One end of a two-dimensional water tank has the shape of a quadrant of a circle of radius 2.5 m. When the tank is full, the vertical component of the force per unit length on the curved surface will be (assume, density of water as 1000 kg/m³)
- A5133.8 kgf
- B4906.3 kgfCorrect
- C4674.5 kgf
- D4103.4 kgf
Solution
Concept
Vertical force = weight of liquid above the surface
Formula
Fv = ρ g × (area above the curve) × 1 m
Step-by-step solution
1. The liquid above the quadrant has area πR²/4 = π × 2.5²/4 = 4.909 m². 2. Fv = 1000 × 4.909 ≈ 4909 kgf per metre length. 3. The nearest option is 4906.3 kgf.
Explanation
Vertical component = weight of the water in the quadrant.
Why the other options are wrong
Other values do not match πR²/4 × 1000.
Shortcut
Fv = πR²/4 × 1000 kgf.
Correct answer: B) 4906.3 kgf