The question is as follows: Here is a demonstration Pascal used to show the impo

Question

The question is as follows: 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 5.010?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 12m high, the barrel bursts. -- First, find the weight (N) of the water in the tube. A) What was the pressure on the water on the lid of the barrel? (Pa) B) What was the net force on the lid due to water pressure? (N)

Explanation / Answer

   Area of lid A_1 = 0.25 m^2
Area of cross-section of the tube A_2 = 5*10^-5 m^2
Height of the water column h = 12 m
  a) Weight of water column in the tube W = mg                                                                =V g                                                              = A_2 h g
                 W = 5*10^-5 * 12 * 10^3 * 9.8                      = 5.88 N   b) Pressure P= Force / area                                           = W/A_2                                = 5.88 /(5*10^-5)              = 1.176 * 10^5 N/m^2
  c) Force on lid F = P * A_1                           = 1.176 * 10^5 * 0.25 m^2                                                     = 29.4 * 10^3 N

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