[HP Prime] Calculating Prandtl Number with Units (bug found in USIMPLIFY)

[Timothy Roche]

Trying the units capabilities of Prime by calculating the Prandtl Number with some inconvenient units:

N_Pr=Cp*mu/k

Cp=0.853 J g-1 oC-1

mu=1936 lbm ft-1 h-1

k=0.286 W m-1 oC-1

N_Pr=2390 (dimensionless answer)

Lessons learned:

• Calculating the product (Cp*mu) gives an error when using degrees celsius for change-in-temperature units.
• An error also results when calculating the quotient (Cp/k) with change in temperature in degree celsius.
  
• Prime's Units function is not capable of distinguishing between temperature units (T) and change-in-temperature units (delta_T). (Change in degrees celsius is equivalent to change in kelvins.)
• Use absolute temperature when you mean change in temperature as a work around.
  
• After replacing ^oC with K, the calculators result is 5774.153 846 15 lb ft^-1 h^-1 J g^-1 W^-1 m. The value is correct for the reported units; just not very helpful.
  
• Simplify the answer using USIMPLIFY(): calculator yields 5774.153 846 15. Units are all canceled, but the value is incorrect. BUG!
  
• Simplify using MKSA() yields 2386. 913 210 68. Correct!
  
• Converting from given units to dimensionless units (no units) is not possible. You can convert from the hodge podge set of units that this calculation yields to any other combination that is the equivalent of dimensionless (eg: Hz*s works, for instance).
• It might be good to have a dimensionless-unit symbol in order to use CONVERT for this task. Or USIMPLIFY must be altered to handle situations like the one above.
  
• One last observation: the calculator's symbol for capital J is very difficult to read, particularly when following an underscore (_J) as necessary when entering units.
  

Tim

Edited: 10 Nov 2013, 12:56 a.m.

[cyrille de Brébisson]

Hello,

Thanks for the find!

Cyrille