Devices to measure Pressure

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Devices to measure Pressure

• In chemical and other industrial processing
  plants it is often important to measure and
  control the pressure in a vessel or process
  and/or the liquid level in a vessel.
• Also, since many fluids are flowing in a pipe or
  conduit, it is necessary to measure the rate at
  which the fluid is flowing.
• Many of these flow meters depend upon devices to
  measure a pressure or pressure difference.
• MANOMETERS are mainly used

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MANOMETERS

• Simple U tube manometer
• Pressure pa is exerted on one arm of the U tube
  and pb on the other arm.
• Both pressures pa and pb are pressure taps from a
  fluid meter
• The top of the manometer is filled with liquid B,
  having a density of rB, and the bottom with a
  more dense fluid A, having a density of rA
• Liquid A is immiscible with B.
• To derive the relationship between pa and pb
  .

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• We know, p2 p3

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• Write an assignment on Different types of
  Manometers

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Prob 1

• A manometer, as shown in Fig. is being used to
  measure the pressure drop across a flow meter.
  The heavier fluid is mercury, with a density of
  13.6 g/cm3, and the top fluid is water, The
  reading on the manometer is 32.7 cm. Calculate
  the pressure difference in N/m2
• Ans 4.04 x 104 N/m2

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Prob 2

• A simple U tube manometer is installed across an
  orifice meter. The manometer is filled with Hg
  (specific gravity 13.6) the liquid above the Hg
  is CCl4 (s.g 1.6). The manometer reads 200mm.
  What is the pressure difference over the
  manometer.
• Ans 23,544 N/m2

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Prob 3

• A U-tube manometer filled with mercury is
  connected between two points in a pipeline. If
  the manometer reading is 26 mm of Hg, calculate
  the pressure difference between the points when
  (a) water is flowing through the pipe (b) air at
  atmospheric pressure and 20ºC is flowing in the
  pipe. Density of mercury 13.6 gm/cc Density of
  water 1 gm/cc Molecular weight of air 28.8

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• (a) Water is flowing through the pipe
• Dp (rm - r)gh (13600 - 1000) x 9.812 x 0.026
  3214.4 N/m2
• (b) Air at atmospheric pressure and 20ºC is
  flowing in the pipe
• r 28.8 x 101325/(8314 x 293) 1.2 kg/m3
• Dp (rm - r)gh (13600 - 1.2) x 9.812 x 0.026
  3469.2 N/m2

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From doran..
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Newtonian Non-Newtonian fluids

• It has been found that the Shear stress for flow
  of fluid is directly proportional to the velocity
  gradient (velocity/distance).
• Introduce the proportionality constant
  viscosity we get Newtons law of
  viscosity
• A fluid obeys this law is Newtonian
  fluid....(i.e. constant viscosity)
• -----otherwise Non-Newtonian fluid

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• All gases and most liquids which have simpler
  molecular formula and low molecular weight such
  as water, benzene, ethyl alcohol, CCl4, hexane
  and most solutions of simple molecules are
  Newtonian fluids.
• Generally non-Newtonian fluids are complex
  mixtures slurries, pastes, gels, polymer
  solutions etc.,

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Various non-Newtonian Behaviors

• Bingham-plastic Resist a small shear stress but
  flow easily under larger shear stresses. e.g.
  tooth-paste, jellies, and some slurries.
• Pseudo-plastic Most non-Newtonian fluids fall
  into this group. Viscosity decreases with
  increasing velocity gradient. e.g. polymer
  solutions, blood.
• Pseudo-plastic fluids are also called as Shear
  thinning fluids. At low shear rates(du/dy) the
  shear thinning fluid is more viscous than the
  Newtonian fluid, and at high shear rates it is
  less viscous.
• Dilatant fluids Viscosity increases with
  increasing velocity gradient. They are uncommon,
  but suspensions of starch and sand behave in this
  way.
• Dilatant fluids are also called as shear
  thickening fluids.

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Rheology of fermentation broth

• The fungus Aureobasidium pullulans is used to
  produce an extra cellular polysaccharide by
  fermentation of sucrose. After 120 h
  fermentation, the following measurements of shear
  stress and shear rate were made with a rotating
  cylinder viscometer. Plot the rheogram for this
  fluid and name the fluid type.

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Shear stress (dyn/cm2) Shear rate (s-1)
44.1 10.2
235.3 170
357.1 340
457.1 510
636.8 1020
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Mechanism of Fluid Flow

• When a fluid flows through a pipe or channel, the
  character of the flow can vary according to the
  conditions.
• The forms of flow can best be visualized by
  reference to a classical experiment on the flow
  of water through a circular tube, first carried
  out by Osborne Reynolds in 1883.
• Reynolds studied the effect of varying the
  conditions on the character of flow and on the
  appearance of the thread of colored liquid. This
  can be illustrated, for example, by varying the
  velocity of the water through the tube.
• When the velocity is low, the thread of colored
  liquid remains undisturbed in the centre of the
  water stream and moves steadily along the tube,
  without mixing, this condition is known as s
  viscous, or laminar flow.(Streamline flow)

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Reynolds experiment
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• At moderate velocities, a point is reached (the
  critical velocity) at where the thread begins to
  waver, although no mixing occurs. This is the
  phase of transitional flow.
• As the velocity is increased to high values
  eddies begin to occur in the flow, so that the
  colored liquid mixes with the bulk of the water
  immediately after leaving the jet. Since this is
  a state of complete turbulence the condition is
  known as turbulent flow.
• As a result of his experiments Reynold found that
  flow conditions were affected by four factors
• Diameter of pipe
• Velocity of fluid
• Density of fluid
• Viscosity of fluid
• These were connected together in a particular
  way and could be grouped into a particular
  expression known now as Reynolds Number NRe or
  Re

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NRe

• Reynolds number is given by.
• It can be seen that all the units cancel out
  i.e. Re is dimensionless.

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Significance of Re

• For a straight circular pipe

Type of flow Reynolds no. Velocity
Laminar lt2100 Low
Turbulent gt4000 High
Transition 2100ltRelt4000 Moderate
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Prob 1

• Reynolds Number in a Pipe
• Water at 303 K is flowing at the rate of 10
  gal/min in a pipe having an inside diameter (ID)
  of 2.067 in. Calculate the Reynolds number. Given
  r0.996 g/cc m0.8007 Cp
• 1 gal 3.785L
• Change all the units to SI
• D (2.067)0.0254 m
• Since velocity flowrate / CSA
• ?v 10(3.785x10-3) m3 / (60 sec) (p/4)D2 m2
• r0.996 x103 kg/m3
• m0.8007 10-3 kg/m.s
• NRe 19030 lt 2100 (LAMINAR)

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Prob 2

• NRe for milk flow
• Whole milk _at_ 293K having a density of 1030 kg/m3
  and viscosity 2.12 cP is flowing at a rate of
  0.605 kg/s in a glass pipe having a dia of
  63.5mm.
• Cal NRe
• Cal the flow rate needed in m3/s for Re2100 and
  velocity in m/s

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• Vol.flow rate Mass flow rate / density
• Velocity Vol.flow rate / CSA
• v (0.605 / 1030) / (p/4) (63.5x10-3)2
• NRe 5722 Turbulent
• If NRe 2100
• v 0.0608 m/s
• Q 2.155x10-4m3/s

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Prob 3

• Pipe dia Re
• An oil is being pumped inside a 10mm dia pipe _at_
  Re of 2100. The oil density is 855 kg/m3 and
  viscosity is 2.1x10-2 Pa-s.
• What is the velocity in the pipe?
• It is desired to maintain the same Re 2100 and
  the same velocity as in part (a) using a second
  fluid with a density of 925 kg/m3 and viscosity
  1.5x10-2 Pa-s. What pipe dia should be used?

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• a). Pa-s kg/m-s
• v 5.158 m/s
• b). D 6.6 mm