Fluid Mechanics

Question 1

What is a fluid?

Answer 1

A substance which at rest, cannot sustain shear stress

Question 2

What does a steady flow mean?

Answer 2

The properties do not change with time

Question 3

What is viscosity?

Answer 3

The means by which fluids resist and transmit shear forces between layers.

Question 4

What is an inviscid fluid?

Answer 4

A fluid that has 0 viscosity and cannot transmit shear forces, does not exist in real life

Question 5

What are the two measures of viscosity?

Answer 5

Dynamic (μ) and Kinematic (ν)

Question 6

How are the two measures of viscosity related?

Answer 6

v = μ / ρ
kinematic = dynamic / fluid density

Question 7

What does a Newtonian fluid mean?

Answer 7

It has constant viscosity regardless of the shear force they are under

Question 8

What equation do Newtonian fluids obey?

Answer 8

τ =μ du/dy

Question 9

What will the fluid next to a surface obey?

Answer 9

The no slip condition, it will move at the same speed as the surface

Question 10

What can you safely assume about a fluid in a small gap?

Answer 10

The velocity profile will be linear

Question 11

How do you find the force or torque required to move a fluid?

Answer 11

Integrate the shear force over the area

Question 12

What is gauge pressure?

Answer 12

Pressure relative to Patm
Absolute pressure - Patm

Question 13

What is absolute pressure?

Answer 13

Pressure relative to 0

Question 14

What are 2 properties of how pressure acts?

Answer 14

• Uniformly in all directions
• Normal to surfaces

Question 15

Pressure Force = ?

Answer 15

Pressure x Area

Question 16

What is the hydrostatic equation?

Answer 16

dp /dz = ρg

Question 17

How can you find pressure if it varies as a function of depth?

Answer 17

p = pₐ +∫ pg.dz (from 0 to h)

Question 18

What is true about the pressure at a given distance from the free surface?

Answer 18

It will be the same, regardless of the container shape

Question 19

What is the manometer equation

Answer 19

P₁ - P₂ = (PL -pₐ) gh
*Note that if the manometer is inclined, that reduces the measurement error by increasing the distance moved for a given pressure

Question 20

What does Archimedes’ Principle state?

Answer 20

The upthrust on a body in a fluid is equal to the weight of displaced fluid

Question 21

What does it mean for a gas to be compressible?

Answer 21

The density of a gas can change

Question 22

Why is it easier to work in gauge pressure for questions in Fluids?

Answer 22

atmospheric pressure will often cancel out

Question 23

What is the equation for the force on a submerged body in a constant density fluid?

Answer 23

F =limits:0 s ∫ ρgz. ds
s and z are not always the same!!
NOT ON FORMULA SHEET

Question 24

What is the equation for the moment on a submerged body in a constant density fluid?

Answer 24

M =limits:0 s ∫ ρgzs. ds

Question 25

What equation allows you to find where the pressure force acts on a submerged body?

Answer 25

M = F X꜀ₒₚ (centre of pressure)

Question 26

What are the 2 methods for finding the S꜀ₒₚ on submerged objects?

Answer 26

A) 1 - Use integration equations to find M and F 2 Use M=FX꜀ₒₚ to find X꜀ₒₚ B) Fᵧ = Weight of fluid above it Fₓ = Avg Pressure x Projected Area

Question 27

What is the resultant force on a vertical surface in a constant density fluid in a depth of 0 to h? Where does it act?

Answer 27

F = 1/2 ρgh² acting at 2h/3 from the surface

Question 28

What do streamlines represent?

Answer 28

The trajectories of particles in a steady flow

Question 29

When does flow separation happen?

Answer 29

When the flow is passing over a surface with a large curvature and/or there is a low-high pressure gradient

Question 30

What does the assumption of inviscid flow mean?

Answer 30

the viscosity is 0, the flow cannot separate and there is no friction between the flow and a body. It simplifies fluid dynamics equations without sacrificing too much accuracy as long as there isnt much flow seapration

Question 31

What does the assumption of incompressibility mean and when does this assumption break down?

Answer 31

Changes in density are negligible When the air speed approaches the speed of sounds, or large pressure changes, effects due to compressibility must be considered

Question 32

What is the fundamental continuity equation / principle?

Answer 32

ṁᵢₙ = ṁₒᵤₜ mass must always be conserved

Question 33

What is true for an incompressible flow's volumetric flow?

Answer 33

It is constant because of Constant density Qin = Qout

Question 34

What is ṁ equal to for uniform flow

Answer 34

ṁ =ρAV

Question 35

What is Q equal to for uniform flow

Answer 35

Q = AV

Question 36

How is ṁ calculated for non uniform flow?

Answer 36

∫pV.dA

Question 37

What is kinetic energy flux equal to for uniform flow?

Answer 37

KE flux = 1/2 ρAV³

Question 38

What is momentum flux equal to for a uniform flow?

Answer 38

Momentum flux =ρAV²

Question 39

What does dA equal to for a circle with radius r?

Answer 39

dA =2πr.dr (when speed varies with radius)

Question 40

What does dA equal to for a rectangle with width w?

Answer 40

dA = wdy (when speed varies in vertical direction)

Question 41

How do you calculate the average speed of a non-uniform flow?

Answer 41

U = rh /ρA

Question 42

Describe the technique of applying continuity to a system?

Answer 42

- Draw a Control Volume - Make sure the flow is steady > Set control volume to move if necessary > Work out the relative velocities into and out of the control volume - Write down all the mass flows and apply ṁᵢₙ = ṁₒᵤₜ