Question

A mercury manometer is used to measure the static pressure at a point in a water pipe as shown in figure. The level difference of mercury in the two limbs is 10 mm. The gauge pressure at that point is

• A. 1236 Pa
• B. 1333 Pa
• C. Zero
• D. 98 Pa

Answer 1

The correct option is A 1236 Pa

Method I;
Considering density of water be 1000kg/$m^3$ and that of mercury be 13600kg/$m^3$,
Gauge pressure =(${\rho }_m-{\rho }_w$)gh
=(13600-1000)$\times 9.81\times 10\times {10}^{-3}$
=1236 Pa
Method II:
Given: Level difference of mercury in the two limbs, x=10mm
$Now,h_w=x(\frac{{\rho }_{Hg}}{{\rho }_w}-1)=10(\frac{13600}{1000}-1)$
$=10\times 12.6=126mmofwater$
=0.126 m of water
Gauge pressure,
$P={\rho }_{w}g{h}_w=1000\times 9.81\times 0.126$
= 1236.06 = 1236 Pa