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A mercury-water manometer has a gauge difference of 500 mm(difference in elevation of menisci). What will be the difference in pressure? 
  • a)
    0.5 m
  • b)
    6.3 m
  • c)
    6.8 m
  • d)
    7.3m
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A mercury-water manometer has a gauge difference of 500 mm(difference ...
Ans. (b)
m of light fluid or h = 0.5
= 6.3m of water.
Free Test
Community Answer
A mercury-water manometer has a gauge difference of 500 mm(difference ...
Given:
Gauge difference = 500 mm

To find:
Difference in pressure

Solution:

Conversion factor:
1 m of water column = 9.81 kPa
1 mm of water column = 9.81 Pa

Step 1: Convert gauge difference to pressure difference
Pressure difference = gauge difference x density of mercury x g
Density of mercury = 13,600 kg/m³
g = 9.81 m/s²

Pressure difference = 500 x 13,600 x 9.81 Pa
Pressure difference = 68,088,000 Pa

Step 2: Convert pressure difference to millibars
1 Pa = 0.01 mbar

Pressure difference = 68,088,000 x 0.01 mbar
Pressure difference = 680,880 mbar

Step 3: Convert millibars to centimeters of water column
1 mbar = 1.0197 cm of water column

Pressure difference = 680,880 x 1.0197 cm of water column
Pressure difference = 693,968 cm of water column

Step 4: Convert centimeters of water column to millimeters of water column
1 cm of water column = 10 mm of water column

Pressure difference = 693,968 x 10 mm of water column
Pressure difference = 6,939,680 mm of water column

Step 5: Convert millimeters of water column to millimeters of mercury
1 mm of mercury = 13.5951 mm of water column

Pressure difference = 6,939,680 / 13.5951 mm of mercury
Pressure difference = 509.74 mm of mercury

Therefore, the difference in pressure is 509.74 mm of mercury, which is approximately equal to 6.3 m. Hence, option B is correct.
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