Question

A U-shaped tube open to the air at both ends contains some mercury. A quantity of water is carefully poured into the left arm of the U-shaped tube until the vertical height \(h_{W}\) of the water column is \(22.0 \mathrm{~cm}\) as shown in (Figure 1)

Answer 1

The U Tube contains water or mercury in a U-shaped tube, and is usually used to measure gas pressure. One end of the U tube is exposed to the unknown pressure field and the other end is connected to a reference pressure source (usually atmospheric pressure), shown in the schematic below.

Unknown Pressure P- Reference Pressure PRef h Fluid A (Gas in most cases) Fluid C (Atmospheric pressure in most cases) Ah Fluid B (Liquid, e.g. water or mercury)

Typical U Tube

By comparing the level of the liquid on both sides of the U tube, the unknown pressure can be obtained from fluid statics,

p+PA8(k+Ah)=Pg84k+pcgh+Pref *P= Prep +(PB-PA)84h+(°C-PA)gh

If fluid C is the atmosphere, fluid B is the liquid in the U tube (e.g. water or mercury), and fluid A is a gas, then we can assume that r_B » r_A, r_C. The pressure contributed by the weight of gas within the U tube can therefore be neglected.

The gage pressure of the gas can be approximated by,

po togeth Ref =php Ref Pgage -P PB241