A barrel will rupture when the gauge pressure inside reaches 345 kPa. A vertical pipe is attached to the lower end of the barrel. The barrel and pipe are filled with oil, density of 1200 kg/m3. How long can the pipe be if the barrel is not to rupture?
pressure=h*1.2*9.8 kpa
set that equal to 345kpa, solve for h in meters
To determine the maximum length of the vertical pipe attached to the barrel without causing it to rupture, we need to consider the pressure difference between the top and the bottom of the pipe.
Let's assume that the barrel is completely filled with oil, creating a continuous column of fluid inside the barrel and the pipe. The pressure at any point within the fluid column can be calculated using the equation:
P = P₀ + ρgh
Where:
P is the pressure at a certain depth in the fluid column,
P₀ is the pressure at the surface of the fluid column (in this case, atmospheric pressure, which we can assume to be 101.3 kPa),
ρ is the density of the fluid (1200 kg/m³ for oil),
g is the acceleration due to gravity (9.8 m/s²), and
h is the height or depth of the fluid column.
Knowing that the barrel will rupture when the gauge pressure inside reaches 345 kPa, we need to calculate the maximum allowable pressure at the bottom of the vertical pipe to ensure there is no rupture. To do this, we need to convert the gauge pressure to absolute pressure:
P_needed = P_gauge + P_atmospheric
P_needed = 345 kPa + 101.3 kPa
P_needed = 446.3 kPa
Now, let's calculate the height or depth of the fluid column that corresponds to the maximum allowable pressure:
P_bottom = P₀ + ρgh
446.3 kPa = 101.3 kPa + (1200 kg/m³)(9.8 m/s²)h
345 kPa = (1200 kg/m³)(9.8 m/s²)h
h = 345 kPa / (1200 kg/m³ * 9.8 m/s²)
h ≈ 0.028 m
So, the maximum height or depth of the vertical pipe attached to the barrel should be approximately 0.028 meters to ensure the barrel does not rupture.