Hydrostatic Resultant on a Vertical Wall — Per Metre Length A water tank contains water to a depth of 1.3 m. What is the hydrostatic force exerted by the water on one metre length of a vertical side wall?

Introduction / Context: Calculating the total hydrostatic thrust on vertical walls is fundamental for tank, dam, and gate design. For a rectangular vertical panel, the pressure varies linearly with depth, and the resultant equals the pressure at the centroid times the area.

Given Data / Assumptions:

• Water depth h = 1.3 m; width considered = 1.0 m (per metre length).
• Density ρ ≈ 1000 kg/m^3; gravitational acceleration g ≈ 9.81 m/s^2.
• Hydrostatic (static fluid) conditions; atmospheric pressure cancels on both sides.

Concept / Approach: For a vertical rectangle of height h and width b, the resultant hydrostatic force is F = ρ g A y_c, where A = b h and y_c = h/2 is the centroidal depth. This leverages the linear pressure distribution p = ρ g y.

Step-by-Step Solution:

Verification / Alternative check: Average pressure on the panel = ρ g (h/2) = 9.81 * 0.65 ≈ 6.377 kPa; multiply by area 1.3 m^2 gives ≈ 8.29 kN, confirming the result.

Why Other Options Are Wrong: 2.89 kN is far too small; 9.28 kN is too large for 1.3 m depth; 28.9 kN corresponds to much larger depths or widths.

Common Pitfalls: Using p at the bottom times area (overestimates); forgetting that resultant acts at the centre of pressure, not at the centroid (important for moment calculations, though not needed for the magnitude here).

Final Answer: 8.29 kN per metre length of wall.