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.)

Concept:

The total water force acting on the bottom of the tank can be determined using the basic principles of fluid mechanics. When the tank is completely filled with water, the force exerted by the water on the bottom of the tank is equal to the weight of the water. This can be calculated using the formula:

\( F = ρ \cdot g \cdot V \)

where:

• \(ρ\) is the density of water (1000 kg/m³)
• \(g\) is the acceleration due to gravity (9.81 m/s²)
• \(V\) is the volume of water in the tank

Calculation:

Given:

• Height of the tank, \(h = 4 m\)
• Width of the tank, \(w = 3 m\)
• Length of the tank, \(l = 3 m\)
• Density of water, ρ = 1000 kg/m³
• Acceleration due to gravity, g = 9.81 m/s²

First, calculate the volume of the tank:

\( V = l \cdot w \cdot h \)

\( V = 3 \, \text{m} \cdot 3 \, \text{m} \cdot 4 \, \text{m} \)

\( V = 36 \, \text{m}^3 \)

Next, calculate the total water force:

\( F = ρ \cdot g \cdot V \)

\( F = 1000 \, \text{kg/m}^3 \cdot 9.81 \, \text{m/s}^2 \cdot 36 \, \text{m}^3 \)

\( F = 353160 \, \text{N} \)

Convert the force from Newtons to kilonewtons:

\( F = 353160 \, \text{N} \cdot \frac{1 \, \text{kN}}{1000 \, \text{N}} \)

\( F = 353.16 \, \text{kN} \)

Therefore, the total water force acting on the bottom of the tank when it is completely filled with water is 353.16 kN.