the propane gas tank has an inner diameter of 1500mm and wall thickness of 15mm. If the wall is pressurized to 2MPa, determine the absolute maximum shear stress in the wall of tank.
To determine the absolute maximum shear stress in the wall of the propane gas tank, we can use the formula for shear stress in a cylindrical pressure vessel:
τ = (P * r) / t
Where:
τ = shear stress
P = pressure
r = inner radius of the tank
t = thickness of the tank wall
First, we need to calculate the inner radius of the tank. The inner diameter is given as 1500mm, so the radius can be determined by dividing the diameter by 2:
r = 1500mm / 2 = 750mm = 0.75m
Next, we need to convert the pressure from megapascals (MPa) to pascals (Pa) since the formula requires SI units. There are 1 million pascals in 1 megapascal, so:
P = 2MPa * 1,000,000 = 2,000,000 Pa
Finally, we can substitute the values into the formula to find the maximum shear stress:
τ = (2,000,000 Pa * 0.75m) / 15mm
Before evaluating this expression, we need to convert the thickness from millimeters to meters:
t = 15mm / 1000 = 0.015m
Now we can calculate the shear stress:
τ = (2,000,000 Pa * 0.75m) / 0.015m
= 100,000,000 Pa
Therefore, the absolute maximum shear stress in the wall of the propane gas tank is 100,000,000 Pa.