Fluids Homework Help: Pascal's Barrel Burst Problem

[ouma serumula]

help

in working out his principal,pascal showed dramatically how force can be multiplied with fluid pressure.he placed a long thin tube of 0.30cm radious vertically into a 20cm radious wine barrel.He found that when the barrel was filled with water and the tube filled to a height of 12m.the barrel burst.calculate the mass of fluid in the tube and the net force exerted by the water in the barrel on the lid just before ruptured.
PLZ EXPLAINE IN DETAILS

 

[EnumaElish]

For the mass, first you need to calculate the area of a circle with 0.3 cm radius, then multiply it with 12m = 1200cm to get the volume in cm³. Then multiply volume with the density of water, which is 1g/cm³ (see this link). So mass (in grams) = volume (in cm³) for water.

 

[EnumaElish]

Now force is mass times gravitational acceleration: $F = M\times g = M\times 9.81 m/s^2$.

In your case mass = volume. Suppose the volume of the water in the tube is V cm³ (V is the volume that you are supposed to calculate in the first step above, you should put in the number you calculated for volume). Then its mass is V grams. So the force exerted at the bottom of the tube is f = (V grams) times (9.81 m/s²) or approximately 10V g m/s².

Show the force on the lid as F. You need to calculate the area of a circle with a 20cm radius. Let's say this area is A. Also say that the area of the circle with the 0.3cm radius is a. Hydraulic principle^* says that F/f = A/a, or F = f A/a. Since you have calculated f and also calculated A and a, you can calculate F.

^* "A force acting on a small area can create a much larger force by acting on a larger area by virtue of hydrostatic pressure," as explained under Hydraulic machinery in Wikipedia, the free encyclopedia.

 

[EnumaElish]

Check out http://hyperphysics.phy-astr.gsu.edu/hbase/pasc.html

The force on the bottle cap is similar to the force exerted by water in the tube in your example. The force acting on the bottom of the bottle is similar to the force acting on the lid in your example.