Both ends of the U-tube mercury manometer of Fig. P2.52 are initially open to the atmosphere and

Question:

Both ends of the U-tube mercury manometer of Fig. P2.52 are initially open to the atmosphere and under standard atmospheric pressure. When the valve at the top of the right leg is open, the level of mercury below the valve is \(h_{1}\). After the valve is closed, air pressure is applied to the left leg. Determine the relationship between the differential reading on the manometer and the applied gage pressure, \(p_{\mathrm{g}}\). Show on a plot how the differential reading varies with \(p_{\mathrm{g}}\) for \(h_{1}=25,50,75\), and \(100 \mathrm{~mm}\) over the range \(0 \leq p_{\mathrm{g}} \leq 300 \mathrm{kPa}\). Assume that the temperature of the trapped air remains constant.

Figure P2.52