Hydrostatic resultants – liquid pressures on both sides of a vertical wall When a vertical wall is subjected to hydrostatic pressures due to liquids on both sides, the net resultant hydrostatic pressure on the wall equals the __________ of the two individual resultants:

Introduction:
Structures like partition walls or lock gates may have liquids on both sides. Determining the net hydrostatic force guides sizing and stability checks.

Given Data / Assumptions:

• Each side has a hydrostatic pressure distribution producing a resultant force F1 and F2 acting normal to the wall and directed from liquid to wall.
• Liquids act on opposite faces, so their forces are in opposite directions.
• Wall is planar and vertical; densities and depths may differ on the two sides.

Concept / Approach:
Since the forces act oppositely, the net resultant magnitude is |F1 − F2|, directed toward the side with the larger hydrostatic resultant. Line of action is determined by centers of pressure, which generally differ for the two sides.

Step-by-Step Solution:
1) Compute each side's resultant: F = w * A * x_c for horizontal plates or via integration for vertical plates.2) Determine directions: they oppose each other through the wall.3) Combine vectorially along the wall normal: F_net = |F1 − F2|.4) Locate the net line of action by taking moments of individual forces about a reference.

Verification / Alternative check:
Special case with equal liquids and equal depths on both sides gives F1 = F2, so net force is zero, matching intuition.

Why Other Options Are Wrong:

• Sum / means: these do not reflect opposing directions; only difference captures cancellation.

Common Pitfalls:
Forgetting to recompute the line of action after taking the difference; ignoring different densities or depths.

Final Answer:
difference