Question

Here is a demonstration Pascal used to show the importance of a fluid's pressure on the fluid's depth : An oak barrel with a lid of area 0.25 m^2 is filled with water. Along, thin tube of cross-sectional area 5.5×10−5 m^2 is inserted into a hole at the center of the lid, and water is poured into the tube. When the water reaches 12 {\rm m} high, the barrel bursts.
What was the weight of the water in the tube?
What was the pressure of the water on the lid of the barrel?
What was the net force on the lid due to the water pressure?

Answer 1

A 5.9 N

B 1.2x10^5 Pa

C 2.4x10^4 N

Answer 2

Part A
Density of Water is 999.97kg/m3
Volume of tube is (12m*5.5x10-5m2) = 6.6x10-4m3
Density times Volume = mass
999.97kg/m3*6.6x10-4m3 = .65998kg
Weight = m*g = .65998kg*9.8m/s2 = 6.5kg*m/s2 or 6.5N

Part B
P=F/A
6.5kg*m/s2/5.5x10-5m2 = 1.2x10^5kg/m*s2 or 1.2x10^5Pa

Part C
Density times height times gravity times area
phgA
999.97kg/m3*12m*9.8m/s2*.25m2 = 2.9x10^4Kg*m/s2 or 2.9x10^4N