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P3.138*: Viscosity in a Capillary Tube

P3.138*: Viscosity in a Capillary Tube. Solved By: Rebecca Currier Patrick Thomas Andrew Quinn Nicole Hataway. The Problem. A viscometer Consists of a tank and a long vertical capillary tube The laminar head loss is given by:. Find:.

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P3.138*: Viscosity in a Capillary Tube

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  1. P3.138*: Viscosity in a Capillary Tube Solved By: Rebecca Currier Patrick Thomas Andrew Quinn Nicole Hataway

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

  3. Find: a) If d, L, H, Q , T, and ρ are known, write an expression for the viscosity. b) Calculate the viscosity: T=20oC, ρ=681 kg/m^3 d=0.041 in (1.0414mm) Q=0.310mL/s L=36.1 in (0.91694m) H=0.154m. 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.

  4. Assumptions • Neglect Entrance Losses • Laminar Flow • Standard Temperature and Pressure Conditions • Steady • Incompressible • Viscous • Liquid (We chose Gasoline, experimental ρ=681 kg/m^3)

  5. 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

  6. Plug in equation for friction head, rearrange for viscosity Part A

  7. Plug values into equation from Part A: T=20oC, ρ=681 kg/m^3, d=0.041 in (1.0414mm), Q=0.310mL/s, L=36.1 in (0.91694m), H=0.154m. ANSWER: Part B

  8. Actual value of viscosity is 2.92e-4 kg/(m*s) per Table A.3 Use percent error formula to determine how far off calculated value is from gasoline’s actual viscosity Part C

  9. Recalculate part A, but eliminate the friction factor alpha (2) New % error is: Part D

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

  11. 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 Relation to Biofluids

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