A tank has height and width as 4 m and 3 m, respectively. Determine the total water force, in kN, acting on the bottom of the tank when it is completely filled with water. Take density of water as 1000 kg/m³ and acceleration due to gravity as 9.81 m/sec². (Take the length of tank as 3 m.)
- A400.57
- B351.26
- C353.16Correct
- D345.13
Solution
Concept
Force on a horizontal surface = pressure at that depth × area.
Formula
F = ρ g h A
Step-by-step solution
1. Bottom area A = length × width = 3 × 3 = 9 m² 2. Depth of water h = 4 m 3. Pressure at bottom p = ρ g h = 1000 × 9.81 × 4 = 39240 N/m² 4. Force F = p × A = 39240 × 9 = 353160 N 5. F = 353.16 kN
Explanation
The bottom of the tank is horizontal, so the pressure is the same at every point. Pressure at 4 m depth is 39.24 kN/m². Multiply by the bottom area of 9 m² to get 353.16 kN.
Why the other options are wrong
A, B and D do not match ρ g h A = 353.16 kN. They may come from using a wrong g value or a wrong area.
Shortcut
F = 9.81 × h × A = 9.81 × 4 × 9 = 353.16 kN
Common mistake
Using the average depth h/2. That rule is for vertical side walls, not for the horizontal bottom.
Correct answer: C) 353.16