an open tube of length L and cross-sectional area A is fixed to the top of a cyl
ID: 2262539 • Letter: A
Question
an open tube of length L and cross-sectional area A is fixed to the top of a cylindrical barrel of diameter D and height H. The barrel and tube are filled with water (to the top of the tube). Calculate the ratio r of the hydrostatic force on the bottom of the barrel to the gravitational force on the water contained in the barrel. (You need not consider the atmospheric pressure.) State your answer in terms of the given variables. Please right it out in as clear of a way as possible. RESPONSES FROM EARLIER POSTS WILL NOT GET POINTS. THANKS!
-Thank You
Explanation / Answer
The hydrostatic pressure p is dgh where d is the density of water (1000kg/m^3) g is the accn due to gravity, and h is the total height (L + H)
p = dg(L + H)
the total hydrostatic force Fh on the bottom of the barrel will be p times its area - (pi*D^2/4)
Fh = pi*D^2*d*g*(L + H)/4
The weight of water in the container is V*d = d{L*A + H*pi*(D^2)/4}
r = Fh/(V*d) = pi*D^2*g*(L + H)/4d{L*A + H*pi*(D^2)/4}
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.