Question

The pressure in a pipe at X is to be measured by an open manometer as shown in the figure. Fluid A is oil with a specific gravity of 0.8 and Fluid B is mercury with a specific gravity of 13.6. The absolute pressure at X is  kN/m\(^2\). (round off to one decimal place).} 
[Assume Density of water = 1000 kg/m³, gravity = 9.81 m/s², atmospheric pressure = 101.3 kN/m².]

 

Hint:

In problems involving manometers with different fluids, use the specific gravity of the fluids to convert to their respective densities, and then apply the hydrostatic pressure formula \( P = \rho g h \) for each fluid to calculate the total pressure.

Answer 1

We are given that Fluid A has a specific gravity of 0.8 and Fluid B has a specific gravity of 13.6. The density of water is 1000 kg/m³, which is required to find the absolute pressure at X. The pressure at X can be calculated by considering the pressure contribution from both fluids. Step 1: Calculate the pressure contribution from Fluid B (Mercury) Since specific gravity \( SG_B \) is 13.6, the density of mercury \( \rho_B \) is: \[ \rho_B = SG_B \times \rho_{\text{water}} = 13.6 \times 1000 \, \text{kg/m}^3 = 13600 \, \text{kg/m}^3 \] The pressure due to Fluid B, \( P_B \), at a height of 75 cm is: \[ P_B = \rho_B g h = 13600 \times 9.81 \times 0.75 \, \text{kN/m}^2 = 1000.56 \, \text{kN/m}^2 \] Step 2: Calculate the pressure contribution from Fluid A (Oil) The specific gravity of Fluid A is 0.8, so the density of oil \( \rho_A \) is: \[ \rho_A = SG_A \times \rho_{\text{water}} = 0.8 \times 1000 \, \text{kg/m}^3 = 800 \, \text{kg/m}^3 \] The pressure due to Fluid A, \( P_A \), at a height of 25 cm is: \[ P_A = \rho_A g h = 800 \times 9.81 \times 0.25 \, \text{kN/m}^2 = 196.2 \, \text{kN/m}^2 \] Step 3: Calculate the total pressure at X The total pressure at X is the sum of the atmospheric pressure and the pressures due to Fluid A and Fluid B: \[ P_X = P_{\text{atm}} + P_B + P_A = 101.3 + 1000.56 + 196.2 = 1398.06 \, \text{kN/m}^2 \] Thus, the absolute pressure at X is approximately: \[ \boxed{1400.0} \, \text{kN/m}^2 \]