An open-tube manometer is used to measure the gauge pressure in a tank.If the manometer is filled with mercury, and the open end is at a height of 15 cm above the end attached to the tank, what is the gauge pressure in the tank? The density of mercury is 14 x 10³ kg/m³. A)2.1 x 10³ Pa B)2.1 x 10⁴ Pa C)4.0 x 10⁴ Pa D)1.2 x 10⁵ Pa E)2.1 x 10⁶ Pa

Question

Quizplus · Accepted Answer

The difference in height between the mercury levels in the two arms of the manometer is 15 cm. Since the density of mercury is known, we can use the equation for pressure difference in a manometer:

ΔP = ρgh

where ΔP is the pressure difference, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the difference in height.

Substituting known values, we get:

ΔP = (14 x 10^3 kg/m^3) x (9.81 m/s^2) x (0.15 m) 
ΔP = 2.1 x 10^4 Pa

This is the pressure difference between the tank and atmosphere. Since we are interested in gauge pressure (pressure relative to atmospheric pressure), we need to add atmospheric pressure to this value. Assuming standard atmospheric pressure of 101,325 Pa, we get:

P = 2.1 x 10^4 Pa + 101,325 Pa 
P ≈ 2.1 x 10^5 Pa

This corresponds to choice (B).

An Open-Tube Manometer Is Used to Measure the Gauge Pressure