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.
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.