P3.138*: Viscosity in a Capillary Tube

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P3.138 Viscosity in a Capillary Tube

• Solved By Rebecca Currier
• Patrick Thomas
• Andrew Quinn
• Nicole Hataway

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The Problem

• A viscometer
• Consists of a tank and a long vertical capillary
  tube
• The laminar head loss is given by

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Find

• a) If d, L, H, Q , T, and ? are known, write an
  expression for the viscosity.
• b) Calculate the viscosity T20oC,
• ?681 kg/m3
• d0.041 in (1.0414mm)
• 
  Q0.310mL/s
• L36.1 in (0.91694m)
• H0.154m.
• c) Compare the experimental result with the
  published value of viscosity at this temperature,
  and report a percent error.
• d) Compute the percentage error in the
  calculation of viscosity that would occur if a
  student forgot to include the kinetic energy flux
  correction factor in part (b). Explain the
  importance of the kinetic energy flux correction
  factor in a problem such as this.

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Assumptions

• Neglect Entrance Losses
• Laminar Flow
• Standard Temperature and Pressure Conditions
• Steady
• Incompressible
• Viscous
• Liquid (We chose Gasoline, experimental ?681
  kg/m3)

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The Setup

• Start with the incompressible steady flow energy
  equation (3.71)
• Neglect pressure head because both the inlet and
  the outlet are open to the atmosphere
• Height at outlet 0
• Neglect incoming fluid velocity

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Part A

• Plug in equation for friction head, rearrange for
  viscosity

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Part B

• Plug values into equation from Part A
• T20oC, ?681 kg/m3, d0.041 in (1.0414mm),
  Q0.310mL/s,
  L36.1 in (0.91694m), H0.154m.
• ANSWER

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Part C

• Actual value of viscosity is 2.92e-4 kg/(ms) per
  Table A.3
• Use percent error formula to determine how far
  off calculated value is from gasolines actual
  viscosity

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Part D

• Recalculate part A, but eliminate the friction
  factor alpha (2)
• New error is

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Discussion

• Several different variables affect viscosity
• These factors are dependent on each other-
  changing the fluid density did not yield an
  equally changed viscosity

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Relation to Biofluids

• Scenario is analogous to bladder/urethra setup
• Equation could be used to mathematically model
  urine flow in catheterized patient
• Entrance effects would need to be considered in
  the bladder model, because the urethra is much
  shorter than the capillary tube in this problem