 33
 3
 Homework Statement
 A container is made up of a vertical cylinder, diameter ##D=9.0 cm##, on which is placed an horizontal tube, diameter ##d=3.0 cm##, with axis at a distance ##l=5.0 cm## from the bottom of the cylinder. The other end of the horizontal tube is plugged and the container is filled with water until the height of ##h=50 cm## (see picture). Assuming that the surface is perfectly smooth (no friction), determine the value of the necessary force to keep the container still when the plug has been removed. [Advice: the lowering speed of the column of water should NOT be neglected.]
 Homework Equations
 Bernoulli's Principle: ##p+ρgz+\frac{1}{2}ρv^2=constant##
I'll call ##v_2## the flow speed on the horizontal tube and ##v_1## the lowering speed of the column.
Even if the lowering speed isn't negligible, the problem says "...when the plug has been removed", so can I consider the height unchanged?
In order to find the force, I need the pressure when the plug is off. Is it ##p'=p_{atm}+ρg(hl)+\frac{1}{2}ρv_2^2## ?
First thing I know is ##v_1*A_1=v_2*A_2## (##A_1## and ##A_2## are the two section).
Second thing I know is ##p_{atm}+\frac{1}{2}ρv_2^2=p_{atm}+ρg(hl)+\frac{1}{2}ρv_1^2## thanks to Bernoulli's principle.
So I can find ##v_2##.
The force should be
$$F=p'*A=[p_{atm}+ρg(hl)+\frac{1}{2}ρv_2^2]*(\frac{D}{2})^2*π $$
Is something wrong?
Attachments

24.2 KB Views: 18