Suppose mercury with density = 13600 kg/m³ has a height difference of h = 20 cm = 0.20 m in an open limb, with g = 9.8 m/s². The gauge pressure is g h = 26656 Pa, and the absolute pressure is P_atm + 26656 Pa ≈ 101325 + 26656 = 127981 Pa.

Suppose mercury with density = 13600 kg/m³ has a height difference of h = 20 cm = 0.20 m in an open limb, with g = 9.8 m/s². The gauge pressure is g h = 26656 Pa, and the absolute pressure is P_atm + 26656 Pa ≈ 101325 + 26656 = 127981 Pa.

teach me manometer problems

Answer: To solve any manometer problem: choose a horizontal datum at the lowest fluid interface, set the total pressures in both limbs equal (P_left = P_right), and solve for the unknown pressure or column height using $P = rho * g * h$ .

Step-by-step solution

Step 1: Fundamental Principle of Hydrostatics

In a continuous, static fluid of uniform density $\rho$ , pressure depends only on vertical depth. At any two points separated by a vertical height difference $h$ , the pressure increases by $\rho g h$ going downward.

Step 2: Pascal's Law and Equal Levels

Points at the same horizontal level within the same continuous, homogeneous fluid must experience equal hydrostatic pressure. To solve any manometer problem, choose a horizontal reference datum at the lowest interface between two fluids.

Step 3: Open-End U-Tube Manometer Equation

Consider a gas container connected to an open U-tube filled with liquid of density $\rho$ . If the liquid is pushed higher in the open limb by a height difference $h$ , the pressure at the datum in the left limb is $P_{\text{gas}}$ , while in the right limb it is $P_{\text{atm}} + \rho g h$ . Equating both gives the absolute pressure.

Step 4: Worked Example: Calculating Gas Pressure

Suppose mercury with density $\rho = 13600 \text{ kg/m}^3$ has a height difference of $h = 20 \text{ cm} = 0.20 \text{ m}$ in an open limb, with $g = 9.8 \text{ m/s}^2$ . The gauge pressure is $\rho g h = 26656 \text{ Pa}$ , and the absolute pressure is $P_{\text{atm}} + 26656 \text{ Pa} \approx 101325 + 26656 = 127981 \text{ Pa}$ .

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