Question 3.6: A U-tube differential manometer, as shown in Figure 3.11, co......
6 A U-tube differential manometer, as shown in Figure 3.11, connects pipes A and B. Pipe A contains a liquid of specific gravity 1.6 under a pressure 10.3 N/cm², and pipe B contains oil of specific gravity 0.8 under a pressure 17.16 N/cm². Pipe A lies 2.5 m above pipe B. Find the difference of pressures measured by mercury as the fluid filled in U-tube if the mercury level in the left limb remains at 1.5 m below B.
Let the difference of mercury level be h m (Figure 3.11). The pressures, specific gravities, difference of levels of points A and B, datum level are shown in the figure.
Now, the pressure above datum level XX in the left limb is:
10.3 × 10^{4} + (1.6 ×9.81 × 1000)(2.5 + 1.5) + (13.6 × 9.81 × 1000) × h
and the pressure above datum level XX in the right limb is:
17.16 × 10^{4} + (0.8 × 9.81 × 1000) × (h + 1.5)
Equating Eqs. (i) and (ii) and simplifying, we get
(12.5568 × 10^{4} )h =1.7424 × 10^{4}
Therefore, h=\frac{1.7424 ×10^{4} }{12.5568×10^{4} }=0.13876 cm of mercury
