Regarding Fluids and hydrostatic force ratios

[pendulumboy]

http://img255.imageshack.us/img255/7909/hrw71431.gif
http://g.imageshack.us/img255/hrw71431.gif/1/
An open tube of length L = 1.8 m and cross-sectional area A = 4.6 cm^2 is fixed to the top of a cylindrical barrel of diameter D= 1.2m and height H=1.8 m

The barrel and the tube are filled with water (to the top of the tube). Calculate the ratio of hydrostatic force on the bottom of the barrel to the gravitational force on the water contained in the barrel. Ignore atmospheric pressure for this question.

Homework Equations

P= patm + pgh
Weight=mg=pVg

The Attempt at a Solution

So I tried calculating the volume of the cylinder, tube then subbing it into the equation
Weight=mg=pVg
however it did not work properly as the answer is supposed to be 2.

Did i convert the Area to Radius wrong? Or is there another way I am supposed to go about thisI set up my ratio as = Weight of Barrel + Tube / Weight of barrel only

V of barrel = Pi * (0.6)^2 * 1.8 = 2.03575204
I subbed this into W=mg=pVg = 1000 g/m^3 * 2.03575204 * 9.8 m/s^2
W=19950

I'm not sure how to go about the tube part as it given us the cross sectional area

 

[pendulumboy]

can someone please direct me in the right direction

 

[nlightner]

. To find the volume of the tube I would need the length of the tube. Can you help me out with that?First, let's calculate the volume of the tube. We know the cross-sectional area (A) and the length (L), so we can use the formula V = AL to find the volume.
V = 4.6 cm^2 * 1.8 m = 0.00828 m^3

Next, we can calculate the weight of the water in the tube using the formula W = mg = pVg. We know the density of water (p) is 1000 kg/m^3 and the volume (V) we just calculated, so we can plug those values in.
W = 1000 kg/m^3 * 0.00828 m^3 * 9.8 m/s^2 = 81.184 kg

Now, let's calculate the weight of the barrel and the tube combined. We already calculated the weight of the water in the tube, so we just need to add the weight of the barrel. The volume of the barrel is given as Pi * (0.6)^2 * 1.8 = 2.03575204 m^3. So we can use the same formula as before to calculate the weight.
W = 1000 kg/m^3 * 2.03575204 m^3 * 9.8 m/s^2 = 19950.0096 kg

Finally, we can calculate the ratio of the hydrostatic force on the bottom of the barrel to the gravitational force on the water contained in the barrel. We just need to divide the weight of the barrel and tube combined by the weight of the water in the tube.
Ratio = 19950.0096 kg / 81.184 kg = 245.78

However, the answer is supposed to be 2. This could be because of rounding errors in the given values or in the calculations. It's also possible that the question is asking for the ratio of the hydrostatic force on the bottom of the barrel to the weight of the barrel only, in which case the correct answer would be 19950.0096 kg / 19950 kg = 1.000048.

In conclusion, the ratio of the hydrostatic force on the bottom of the barrel to the gravitational force on the water contained in the barrel is either