a water tank is 10 m in diameter and 16m high. if the tank is to be completely filled, determine the minimum thickness of the tank plating if the stress is limited to 60 MPa
To determine the minimum thickness of the tank plating, we need to consider the pressure exerted by the water on the walls of the tank.
The pressure at the bottom of the water tank can be calculated using the formula:
Pressure = Density of Water × Gravitational Acceleration × Height of Water Column
The density of water is approximately 1000 kg/m^3, and the gravitational acceleration is 9.8 m/s^2. The height of the water column is the same as the height of the tank, which is 16 m.
So, the pressure at the bottom of the tank is:
Pressure = 1000 kg/m^3 × 9.8 m/s^2 × 16 m = 156800 Pa = 156.8 kPa
Now, the stress on the tank plating is given by:
Stress = Pressure × Thickness of Plating
We are given that the stress should be limited to 60 MPa. Converting this to pascals:
60 MPa = 60 × 10^6 Pa
So, we can write the equation as:
60 × 10^6 Pa = 156.8 kPa × Thickness of Plating
Rearranging the equation to solve for Thickness of Plating:
Thickness of Plating = (60 × 10^6 Pa) / (156.8 kPa)
Calculating this:
Thickness of Plating = 382.7 mm
Therefore, the minimum thickness of the tank plating should be approximately 382.7 mm in order to withstand the given stress limit of 60 MPa.