Fluids Homework Help: Pascal's Barrel Burst Problem

In summary, Pascal showed that force can be multiplied with fluid pressure by placing a long thin tube with a 0.30cm radius into a 20cm radius wine barrel filled with water. When the tube was filled to a height of 12m, the barrel burst. To calculate the mass of fluid in the tube, one must first calculate the area of the circle with a 0.3cm radius and then multiply it by 12m to get the volume in cm3. The mass can then be calculated using the density of water. The net force exerted by the water in the barrel on the lid just before it ruptured can be calculated by multiplying the mass by the gravitational acceleration. The force on the lid can also
  • #1
ouma serumula
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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
 
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  • #2
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.
 
  • #3
Now force is mass times gravitational acceleration: [itex]F = M\times g = M\times 9.81 m/s^2[/itex].

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.
 
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  • #4
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.
 
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What is Pascal's Barrel Burst Problem?

Pascal's Barrel Burst Problem is a classic physics problem that involves the calculation of pressure exerted by a fluid on the walls of a container. It is named after the French mathematician and physicist, Blaise Pascal, who first described this phenomenon.

What are the key concepts involved in solving the Pascal's Barrel Burst Problem?

The key concepts involved in solving this problem are Pascal's principle, which states that pressure applied to a fluid in a closed container is transmitted equally to all parts of the container, and the equation for pressure, which is P = F/A (pressure = force/area).

What are the steps to solve the Pascal's Barrel Burst Problem?

The steps to solve this problem are as follows:

  1. Determine the dimensions of the container and the fluid inside.
  2. Calculate the surface area of the container that is in contact with the fluid.
  3. Find the force exerted by the fluid on one side of the container using the equation P = F/A.
  4. Multiply the force by the surface area to get the total force exerted on the container by the fluid.
  5. Compare the total force with the strength of the container to determine if it will burst or not.

What are some real-world applications of the Pascal's Barrel Burst Problem?

The Pascal's Barrel Burst Problem has many real-world applications, such as calculating the pressure exerted by water on the walls of a dam, determining the strength of an underwater structure, and designing hydraulic systems in machines and vehicles.

What are some common mistakes made when solving the Pascal's Barrel Burst Problem?

Some common mistakes made when solving this problem include using the wrong units for pressure and force, not considering the weight of the fluid in the container, and not taking into account the thickness and material of the container walls. It is important to carefully check all the given values and units and to use the correct equations to avoid these mistakes.

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