Question 1.45 in the book, The mass flow rate of water in a tube is measured usi

Question

Question 1.45 in the book,

The mass flow rate of water in a tube is measured using a beaker to catch water during a timed interval. The nominal mass flow rate is 100 g/s.
Assume that mass is measured using a balance with a least count of 1 g and a maximum capacity of 1 kg, and that the timer has a least count of 0.1s.

Estimate the time intervals and uncertainties in measured mass flow rate that would result from using 100, 500, and 1000 mL beakers.

Would there be any advantage in using the largest beaker?

[Assume the tare mass of the empty 1000 mL beaker is 500 g.]


Please show some steps at least so I can follow.

Thank you so much in advance.

Explanation / Answer

to estimate time interval assume beaker is filled to max vol in case of 100 ml and 500ml and to max allowable mass of water(500) in case of 1000ml of beaker.

m'=m/t =>t=m/m'=v/m'

tabulating results:

v=100ml    500ml     1000ml

t=1s          1s           1s

apply methedology of uncertainty analysis:

computing equation:

Um'=[(m.m/(m'.m)xUm)2+(m.m/(m'.t)xUt)2]1/2

the uncertainty are expected to be (+ or -)half the least count of the measuring instrument:

m=0.5g   t=0.05s

(m.m/(m'.m)=t.1/t=1 (m.m/(m'.t)=(t)2 /m x[-m/(t)2]=-1

Um'=[(Um)2+(-Ut )2]1/2

tabulating results:

beaker vol      waterm errorm    %m        t     errort         %t       uncertainty in m'

100                100         (+,-)0.50 (+,-)0.50 1.0   (+,-)0.050   (+,-)5      (+,-)5.03

500                500         (+,-)0.50 (+,-)0.10 5.0   (+,-)0.050   (+,-)1.0      (+,-)1.0

1000               500         (+,-)0.50 (+,-)0.10 5.0   (+,-)0.050   (+,-)1.0      (+,-)1.0

sice the scales have the capacity of 1kg and tare mass of tha 1000ml beaker is 500gn.so there is no adnvantege in using the large beaker.the uncertainy in m' using the large beaker could be reduced to (+,-)0.5% .if a scale with greater capacity same least count ware available

plz rate it took so much effort to solve this problem

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