A cylindrical barrel of diameter D and mass m (when empty) is filled with water to an initial height ho. The barrel is placed on wheels, and at its side, right at the bottom, it has a hole discharging a water jet of diameter d. The water jet produces a reaction force acting on the barrel, and the latter starts moving. (a) Find the velocity v at which the water jet is leaving the barrel through the hole if the level has dropped to h. What assumption must be made about the barrel speed for this to be valid? (b) Calculate the rate of change of the water level in time in terms of
A cylindrical barrel of diameter D and mass m (when empty) is filled with water to an initial height ho. The barrel is placed on wheels, and at its side, right at the bottom, it has a hole discharging a water jet of diameter d. The water jet produces a reaction force acting on the barrel, and the latter starts moving. (a) Find the velocity v at which the water jet is leaving the barrel through the hole if the level has dropped to h. What assumption must be made about the barrel speed for this to be valid? (b) Calculate the rate of change of the water level in time in terms of
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:A cylindrical barrel of diameter D and mass m (when empty) is filled
with water to an initial height ho. The barrel is placed on wheels, and
at its side, right at the bottom, it has a hole discharging a water jet of
diameter d. The water jet produces a reaction force acting on the barrel,
and the latter starts moving.
(a) Find the velocity v at which the water jet is leaving the barrel
through the hole if the level has dropped to h. What assumption
must be made about the barrel speed for this to be valid?
(b) Calculate the rate of change of the water level in time in terms of
the velocity v and then find the dependence of the jet velocity on
time, v(t).
(c) Given that the momentum flow through the hole is
P(t) = (pv) (ad) v,
find the total momentum, P, that has left the barrel with the water
jet from the initial time when the water level in the barrel was ho to
the moment it was empty. Hence, find the terminal velocity V of the
empty barrel assuming that its motion on the wheels is frictionless.
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