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CHEE 291 TEST 2 > Module F: Fluids > Flashcards

Module F: Fluids Flashcards

1
Q

What is velocity, flow rate and flux and how is it measured?

A

Velocity: distance per unit time [m/s]
Flow rate: volume or mass per unit time [m3/s] or [kg/s]
Flux: flow rate for given AREA [m3/(sm2)] or [kg/(sm2)]

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2
Q

What happens when water flows through a pipe?

A

Molecules stick to the walls of the pipe;

Molecules stick to each other (viscosity);

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3
Q

Velocity vs Velocity Profile

A

Velocity profile shows:
Magnitude of velocity
BUT ALSO
Characteristics of the flow like direction, change due to shape of the domain…

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4
Q

What is the volumetric flow rate through a pipe?

A

Q=uA,
where Q= flow rate in m^3/s
u= average fluid velocity in m/s
A= area of pipe in m^2

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5
Q

What is the mass flow rate through a pipe?

A

𝑚 = 𝜌𝑄 = 𝜌𝑢𝐴

m = mass flow rate in kg/m^3
p: fluid density
Q = flow rate in m^3/s

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6
Q

Is mass flow rate constant? Is velocity?

A

If mass flow rate is constant in and out of the pipe, velocity must be adjusted to compensate: smaller area, bigger velocity and vice versa!

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7
Q

What is more accurate, mass or volume flow rates?

A

Mass, given that it is not affected by changes in temperature and pressure!

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8
Q

Laminar vs turbulent flows

A

Laminar: fluid movement parallel to the pipe, relatively low velocities
Turbulent: more complex patterns, rapid variation of pressure and flow velocity

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9
Q

What are the direct methods for measuring mass or volume flow rate using PHYSICAL DISPLACEMENT?

A
  • Turbine or paddlewheel meters
  • Positive displacement meters
  • Bubble meters
  • Variable area meters/ rotameters
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10
Q

What are the indirect methods for measuring mass or volume flow rate using PHYSICAL EFFECTS?

A
  • Thermal anemometry

- Vortex Shredding

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11
Q

DIRECT: Turbine or paddlewheel meter - how does it work? What affects flow rate?

A

[Flow enters cylindrical tube, will cause rotation of turbine wheel, number of rotations per unit time measured by electrical methods]

Rotation speed is DIRECTLY PROPORTIONAL to flow rate (higher flow rate = higher rotation speed)

Dependent on pulses: detectors measure number of pulses per minutes, must be multiplied by the amount of volume in each pulse

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12
Q

DIRECT: Turbine or paddlewheel meter: what are the ideal conditions, accuracy and limitations?

A
  • Low viscosity ( low opposition to flow)
  • High velocity flows

Accuracy: 0.2% at most

  • Affected by particulates and gases (air bubbles for example) which introduce error
  • Require calibration to determine the flow/ pulse
  • Flow rate = volume/ pulse * # pulses/ time
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13
Q

DIRECT: Positive Displacement Meters - how does it work? What affects flow rate?

A

[ Fluid enters, specific volume of the fluid is trapped between rotating components, which causes rotation of object at a given velocity, a counter records the number of rotations (each rotation corresponds to a fixed volume of fluid)]

Flow rate is proportional to rotational velocity

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14
Q

DIRECT: Positive Displacement Meters - What are the ideal conditions, accuracy and limitations?

A 
Low friction (friction slows down rotation speed which underestimates flow rate) 
Used to monitor domestic water consumption + in oil industry

0.5 to 2% accuracy depending on design

[robust, low-maintenance, long-life devices]

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15
Q

DIRECT: Positive Displacement Meters - Examples

A

Rotary piston meter [ cylindrical piston moves inside a cylindrical chamber]
—> Fluid causes rotation of piston around axis - after 1 rotation liquid exits the chamber - counter records number of rotations (corresponding to certain volume of fluid

Syringe pump [for low flow rates and microfluids]
—-> Motor turns a screw that pushes on the plunger of a syringe

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16
Q

DIRECT: Bubble Meters- how does it work? What affects flow rate?

A

GAS is introduced through a tee at the bottom of the tube, interacts with bubble from soap solution, time it takes for bubble to move through BURETTE is monitored

Flow rate = volume between marks/ travel time of bubble

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17
Q

DIRECT: Bubble Meters - What are the ideal conditions, accuracy and limitations?

A

Low flow rates, GASES ONLY

[Simple, low cost, bubble does not resist flow]

Need a stopwatch, produces human error - reading error, time stopping error, varies with different burette characteristics

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18
Q

Key terms: Define drag force and buoyancy

A

Drag force: force exerted by the fluid on the object (bob) in the direction of the flow

Buoyancy: an upward force exerted by a fluid that opposes the weight of a partially or fully immersed object

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19
Q

DIRECT: Variable Area Meters/ Rotameters - how does it work? What affects flow rate?

A

Fluid enters a tapered tube with graduated scale, (containing float), float stabilizes at position that balances drag force by the fluid + buoyancy with the gravitational force.

The drag force is proportional to flow rate, s.t. Fg (gravitational force) = Fd (drag) + Fa (buoyancy)

Cr (characteristic constant of the rotameter) is used to represent the drag force per area, which accounts for:

  • Drag coefficient
  • Properties of the fluid
  • Properties of the float
  • Annular area between float and walls of the tube
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20
Q

DIRECT: Variable Area Meters/ Rotameters- What are the ideal conditions, accuracy and limitations?

A

Can be used for liquids and gases, easy to use.

Limitations: relies on visual inspection for flow measurement (reading errors), calibration constants vary for each fluid and mixtures.

0.5 to 5% accuracy

Measurement range can be changed by: changing mass of float, increasing diameter, changing the length of the tube

[Sensitivity can change according to the geometry of the tube, i.e. making column thinner increases sensitivity]

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21
Q

MASS FLOW METERS: Conveyor-based method how does it work? What affects flow rate?

A

Solids (particles and powders) are placed on conveyor, placed on top of load cell, conveyor moves at velocity v.

Q = Mv/L

Q: mass flow rate
M: mass of the material measured
L: length of conveyor
v: velocity of conveyor

22
Q

What are INDIRECT METHODS for flow rate measurement based on?

A

Not based on fluid displacement but instead on other phenomena that vary as a function of fluid flow rate:

  • Heat transfer from a wire to a fluid
  • Formation of vortices around a body in a pipe
23
Q

INDIRECT: Thermal Anemometry - Basic functioning

A

Current flows through Wheatstone bridge, this generates heat by the hot wire, heat will be removed when current flows past the sensor, this heat is transferred to the moving fluid.

[direction of flow is irrelevant]

24
Q

INDIRECT: Thermal Anemometry - RTD Measurement

A

Given that system includes hot wire, it can be used as an RTD, which is heated by current flow - use wheatstone bridge equation.

25
Q

INDIRECT: Thermal Anemometry - Relating heat generated to velocity of fluid

A
  • Heat is transferred by convection, depends on the heat transfer area, temperatures of hot (wire) and cold (surrounding fluid)

q = Ah (T1-T2)

h (heat transfer coefficient),

  • Varies with geometry and flow conditions
  • Describes the effects of fluid velocity, flow patterns mixing, fluid properties

We consider that heat generated by wire = heat transferred to fluid
qw=qfluid,

26
Q

INDIRECT: Thermal Anemometry - Link between Excitation Voltage and fluid velocity

A
  1. Wire is heated up
  2. When heated wire transfers heat to surrounding fluid
  3. The magnitude of this heat (q) is equal to the power (P) which changes according to P = Iwire^2 Rwire
  4. Heat transfer (q) by convection is dependent on heat transfer coefficient (h) which is dependent on fluid velocity
  5. If we consider that the temperature of the wire and temperature of the surrounding fluid are constant, we need to adjust the excitation voltage of the wheatstone bridge
  6. Equating 3+4 yields an equation for excitation voltage according to density, velocity and fitting constants
27
Q

INDIRECT METHODS: Vortex Shredding- how does it work? What affects flow rate?

A

Take pipe, insert a bluff body, fluid flows through pipe and is disturbed by the bluff body, the frequency of the vortices (disturbances) can be correlated with volumetric flow rate

[oscillatory motion can be detected by different sensors : pressure, optical, magnetic…]

Frequency of the vortices is proportional to the average flow velocity of the fluid moving past the bluff body

28
Q

INDIRECT METHODS: Vortex Shredding– What are the ideal conditions, accuracy and limitations?

A

The strouhal number (dependent on frequency, diameter of the wire used as the bluff body, and velocity of the fluid) and the c factor (to account for the reduced area of the pipe because of the bluff body) change for each bluff body;

Q= mf

m: slope of the calibration curve
f: frequency

29
Q

Flow Meter Calibration - What are the three instruments?

A

Calibrated tank method, pipe prover, high quality positive displacement meter

30
Q

Flow meter Calibration - Calibrated tank method - Explanation?

A

Take tank with volume known to high accuracy, fill tank with fluid and measure time that it takes to empty tank

31
Q

Flow meter Calibration - Pipe Prover method - Explanation?

A

Take bypass valve with sphere detectors inserted, start fluid flow, which causes movement of spheres, sphere detectors record time that it takes to move from one sphere to another

32
Q

Flow meter Calibration - High quality positive displacement meters - Explanation?

A

Method used for GASES [accounts for compressibility and density changes]

33
Q

VISCOSITY: What is it?

A

Measure of a fluid’s internal resistance to flow or deformation

Occurs as a result of intermolecular interactions between molecules in a fluid.

The thicker the material, the larger the viscosity

34
Q

VISCOSITY: What are the two types?

A

Dynamic viscosity: FORCE required to cause a fluid to flow at a certain rate.

Kinematic viscosity: SPEED at which fluid moves when force is applied (force is often just Fg) = proportional to time required to drain capillary

35
Q

VISCOSITY: Dynamic viscosity - What are the two types?

A

Ideal or real:

= Ideal (Newtonian) means that viscosity only depends on temperature and pressure

viscosity slope is constant over a range of shear stresses

= real (non-newtonian) means that viscosity depends on temperature, pressure but ALSO physical and chemical structure of the sample and shear rate.

viscosity slope is not constant because shear stress VARIES with time

36
Q

VISCOSITY: What is the relationship between shear stress and shear rate?

A

Shear stress, measured in pascals (N/m2), is a function of viscosity (kg/ms) * shear rate (deformation/time - (1/s))

shear stress, force tending to cause deformation of a material

used for NON NEWTONIAN fluids

37
Q

VISCOSITY: What is the relationship between velocity gradient and shear stress?

A

The shear stress applied on a Newtonian fluid is PROPORTIONAL to the velocity gradient, meaning that as velocity increases shear stress increases

38
Q

VISCOSITY: Kinematic viscosity - how is it different from dynamic? What are the units?

A

kinematic viscosity takes gravity into account, s.t. v = dynamic viscosity / density

density takes mass into account

100 cSt (centi-stokes) = 10^-4m^2s^-1

1P = 100 cP = 0.1 Nsm^-2

39
Q

VISCOSITY: Relationship between viscosity and temperature?

A

increasing temperature decreases viscosity - FOR LIQUIDS - cohesive forces dominate

increasing T diminishes increases viscosity - FOR GASES- molecular motion dominates

=== important to maintain a constant temperature during viscosity measurements

40
Q

What are the four methods for measuring viscosity?

A
  • Falling ball viscometer (dynamic viscosity)
  • Calibrated capillary (kinematic)
  • Saybolt viscometer (kinematic)
  • Rotational rheometer
41
Q

VISCOSITY: Falling ball viscometer - how does it work?

A

Placing ball in viscous solution - the higher the viscosity the more resistance on the falling ball

Similar to rotameter, buoyancy applies upward force on the ball, gravity applies downward force and drag force resists movement

42
Q

VISCOSITY: Falling ball viscometer - how can we calculate dynamic viscosity? What do we need to know?

A

The time it takes for the ball to get through the fluid relates to viscosity:

time is dependent on:

  • R: radius of the sphere
  • L: distance between points a and b
  • ps: density of the sphere
  • pf: density of the fluid

and V = volume of the sphere and g = gravitational constant

43
Q

VISCOSITY: Falling ball viscometer - what are the limitations, advantages?

A

[Temperature must be maintained constant = given for viscosity measurements]

  • Measures relatively low viscosity
  • accuracy depends on instrument design
  • Small and portable

Clear fluids only, if not opaque = electrical or light detector must be used

44
Q

VISCOSITY: Calibrated glass capillary column - how does it work?

A

Based on gravity - fluid is allowed to drain

Timer records the time necessary for the meniscus to move from the start mark to the stop mark

45
Q

VISCOSITY: Calibrated glass capillary column - how can we find viscosity?

A

Kinematic viscosity = proportional to the drain time:

V = constant * t

the constant can be found via calibration (called capillary factor) - it accounts for the overall geometry of the column

46
Q

VISCOSITY: Saybolt Viscometer - how does it work?

A

Fluid is allowed to drain in a narrow capillary

Fluid is maintained at constant temperature using a water bath (reservoir) and heaters

47
Q

VISCOSITY: Saybolt Viscometer - how can we find viscosity?

A

Similar to calibrated capillary column, whereby time required for the fluid to drain is proportional to the kinematic viscosity
for FULLY DEVELOPED LAMINAR FLOWS (same velocity profile at any cross-section within the pipe)

v = 0.255t -208/t

48
Q

VISCOSITY: Saybolt Viscometer - how accurate is it?

A

High accuracy measurements (+/- 0.2%)

Can therefore be used to calibrate other instruments

49
Q

VISCOSITY: Rotational Rheometer - how does it work?

A

Measure dynamic viscosity using a motor that generates torque (this is because gravity based methods take a long time)

Fluid is placed between concentric cylinders
Outer cylinder is fixed, inner cylinder rotates

= the torque required to produce a given angular velocity are measures of the viscosity of the fluid (force measurement)

50
Q

VISCOSITY- Rotational Rheometer - advantages

A

Wide range operating conditions (wide range of viscosities)

Different cylinder and plate geometries can be used

CHEE 291 TEST 2 (4 decks)

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