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Problem 1.45
[Difficulty: 3]
Given:
Nominal mass flow rate of water determined by collecting discharge (in a beaker) over a timed
interval is
&
mg
s
=
100
; Scales have capacity of 1 kg, with least count of 1 g; Timer has least
count of 0.1 s; Beakers with volume of 100, 500, 1000 mL are available – tare mass of 1000 mL
beaker is 500 g.
Find:
Estimate (a) time intervals, and (b) uncertainties, in measuring mass flow rate from using each of
the three beakers.
Solution:
To estimate time intervals assume beaker is filled to maximum volume in case of 100 and 500 mL
beakers and to maximum allowable mass of water (500 g) in case of 1000 mL beaker.
Then
&
&&
m=
m
t
and
t
m
mm
∆
∆
∆
∆
∆∀
==
ρ
Tabulating results
∆∀
∆
=
=
100
500
1000
15
mL
mL
mL
ts
s
5
s
Apply the methodology of uncertainty analysis, Appendix E. Computing equation:
2
1
2
2
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎟
⎠
⎞
⎜
⎝
⎛
∆
∂
∂
∆
+
⎟
⎠
⎞
⎜
⎝
⎛
∆
∂
∂
∆
±
=
∆
∆
t
m
m
u
t
m
m
t
u
m
m
m
m
u
&
&
&
&
&
The uncertainties are ± half the least counts of the measuring instruments:
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This note was uploaded on 10/19/2011 for the course EGN 3353C taught by Professor Lear during the Fall '07 term at University of Florida.
 Fall '07
 Lear
 Fluid Mechanics

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