show all the steps and problem formulation The Reynolds number Re is one of the
ID: 2933912 • Letter: S
Question
show all the steps and problem formulation
The Reynolds number Re is one of the most important dimensionless numbers in fluid mechanics. It is defined as rUD Re where p is the fluid density (kg/m3), U is the average velocity (m/s), D is the characteristic size (m), eg, pipe diameter, and is the dynamic viscosity (kg/(ms). You make several measurements for a particular flow situation and obtain the following values along with their reported uncertainty: 9974 3 kg/m 3 U= 12.5 ± 0.9 m/s D-= 9.3 cm ± 0.4 cm = 6.7 ± 0.7 kg/(m s) a) Determine the average value of Re. b) Determine the total absolute uncertainty in Re. c) Which of the four parameters contributes the most to the uncertainty in Re?Explanation / Answer
= 997 +- 3 kg/m3
U = 12.5 +- 0.9 m/s
D = 9.3 cm +- 0.4 cm
= 6.7 +- 0.7 kg (m-s)
(a) Average Value of Re will be calculated by the given formula.
Re= UD/
Re = 997 * 12.5 * 0.093/ 6.7 = 172.98
(b) Total absolute certainty
Re/Re = / + U/U + D/D + /
Re/Re = 3/997 + 0.9/12.5 + 0.4/9.3 + 0.7/6.7
Re/Re = 0.003 + 0.072 + 0.043 + 0.1045 = 0.2225
Re = 172.98 * 0.2225 = 38.488
so total absolute certainty = 38.488
(c0 Out of the four parameters contributes the most of the uncertainty in .
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