Rate

1
Rate

• Mechanical
• Fluid
• Electrical
• Thermal

2
Mechanical Rate

• Speed (s)
• Distance over time
• Velocity (v)
• Displacement over time
• Acceleration (a)
• Rate of change of velocity over time

3
Fluid Rate

• If you were standing next to a river, how could
  you measure the fluid rate?
• How much water flows by a given point
• How fast the river flows (linear rate)
• How wide the river is
• How deep the river is

4
Fluid Rate

• Volume flow rate (V)
• Amount of volume of fluid flowing over time
• V V / t
• m3/s, ft3/min, liters/hr, gallons/day, etc.
• Mass flow rate (m)
• Amount of mass of a fluid flowing over time
• kg/s, slugs/min, etc.
• m m / t

5
Fluid Rate Examples

• If your bathtub has a volume of 1 m3 and takes 3
  minutes to fill up, what is the rate of flow of
  water? (V or m?)
• V V / t
• 1 m3 / 3 min 0.33 m3 / min
• If a space shuttle burns 100,000 kg of fuel in 10
  minutes, what is the rate of fuel consumption? (V
  or m?)
• m m / t
• 100,000 kg/10 min 10,000 kg/min

6
What Affects Fluid Rate

• Prime Mover
• Pressure difference
• Size of pipes
• Diameter Wide, more fluid than narrow
• Number of paths for the fluid to take
• Many paths allow more fluid to flow
• Resistance (Next unit)
• Blockage, friction

7
Fluid Flow

• What goes in, must come out.
• The sum of the fluid flow rates in each pipe adds
  up to the total current.

8
Electrical Rate

• Electrical Current
• Rate of flow of charge over time
• I ?q / ?t
• Measured in Coulombs/second
• Also called an Ampère or Amp (A)
• Measured with an Ammeter
• 1 A is a lot of current
• 6.25 x 1018 electrons/sec!

9
Electrical Rate Example Problem

• A 2 mm long cross section of wire is isolated and
  20 C of charge are determined to pass through it
  in 40 s.
• I ?q / ?t
• 20 C / 40 s
• 0.5 C/s
• 0.5 A

10
Measuring Current

• Because you want to measure all the current
  flowing through the circuit, you hook up an
  ammeter in series
• Voltmeters measure the voltage across only one
  circuit element

11
Conventional Current

• The charges that move are electrons
• But.. By convention, electric field lines point
  the direction a positive charge would move
  (thanks, Ben Franklin)
• Conventional current flows from positive to
  negative
• Even though electrons actually flow the
  opposite way!

12
What Affects Electrical Rate

• Prime Mover
• Voltage applied
• Size and type of conductors (conductivity)
• Diameter Wide, more current than narrow
• Some conductors have more loose electrons
• Number of paths for the charge to take
• Many paths allow more current to flow
• Resistance
• Bumping of electrons

13
Series vs. Parallel Circuits

• Number of paths the charges can take
• Series
• Only ONE path (all charges go through same path)
• Traffic Jam
• Parallel
• Charges split up
• More charge can flow

14
Series vs. Parallel Circuits

• Series
• The amount of current in the first light bulb is
  the same as the current in the second (and any
  subsequent).
• IT I1 I2

• Parallel
• The current splits into two paths, so the total
  current is the sum of all the currents in each
  path.
• IT I1 I2

15
Drift Velocity

• Average displacement of a charge carrier per unit
  of time
• Chaotic, zigzag path characterized by collisions
  with fixed atoms
• Slow progress toward positive terminal
• About 1m/hr, or less than 1cm/s!

16
Drift Velocity

• If charges move so slow, how do you get high
  currents?
• Lots of charges, though at low speeds
• Current doesnt depend on how fast charges are
  moving, just how much charge passes a given
  point.

17
Drift Velocity

• How do lights turn on immediately when you hit
  the switch?
• They might move slow, but all charges in the
  conductor move immediately electric field moves
  at the speed of light!
• They dont have to go all the way from the switch
  to the bulb.. The electrons in the bulbs
  filament are responsible for lighting the bulb
  (like water already in the pipes when you turn on
  the faucet)

18
Alternating Current (AC)

• Current rapidly changing directions
• Another rate
• How fast it changes direction
• Frequency (f )
• Number of cycles per second
• Measured in Hertz (Hz)
• 1 Hz 1 cycle/second
• In the U.S., the frequency of AC is 60 Hz

19
Thermal Rate

• Heat flow rate (Q)
• The amount of thermal energy transferred per unit
  of time because of temperature difference
• Joules (J), calories (cal), British Thermal Units
  (Btu) or ft-lbs per second, minute, hour, day,
  etc.
• Q Q / t

20
Thermal Rate Example

• An air conditioning unit can remove 15,000 Btu of
  heat per hour. If it runs for 3 hours, what
  amount of heat is transferred?
• Q Q / t
• (15,000 Btu/hr)(3 hr)
• 45,000 Btu
• (45,000 Btu)(1054 J/Btu)
• 47,430,000 J

1 Btu 252 cal 1 Btu
778 ftlb 1 Btu 1055 J 1
cal 3.09 ftlb 1 cal 4.18 J
1 kcal 1000 cal
21
What Affects Thermal Rate

• Prime mover
• Temperature Difference
• Type of substance
• Thermal conductivity
• Number of paths
• Cross-sectional area
• Resistance
• Thickness of the substance through which it flows

22
Thermal Conductivity

• Metals have a higher conductivity than thermal
  insulators

23
Review of Rate

• Equations
• v ? x / t
• a ? v / t
• V V / t
• m m / t
• I q / t
• f n / t
• Q Q / t

• Mechanical
• Velocity
• Acceleration
• Fluid
• Volume Flow Rate
• Mass Flow Rate
• Electrical
• Current
• Frequency
• Thermal
• Heat Flow Rate

24
Review of Rate

• Units
• m/s, ft/min, mph, etc
• m/s2, ft/s2, mi/hr/s
• m3/s, ft3/min, liters/hr, gal/day
• Kg/s, slugs/min
• C/s or Amps
• Cycles/sec or Hz
• J/s, Btu/hr, cal/min

• Mechanical
• Velocity
• Acceleration
• Fluid
• Volume Flow Rate
• Mass Flow Rate
• Electrical
• Current
• Frequency
• Thermal
• Heat Flow Rate