Question

A dam of height 12 m is trapezoidal in section with top width of 2 m and bottom width of 8 m. The unit weight of the material of dam and water are 20 kN/m$^3$ and 10 kN/m$^3$ respectively. If the dam is allowed to store water upto a height of 10 m, the horizontal pressure on the dam is

• A. 100 kN
• B. 500 kN
• C. 720 kN
• D. 1000 kN

Hint:

The total horizontal hydrostatic force on any vertical plane surface of height 'h' is always equal to the area of the triangular pressure diagram.
Force = (Area of triangle) = $\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times (wh) \times h = \frac{1}{2}wh^2$.
This force always acts at a height of $h/3$ from the base.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
Water height 10m, w=10 kN/m³. Find horizontal force on dam per unit length.

Step 2: Key Formula (Alternate):
F_H = (1/2)wh². Triangular pressure distribution: zero at surface, wh at base.

Step 3: Detailed Explanation:
F_H = 0.5×10×10² = 0.5×10×100 = 500kN/m. Acts at h/3 = 3.33m from base. Dam dimensions needed for stability checks, not for water pressure calculation.

Step 4: Final Answer:
500 kN (per meter length).