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.
Well, well, well... looks like the propane gas tank is feeling the pressure! Let's see what we can do here.
To determine the maximum shear stress in the wall of the tank, we can use the formula:
τ = (P × r) / t
Where:
τ is the shear stress,
P is the pressure exerted on the wall,
r is the radius of the tank, and
t is the thickness of the wall.
So, first, we need to find the radius of the tank. Since the inner diameter is given, we can simply divide it by 2 to get the radius:
r = 1500mm / 2 = 750mm
Next, we convert the pressure from MPa to Pa:
P = 2MPa × 10^6 = 2,000,000 Pa
Putting it all together:
τ = (2,000,000 Pa × 750mm) / 15mm
Now, let's do a little conversion here. Let's say goodbye to millimeters and convert everything to meters:
τ = (2,000,000 Pa × 0.75m) / 0.015m
Finally, let's calculate the absolute maximum shear stress:
τ = 100,000,000 Pa
So, my friend, the absolute maximum shear stress in the wall of the tank clocks in at 100,000,000 Pa. Tension can be intense!
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.
The formula for shear stress (τ) in a cylindrical pressure vessel is given by:
τ = P * r / t
Where:
τ = Shear stress
P = Pressure inside the vessel
r = Radius of the vessel
t = Wall thickness of the vessel
Given data:
Inner diameter (d) = 1500mm = 1.5m
Wall thickness (t) = 15mm = 0.015m
Pressure (P) = 2MPa = 2 x 10^6 Pa
First, we need to calculate the radius (r) of the vessel:
The radius (r) = inner diameter (d) / 2
r = 1.5m / 2 = 0.75m
Now, we can substitute the values into the formula to calculate the shear stress:
τ = (2 x 10^6 Pa) * (0.75m) / (0.015m)
τ = 100,000,000 Pa
Therefore, the absolute maximum shear stress in the wall of the propane gas tank is 100,000,000 Pa, or 100 MPa.
To determine the absolute maximum shear stress in the wall of the propane gas tank, we can use the formula for shear stress:
Shear stress (τ) = Pressure (P) × Radius (r) / Wall Thickness (t)
However, since the diameter of the tank (1500mm) and the wall thickness (15mm) is given, we need to find the radius (r) first. The radius can be calculated by dividing the diameter by 2:
Radius (r) = Diameter (d) / 2
Now we can substitute the given values into the formulas:
Radius (r) = 1500mm / 2 = 750mm
Shear stress (τ) = 2MPa × 750mm / 15mm
To ensure consistent units, we need to convert the radius from millimeters to meters:
Radius (r) = 750mm / 1000 = 0.75m
Now we can calculate the maximum shear stress:
Shear stress (τ) = 2MPa × 0.75m / 0.015m
Simplifying the equation, we find:
Shear stress (τ) = 100 MPa
Therefore, the absolute maximum shear stress in the wall of the propane gas tank is 100 MPa.