FLUID FLOW /PRESSURE IN STATIONARY FLUIDS

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FLUID FLOW /PRESSURE IN STATIONARY FLUIDS
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Energy

• Forms of energy
• Any fluid in motion possesses 4 kinds of energy

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• Form of Energy Example
• Potential or head - water at top
  of
• 
  tank
• Kinetic or velocity - water doing
  work
• 
  on water wheel
• Static or Pressure - Pressure
  exerted
• 
  inside line
• Heat - Heat
  generated in
• 
  line due to friction

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Examples of conversion of energy

• Pumps - mechanical to velocity
• mechanical to
  pressure
• Steam siphon - Pressure to velocity
• Water hammer - Velocity to pressure
• Filling tank - Pressure to velocity to
  potential

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Total Energy

• The total energy that a fluid in motion has at
  any time is equal to the sum of the form listed
  above. Because energy can neither be created or
  destroyed, it is therefore possible to convert
  one form of energy to another, such as velocity
  into pressure.

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Fluid Flow

• Bernoullis Principle
• when a fluid is in motion, its pressure
  increases whenever its velocity decreases.
• Likewise its pressure decreases whenever its
  velocity increases

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Fluid

• A fluid is a substance which undergoes continuous
  deformation when subjected to a shear stress.

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Factors determining Fluid Flow

• Viscosity
• Property of fluid to resists any force that tends
  to produce flow. This resistance to flow or
  movement is known as viscosity
• It affects the performance of pumps and the
  pressure drop when pumping through a given pipe
  line.

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Factors determining Fluid Flow

• Pipe size
• For a given through put, the pressure drop
  increases rapidly with decreasing pipe diameter
• Roughness
• The degree of roughness of the internal wall of
  the pipe affects fluid flow. Old rusty or pitted
  pipe would offer more resistance to flow (higher
  pressure drop)
• Pipe restrictions
• The number of fittings, valves, etc affects
  friction loss.

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Type of Flow

• Streamline flow fluid flows in smooth layers.
• Flow is in straight
  unbroken lines
• Re lt 2000
• Turbulent flow there is an irregular random
• motion of fluid
  particles
• Re gt 4000
• Transition between above.

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Reynolds Number

• Nature of flow in pipe depends on pipe diameter,
  the density and
• viscosity of the flowing fluid, and the velocity
  of flow.
• Re dvp
• u
• Where Re -
  Reynolds number
• d -
  internal diameter of pipe
• v -
  kinematic viscosity
• p -
  weight density of fluid
• u -
  dynamic viscosity
• The term kinematics refers to the quantitative
  description of fluid
• motion or deformation.
• Kinematic viscosity v u/p u viscosity
• 
  p density

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Pumping

• In plant operations, we quite often want the flow
  to be from a low to a high pressure area. This
  requires use of pumps or compressors.
• In the operation of pumps, pressure drop is of
  utmost importance. To operate a centrifugal pump,
  for example, the suction line can be and often is
  more important than discharge line. Although the
  discharge line may be designed so that the pump
  is capable of putting the required amount of
  liquid through it,

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Pumping

• If the suction line is not large enough or is
  improperly installed, pumping difficulties will
  be experience.
• If pressure drop is such that liquid starts to
  vaporize when it reaches the pump, or if suction
  conditions are not correct, then pump will not
  fill up properly and will become gas bound.
• The pumping rate and discharge pressure will fall
  off, and pump will begin to cavitate and heat up.

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Flow of Gases

• Gases are compressible liquids are
  non-compressible
• In moving a gas through a line, the higher the
  pressure on the system, the more pounds of gas
  that can be transferred for the same volume rate
  of flow.

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The effects on plant operations due to
compressibility of a gas are

• Increased pressure means reduced equipment size
• Gas such as air, under pressure can be used to
  operate pneumatic tools
• Hydrocarbon gases can be compressed, cooled and
  liquefied
• Refrigeration

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Fluid Performing Work

• A column of water will exert a pressure of 0.433
  psi
• for each foot of weight.
• Suppose we build a dam and raised the height of
• the water to 200 feet. That would mean that the
• pressure at the bottom of the dam would be 0.433
  x
• 200 or 86 psi. This says that if turbines were
  installed
• at the bottom of the dam we would have a driving
• force of 86 psi to turn the turbines which can
  be used
• to generate electricity.

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Siphon

• The siphon is a bent tube with branches of
  unequal length open at both ends and it is used
  to move a liquid from a higher point to a lower
  point, over an intermediate point higher than
  either.

C
1 ft
2 ft
A
B
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• Siphon
• Since the upward force at A is greater than B,
  the flow will be from A to B. Suppose the tube is
  filled with water and placed in the vessels as
  shown in the figure above. The water in leg CA
  exerts a head or downward pressure of 1 foot of
  water or 0.433 psi. The water in branch CB exerts
  a head of 3 x 0.433 or 1.299 psi. Therefore, the
  net downward pressure causing flow from A to
  elevation B is 0.866 psi.

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Fluid Rates Measurement

• When pressure is converted to velocity, pressure
  is reduced. The difference in pressure between 2
  points in the line of flow is the principle on
  which common flow meters operate.
• Orifice plate
• Pitot tube
• Venturi tube

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Pressure in Stationary Fluids

• Force - means a push or pull
• Weight - means heaviness
• Pressure - The push or pull or weight or weight
  per unit area
• of the surface acted upon.
• Pressure __ Force_____ __
  Weight____
• Area Acted upon
  Area Acted Upon
• Water weight 62.4 pounds per cubic ft, 1 foot
  high water would therefore
• exert a pressure of
• 62.4lbs x 1 ft 0.433 lbs
• ft3 144 ins2

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Pressure Produced by Liquids

• Since all fluids have weight, they create a
  pressure against the walls that hold them.
• The pressure exerted by a liquid at any given
  point or location in a vessel depends upon the
  height of liquid above it.
• This pressure is independent of the shape of the
  vessel
• The pressure on the btm of all vessels below will
  be the same

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• Pressure Produced by Liquid (cont)
• Different liquids weigh different amount for the
  same volume and therefore would create different
  pressures. 1 cubic foot of water weighs 62.4
  pounds. If this cubic foot of water were put in a
  box 1 foot high, 1 foot wide, and 1 foot long,
  the total force on the bottom of the box would be
  62.4 pounds. This total force would be
  distributed over an area one foot square or 144
  square inches. The pressure on a given square
  inch would be 62.4 pounds divided by 144 square
  inches 0.433 psi.

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• Pressure Produced by Liquid (cont)
• If a box were filled with water that was 2 feet
  high and held 2 cubic feet the pressure would
  equal 62.4 x 2 /144 or 0.866 psi.
• Each foot of water height will develop 0.433 psi.
  For example a 100 foot tower, if filled with
  water, would create 43.3 psi at the bottom of the
  tower.

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Density

• Weight of one cubic foot of material is called
  the density of that material

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Pressures Produced By Gases

• The deep layer of air which blankets the earth
  exerts a pressure much like the water pressure at
  the bottom of the ocean. This pressure is known
  as atmospheric pressure and is about 14.7 PSI at
  sea level. At higher elevation, the atmospheric
  pressure falls.
• The weight of air causes an atmospheric pressure
  of 14.7 psia. Less than 14.7 psia is a vacuum.

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Gauge Pressure

• Most of pressure gauges are calibrated so that
  0 on the gauge is atmospheric pressure.
• Reading therefore is called PSIG

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Standard Pressure

• The volume of a given sample of a gas has almost
  no meaning unless the pressure is specified.
• For uniformity, 760 mm of mercury, or 1 atm, has
  been adopted as the standard pressure.
• All specific properties of gases such as density
  are always at standard pressure.

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Vacuum

• When a pressure is less than atmospheric
  pressure, it is called a vacuum. A vacuum is a
  lack of air or fluid.

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Laws Governing Gas Under Pressure

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Boyle Law

• At constant temperature, the volume of a fixed
  weight of a given gas is inversely proportional
  to the pressure under which it is measured.
• P x V K (at constant temp)
• P1V1 P2V2 at constant temperature
• If the pressure is doubled, volume is halved
• If the pressure is halves, volume is doubled

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Charles Law

• At constant pressure, the volume of a fixed
  weight of gas is directly proportional to the
  absolute temperature
• V kT (at constant pressure)
• V1 T1 (at constant pressure)
• V2 T2

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Daltons Law of Partial Pressure

• Each gas in a gaseous mixture exerts a partial
  pressure equal to the pressure which it would
  exert if it were the only gas present in the same
  volume, and the total pressure of the mixture is
  the sum of the partial pressures of all the
  component gases.
• P total P1 P2 P3 .

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Raoults Law

• Ideal solution - exhibits no change in the
  properties of its constituents
• beyond that of dilution.
• - For our present purpose
  an ideal solution is most
• usefully defined in terms
  of generalization known as
• Raoults law.
• Raoults Law
• - At any given temperature, the vapor pressure
  of any component of a solution (i.e, its partial
  pressure in the mixed vapor in equilibrium with
  the solution) is equal to the product of the mole
  fraction of that component in the solution and
  its vapor pressure in thepure liquid state at the
  same temperature.

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Raoults Law

• Raoults Law (cont)
• Thus in a solution composed of 2 volatile
  liquid A and B, the vapor pressure of which in
  the pure state are PAo and PBo respectively, we
  may write
• PA XAPAo
• PB XBPBo
• Total vapor pressure P of an ideal solution
• P XAPAo XBPBo

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Problem solving

• A sample of gas occupies a volume of 86.8 ml at a
  pressure of 730 mm of mercury and a temperature
  of 27oC. What will be its volume at standard
  pressure and 27oC?
• Solution
• Standard pressure 760 mm hg
• V1 86.8 ml P1
  730 mm
• V2 ? Ml P2
  760 mm
• Pressure is increased from 730 to 760 mm,
  the volume is therefore
• decreased, and the original volume must be
  multiplied by a fraction
• less than 1.
• V2 86.8 x 730/760 83.4 ml
  

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Problem Solving

• Calculate the volume that 22.4 liters of a gas
  measured at the standard pressure would occupy at
  a pressure of 732 mm hg.
• V1 22.4 liters P1
  760 mm
• V2 ? Liters
  P2 732 mm
• Since the pressure is decreased to 730/760
  of its original value,
• the volume is increased by the factor
  760/732
• V2 22.4 liters x 760/732 23.3
  liters

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Problem Solving

• A gas measures 83.4 ml at 1 atm pressure and a
  temperature of
• 27 oC. Calculate its volume at standard
  condition.
• V1 83.4 ml T1
  27 273 300 oK
• V2 ? Ml T2
  273 oK
• Since the temperature is decreased, the
  volume will also be decreased. The original
  volume must therefore br multiplied by a fraction
  less than 1, namely 273/300
• V2 83.4 ml x 273/300 75.9 ml

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Problem Solving

• A sample of gas occupies a volume of 86.8 ml at a
  pressure of 730 mm and a temperature of 27 oC.
  What will be its volume at standard condition?
• V1 86.8 ml T1
  300 oK P1 730
• V2 ? Ml T2
  273 oK P2 760
• Pressure is increased from 730 to 760 mm,
  volume should decrease, we therefore multiply the
  original volume by 730/760. Temperature decrease
  from 300 to 273 oK, likewise volume decreases,
  hence we multiply by the temperature fraction
  273/300, therefore
• V2 86.8 ml x 730/760 x 273/300
  75.9 ml.

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Problem Solving

• 5. A certain gas measures 546 ml at a pressure
  of 1 atm and a temperature of -80 oC. Calculate
  the volume it would occupy at a pressure of 1.5
  atm and a temperature of 30 oC.
• First we change the centigrade temperature
  to absolute
• - 80 oC 80 273 193 oK
• 30 oC 30 273 303 oK
• V1 546 ml P1 1 atm
  T1 193 oK
• V2 ? ml P2 1.5 atm
  T2 303 oK
• V2 546 ml x 1/1.5 x 303/193
  571 ml

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Joule-Thomson Effect

• Gases are cooled upon sudden expansion from high
  to low pressure, even if they do no external
  work.
• As gas expands the molecules pull apart from each
  other, and work must be done to overcome the
  cohesive forces that tend to hold the molecules
  together. Since this work is done at the expense
  of the kinetic energy of the molecules of the
  gas, the temperature is lowered on expansion.

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Standard Volume

• Volume measured at standard condition ie temp
  60 oF
• Pressure 1 atm (14.7psi)
• At standard condition one (1) mole of gas
  occupies 22.4 liters