stress 𝜎 = 𝐹

𝐴

- Shear stress 𝜏 = 𝐹

𝐴 (applied tangentially to an area)

Note: when a fluid is deformed it forms a velocity gradient.

- Velocity gradient; 𝜏 = 𝜇𝑑𝑢

𝑑𝑦

Liquids; viscosity is due to cohesive intermolecular forces between liquid molecules

- At higher temperatures, molecules have higher energy and are able to overcome the

cohesive forces

- ↑ 𝑇 = ↓ 𝜇

Fluid Dynamics Comprehensive Summary

FLUID DYNAMICS COMPREHENSIVE SUMMARY MEC2404 – FLUID MECHANICS 1

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Gases; lower cohesive intermolecular forces

- Resistance to flow arises from random molecular collisions

- ↑ 𝑇 = ↓ 𝜇

Types of fluids

Viscosity can be determined from the slope of a plot of a ‘shear stress’ vs ‘strain rate’ (deformation

rate or velocity gradient.

Slope;

- linear for most common fluids (Newtonian fluids)

- Non-linear for some fluids (Non-Newtonian fluids)

Shear thinning;

- The viscosity decreases with shear

- i.e. slope decreases with increasing shear

Shear thickening;

- The viscosity increases with shear

- i.e. slope decreases with increasing shear

- Example – quicksand

Bingham plastic;

- Does not move until the shear stress exceeds a certain yield stress

- Example – toothpaste

Vapour pressure; Corresponding pressure to the quality of the fluid

- Measure of when a liquid evaporates

- Liquid molecules near the surface with sufficient momentum overcome the intermolecular

cohesive forces will escape the liquid & form gas.

o They exert pressure on the liquid surface

- At equilibrium, number or molecules leaving the surface (evaporation) equals number of

molecules arriving at the surface (condensation)

Vapour pressure is a function of temperature

Boiling; is the formation of vapour bubbles in a liquid when the absolute pressure in the liquid

equals the vapour pressure

- Occurs when the vapour pressure of the liquid reaches the surrounding pressure above the

liquid

- A liquid can be forced to boil by;

o Raising the temperature

o Lowering the pressure at a given temperature

Cavitation; process where pressure falls below vapour pressure causing vapour bubbles, bubbles are

then swept into a high pressure region where they collapse and cause structural damage

Fluid Dynamics Comprehensive Summary

FLUID DYNAMICS COMPREHENSIVE SUMMARY MEC2404 – FLUID MECHANICS 1

4

Pressure Pressure in a fluid at rest is the normal force per unit area exerted on a plane surface (real or

imaginary) immersed in a fluid

- 𝑃 = 𝐹

𝐴

- If pressure is equal on every plane, then the net force generated is zero

- Pressure is measured with respect to a reference level

Absolute pressure; if the pressure is a perfect vacuum

Atmospheric pressure; P0 = 1 atm = 1.01 x 105 Pa = 14.7 psi

Gauge pressure; pressure above atmospheric pressure

- Pabs = Pgauge + P0

Vacuum pressure; negative gauge pressure

Fluid statics / Hydrostatics Fluids at rest, or no relative motion

Hydrostatic forces - Act normally to the surface

- Increase linearly with depth 𝑭 = 𝝆𝒈𝒉

Pressure at a point

- 𝑃 = 𝐹

𝐴 𝐹𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 = 𝑃𝐴

The direction of pressure is defined so that positive pressure generates a force inwards on the

surface

Pressure in a homogeneous incompressible fluid at rest depends only on the depth.

- It is independent of the size and shape of the container

Hydraulic jacks; 𝐹1 = (𝐴1

𝐴2)𝐹2

Manometry Technique to measure pressure using stationary liquid columns. If we know the pressure at a point

and density of all the fluids inside the manometer, the pressure can be calculated at any other point

Open end manometer;

- Pressure difference generates a net force

- Reported as displacement in fluid

- 𝑃1 = 𝑃2 + 𝜌𝑔ℎ

U tube manometer; Commonly used to measure the pressure drop of a fluid flowing in a pipe due to

the viscous losses.