Transport Phen - Fluid Mechanics

Question 1

What is a fluid?

Answer 1

Gases and liquids, able to flow when a force is applied to them.

Formally, the distinguishing feature of a fluid is its inability to resist shearing forces while remaining in static equilibrium.

Question 2

What are shearing forces?

Answer 2

A force acting in a direction parallel to a surface or to a planar cross section of a body, e.g. the pressure of air along the front of an airplane wing.

Shearing forces are unaligned forces pushing one part of a body in one specific direction, and another part of the body in the opposite direction.

Symbol for shearing stress: τ (units of N/m2)

Question 3

What are the features of the phase diagram (of water)?

Answer 3

Pressure (y) against temperature (x) plotted
Upwards curve plotted.

• solid region (above curve and before upwards line)
• liquid region (above curve and after upwards line)
• vapour/gas region (below curve)
• compressible region (above curve beyond critical point)
• supercritical point (beyond critical)
• non-compressible gas region (below curve beyond critical point)

Question 4

What is the supercritical fluid?

Answer 4

Any substance at a temperature and pressure above its critical point, where distinct liquid and gas phases do not exist. It can effuse through solids like a gas, and dissolve materials like a liquid.

Question 5

What does it mean for a liquid to be incompressible?

Answer 5

Their density does not vary with temperature or pressure.

Question 6

How is pressure different to shear stress?

Answer 6

Pressure always acts normal to the surface whereas shear stress always acts parallel to the surface.

Question 7

How is viscosity related to molecular weight?

Answer 7

Liquid viscosity increases rapidly with increasing molecular weight, as there are increased interactions between molecules.

Question 8

What’s 1 poise?

Answer 8

1 g/cm*s

Question 9

What is the no-slip boundary condition for viscosity?

Answer 9

The no-slip condition for viscous fluids assumes that at a solid (stationary) boundary, the fluid will have zero velocity relative to the boundary.

Question 10

What happens on the line of phase diagrams?

Answer 10

Change in phase.

Dew points, bubble points or triple point found.

Question 11

What’s the phase rule?

Answer 11

F + P = c + 2

Where:
F - degrees of freedom
P - number of phases
c - number of components

Question 12

What’s viscosity?

Answer 12

The state of being thick, sticky, and semi-fluid in consistency, due to internal friction.
“cooling the fluid raises its viscosity”

A quantity expressing the magnitude of internal friction in a fluid, as measured by the force per unit area resisting uniform flow.

Question 13

What’s hydrostatic pressure?

Answer 13

The pressure that is exerted by a fluid at equilibrium at a given point within the fluid, due to the force of gravity.

Larger hydrostatic pressures can occur when moving fluid is rapidly brought to rest (e.g. a water hammer in a pipe) or as a result of rapidly rotating equipment (e.g. a centrifugal pump).

Question 14

How can change in pressure with height be found? (Hydrostatic pressure)

Answer 14

dp/dh = -ρ*g

Integrating,

p = -ρg(h2 - h1)

p = -ρgΔh

Question 15

How does (hydrostatic) pressure vary along the horizontal plane?

Answer 15

Pressure is uniform over any horizontal plane i.e. the pressure in a static (or non-moving) fluid is the same in all parts of the fluid that are at the same height. This may not be true if the fluid is moving (or dynamic).

In the vertical plane, pressure changes - as an object moves closer to the fluid surface, pressure decreases.

Question 16

How does (hydrostatic) pressure vary along the vertical plane?

Answer 16

Pressure varies with height (or depth) in the fluid. The rate of fall of pressure p in a stationary fluid of density r as a function of height h is given by:

dp/dh = -ρ*g
p = -ρ*g*Δh

Question 17

What is pressure head?

Answer 17

The height of a liquid column that corresponds to a particular pressure exerted by the liquid column on the base of its container. It may also be called static pressure head.

pressure head = p/ρg

Question 18

What is upthrust / buoyancy?

Answer 18

The upward force acting on a solid that is in a fluid, caused by fluid pressure opposing the weight of the object.

It is equal to the weight of fluid displaced by the solid.

Question 19

What is upthrust equal to?

Answer 19

The weight of the fluid displaced by the solid.

Question 20

What are the 2 types of fluid flow?

Answer 20

Laminar - steady flow, no eddies. Measurements of the fluid velocity at a point are constant with time. (viscous effects as opposed to momentum effects are important)

Turbulent - random eddies, mixing. The velocity at a point in the pipe has a well-defined temporal average, but there are random fluctuations about that average

Question 21

How is Reynolds number, Re, calculated?

Answer 21

Re = ρul/μ
where u and l are a characteristic velocity and length scale, respectively.

It can be considered as the ratio of inertial forces to viscous forces. [Re = Fi : Fv]

Question 22

What does the total energy of a fluid [J/Kg] of mass, m, in motion consist of?

Answer 22

Internal energy, U [J/Kg]

Pressure energy (aka pV work) [J]

Kinetic energy [J]

Potential energy [J]

E = U + pV/m + v²/2 +gh

(some components divided by m for J/Kg)

E = U + p/ρ + v²/2 +gh

Question 23

What is Bernoulli’s principle

Answer 23

p₁/ρ + v₁²/2 +gh₁ = p₂/ρ + v₂²/2 +gh₂

If the fluid has a constant density or behaves as ideal, then the internal energy, U, remains constant if the temperature is constant (so not included in the equation)
Ideal fluid also assumes it is frictionless and there’s no pump so W ᵢₙ/ₒᵤₜ isn’t included either.

Question 24

What conditions are assumed when applying Bernoulli’s principle?

Answer 24

Constant density - incompressible flow

Steady state/flow (no energy is accumulated)

No interchange of mechanical and thermal energy & no forces on sides of the control surface (no viscous, frictional or heat dissipation)

Question 25

What is Bernoulli’s equation, also considering mechanical and thermal energy transfers?

Answer 25

S + p₁/ρ + v₁²/2 +gh₁ = p₂/ρ + v₂²/2 +gh₂ + L

Where:
- S is the energy input between sections 1 & 2 per unit mass of flow

• L is the loss of energy between sections 1 & 2 per unit mass of flow (in J/Kg)

Rates of energy supply/dissipation can therefore be found:

• P input = S * mass flowrate
• P output = L * mass flowrate

Question 26

What is fluid head and how is it found?

Answer 26

The fluid head is the pressure measured by the height to which the fluid being pumped can be raised to by the pressure.

It is found by dividing each term in Bernoulli’s equation by g (m/s2)

Total head = p/ρg + v²/2g +g
which would be the same throughout the fluid is there is no energy in/out.

Question 27

What is Newton’s second law?

Answer 27

Force is equal to the rate of change of momentum.

p = mv

Question 28

What’s the sum of applied forces?

Answer 28

Sum of applied forces is equal to normal forces + forces acting by duct wall

= p₁A₁ - p₂A₂ - F fₗᵤᵢ𝒹

= mu₂ - mu₁

Question 29

How is dynamic viscosity (mu) calculated?

Answer 29

Dynamic viscosity = density * kinematic viscosity

Question 30

Why does the free surface of a liquid tend to contract to the smallest possible area?

Answer 30

Due to the force of surface tension.

Question 31

What’s shear rate?

Answer 31

A.k.a velocity gradient.

The rate of change of velocity at which one layer of fluid passes over an adjacent layer.

Question 32

What’s shear stress?

Answer 32

(Tau)
A measure of friction from a fluid acting on a body adjacent to it.

Tau = shear force / sheared area = Fs/A

Question 33

What are constitutive equations?

Answer 33

Equations relating the suitably defined shear stress and shear rate.

E.g. for a Newtonian fluid,
Shear stress = viscosity * shear rate

Tau = mu*du/dy

Question 34

What are general properties of membrane filtration?

Answer 34

Whilst of great operational significance, permeate flux is in itself a poor indicator of surface condition.

In addition to pore size (or molecular weight cut off) hydrophobicity, roughness and charge are also crucial in determining membrane filtration performance.

In some systems it is possible to separate solutes against their size gradients, or achieve negative rejection ratios.

Selective adsorption of key species in the filtrate can often modify the membrane surface to give favourable characteristics.

Performance after multiple filtration and cleaning cycles is often significantly different to the performance after a single cycle (even if the membrane is properly conditioned).

The rank order of effectiveness of cleaning agents can change depending upon the filtration / cleaning cycle number at which they are compared.

(many food based deposits swell on contact with caustic agents)

Select an appropriate cleaning agent based on material compatibility, and a knowledge of the deposit composition, structure and location.

Cleaning agent temperature and concentration are often more important that transmembrane pressure (TMP) and cross flow velocity (CFV) in controlling the cleaning process.

Question 35

What is the impact of high cleaning agents temperatures (used for membranes)?

Answer 35

Higher cleaning agent temperatures reduce viscosity, and speed up cleaning reactions such as dissolution, peptide bond hydrolysis etc.

Performance improvements can be dramatic even moving from 30 - 50°C. However, too high a temperature can sometimes inhibit the cleaning of membranes.

Question 36

How does transmembrane pressure affect membrane cleaning?

Answer 36

High pressures force the partially cleaned deposit into membrane pores. If possible, clean at zero transmembrane pressure. Try to clean at a lower TMP than that used during the filtration process.

•Surfactant micelles often change shape approaching the cloud point. This can lead to dramatic changes in viscosity and therefore cleaning performance.

Question 37

What are examples of applications of membrane technology?

Answer 37

Electro coating

Daily industry & filtration of milk (and with ultrafiltration in cheese manufacturing)

Food indursty e.g. tomato juice concentration and fruit processing

Water treatment

Pharmaceutical production

Membrane bioreactors

Question 38

What is polysulphone?

Answer 38

A material used for membranes.

Polysulphone (PS) membranes are the most popular in the food industry. Although they foul more than regenerated cellulose membranes (which are very hydrophilic) they are cheap and can handle chemical cleaning formulations (acids and alkalis).

Polyethersulphone (PES), polysulphone (PS) and polyvinylidene difluoride (PVDF) all find use in dairy filtration. They can withstand high temperatures and are chemically resistant. PVDF is hydrophobic, so fluxes are typically lower than for the more hydrophilic membranes.

Question 39

What are the benefits of using UF (in milk and cheese manufacture)?

Answer 39

Benefits of using UF include:
•increasing yield
•reduction of rennet (enzyme)
•reduced volume of milk to handle
•Little or no whey produced as most of the lactose and water has already been removed
•More uniform product
•Can be a continuous and automated process; improving product quality and improved sanitation.