A circular wine barrel 75 cm in diameter will burst if the net upward force exerted on the top of the barrel is 6930 N. A tube 1.1 cm in diameter extends into the barrel through a hole in the top,. Initially, the barrel is filled to the top and the tube is empty above that level. Whats is the mass?
Barrel radius is 1/2 (0.75m) = 0.375 metre.
Area of barrel top = (pi r^2) = 0.441844 m^2.
Maximum pressure on top = (f/a) = 6930/ 0.441844 = 15,684.27Pa..
Height of water column in tube max. = 15,684.27/(1,000 x g) = 1.6 metres.
Tube radius is 1/2 (0.011m) = 0.0055m.
Tube area = (pi r^2) = 0.000095m^2.
Water column volume = (0.000095 x 1.6) = 0.0001521m^3.
Column mass = (0.0001521 x 1,000) = 0.1521kg.
Water column weight max = (0.1521 x g) = 1.4906N.
Water density = 1,000kg/m^3.
g = 9.8 used.
Area of barrel top = (pi r^2) = 0.441844 m^2.
Maximum pressure on top = (f/a) = 6930/ 0.441844 = 15,684.27Pa..
Height of water column in tube max. = 15,684.27/(1,000 x g) = 1.6 metres.
Tube radius is 1/2 (0.011m) = 0.0055m.
Tube area = (pi r^2) = 0.000095m^2.
Water column volume = (0.000095 x 1.6) = 0.0001521m^3.
Column mass = (0.0001521 x 1,000) = 0.1521kg.
Water column weight max = (0.1521 x g) = 1.4906N.
Water density = 1,000kg/m^3.
g = 9.8 used.
