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:
h f la min ar
32LV

2
gd
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.
Assumptions
•Neglect Entrance Losses
•Laminar Flow
•Standard Temperature and Pressure Conditions
•Steady
•Incompressible
•Viscous
•Liquid (We chose Gasoline, experimental ρ=681 kg/m^3)
The Setup
• Start with the incompressible steady flow
energy equation (3.71)
 p

 p

V2
V2

 1
 z   
 2
 z    h
2g
2g
 g
in  g
out
• Neglect pressure head because both the inlet
and the outlet are open to the atmosphere
• Height at outlet = 0
• Neglect incoming fluid velocity
z in
 V2 
  h f
  2
 2 g  out
Part A
• Plug in equation for friction head, rearrange for
viscosity
gd 4( H  L)  2 Q


128LQ
16L
Part B
• Plug values into equation from Part A:
o
• T=20 C, 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:
kg
  7.172E  4
ms
Part C
• 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
Experimental  Actual
Error 
* 100  145.62%
Actual
Part D
• Recalculate part A, but eliminate the friction
factor alpha (2)

gd 4( H  L)
128LQ
Q

16L
• New % error is:
Experimental  Actual
Error 
* 100  147.19%
Actual
Discussion
• Several different variables affect viscosity
• These factors are dependent on each otherchanging the fluid density did not yield an equally
changed viscosity
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