Calculate the pressures at A, B, C and D in the fig.

Given:

• Specific weight of water (\( \gamma \)) = \( 9810 \, \text{N/m}^3 \)
• Specific gravity of oil = \( 0.9 \)
• Specific weight of oil (\( \gamma_{\text{oil}} \)) = \( 0.9 \times 9810 = 8829 \, \text{N/m}^3 \)
• Take atmospheric pressure as 0 for gauge pressure.

Pressure at A (\( P_A \)):

Using the hydrostatic pressure equation:

\( P_A = 0 – \gamma h_{\text{between X and A}} \)

Substitute the values:

\( P_A = – (9810 \times 0.8) \)

Final Value:

\( P_A = -7848 \, \text{Pa} \)

Pressure at B (\( P_B \)):

Using the hydrostatic pressure equation:

\( P_B = 0 + \gamma h_{\text{between X and B}} \)

Substitute the values:

\( P_B = 9810 \times 0.5 \)

Final Value:

\( P_B = 4905 \, \text{Pa} \)

Neglecting air, the pressure at C (\( P_C \)) is:

\( P_C = P_B = 4905 \, \text{Pa} \)

Pressure at D (\( P_D \)):

Using the hydrostatic pressure equation:

\( P_D = P_C + \gamma_{\text{oil}} h_{\text{between C and D}} \)

Substitute the values:

\( P_D = 4905 + (8829 \times 1.9) \)

Final Value:

\( P_D = 21680 \, \text{Pa} \)