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?
To determine the maximum length of the pipe without causing the barrel to rupture, we need to consider the hydrostatic pressure exerted by the oil column inside the pipe.
The hydrostatic pressure is given by the equation:
P = ρgh
Where:
P is the pressure at a certain depth in the fluid (hydrostatic pressure)
ρ is the density of the fluid
g is the acceleration due to gravity
h is the height or depth of the fluid column
In this case, the pressure inside the barrel should not exceed 345 kPa, and we are given the density of the oil as 1200 kg/m3.
Using the given information and the equation for hydrostatic pressure, we can calculate the maximum height or depth that the oil column in the pipe can reach without exceeding the rupture pressure of the barrel.
Let's solve for h:
345 kPa = (1200 kg/m3) * (9.8 m/s2) * h
Converting kPa to Pa:
345,000 Pa = (1200 kg/m3) * (9.8 m/s2) * h
Simplifying the equation:
h = (345,000 Pa) / (1200 kg/m3 * 9.8 m/s2)
h = 29.6 meters
Therefore, the maximum length of the pipe can be 29.6 meters without causing the barrel to rupture.