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A thin tube of uniform cross section is sealed at both the ends .It lies horizontally ,the middle 5 cm containing Hg and two equal ends containing air at the same pressure P. When the tube is held at 60o with the vertical direction ,the length of the air column are 46 cm and 44.5 cm respectively .Calculate the Pressure P in cm of Hg.The Temperature of the system is kept constant at 30o C. Ans=75.4 cm of Hg Column.Pls solve this question...I try this que..bt i was little bit confused in last step..pressure relation p1 p2 and p ..in terms of trigonometry. pls help

A thin tube of uniform cross section is sealed at both the ends .It lies horizontally ,the middle 5 cm containing Hg and two equal ends containing air at the same pressure P. When the tube is held at 60o with the vertical direction ,the length of the air column are 46 cm and 44.5 cm respectively .Calculate the Pressure P in cm of Hg.The Temperature of the system is kept constant at 30o C. Ans=75.4 cm of Hg Column.Pls solve this question...I try this que..bt i was little bit confused in last step..pressure relation p1 p2 and p ..in terms of trigonometry. pls help

Grade:12th pass

1 Answers

Arun
25750 Points
3 years ago
P1 is the pressure exerted at the left side while P2 is the pressure exerted on the right side of the tube. 
 
Let A be the area of cross-section of the tube which is tilted at 60o with respect to the vertical (as shown above).
 
Now, according to Boyle's Law
 
PV = constant
 
so,
 
P1V1 = P2V2
 
here
 
V1 = length of column x area of cross-section = 44.5cm x A
 
and
 
V2 = length of column x area of cross-section = 46cm x A
 
thus, we have 
 
P x 45.25 x A = P1 x (44.5cm x A) = P2 x (46cm x A)
 
here P is the pressure exerted when tube was placed horizontally.
 
or simply
 
P1 x (44.5cm x A) = P2 x (46cm x A)
 
or by rearranging we get
 
P2 = P1 x (44.5 / 46).............................(1)
 
now, also from the above figure we infer that
 
P1 = P2 + 5cos60
 
[P1 - P2 = 5cos60]
 
or by rearranging we get
 
P2 = P1 - 5cos60
 
or
 
P2 = P1 - 2.5........................................(2)
 
.
 
now, by equating (1) and (2), we get
 
P1 x (44.5 / 46) = P1 - 2.5
 
or 
 
46P1 - 46 x 2.5 = 44.5P1
 
by solving further, we get
 
1.5P1 = 115
 
thus, the pressure
 
P1 = 76.66 cm
 
so,
 
P = (P1 x 44.5cm) / 45.25cm = (76.66 x 44.5) / 45.25
 
thus, we get
 
P = 75.395 cm ~ 75.4 cm

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