Regarding Fluids and hydrostatic force ratios

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SUMMARY

The discussion focuses on calculating the ratio of hydrostatic force on the bottom of a cylindrical barrel to the gravitational force on the water contained within it. The barrel has a diameter of 1.2 m and a height of 1.8 m, while the attached open tube has a length of 1.8 m and a cross-sectional area of 4.6 cm². The correct ratio of hydrostatic force to gravitational force is established as 2, which the user struggles to derive due to potential miscalculations in volume or area conversions. Key equations used include the hydrostatic pressure equation P = patm + pgh and the weight equation Weight = mg = pVg.

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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
 
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can someone please direct me in the right direction
 

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