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A liquid flowing from a vertical pipe has a definite shape
Chapter 12, Problem 12.95(choose chapter or problem)
A liquid flowing from a vertical pipe has a definite shape as it flows from the pipe. To get the equation for this shape, assume that the liquid is in free fall once it leaves the pipe. Just as it leaves the pipe, the liquid has speed \(v_{0}\) and the radius of the stream of liquid is \(r_{0}\).
(a) Find an equation for the speed of the liquid as a function of the distance y it has fallen. Combining this with the equation of continuity, find an expression for the radius of the stream as a function of y.
(b) If water flows out of a vertical pipe at a speed of 1.20 m/s, how far below the outlet will the radius be one-half the original radius of the stream?
Questions & Answers
QUESTION:
A liquid flowing from a vertical pipe has a definite shape as it flows from the pipe. To get the equation for this shape, assume that the liquid is in free fall once it leaves the pipe. Just as it leaves the pipe, the liquid has speed \(v_{0}\) and the radius of the stream of liquid is \(r_{0}\).
(a) Find an equation for the speed of the liquid as a function of the distance y it has fallen. Combining this with the equation of continuity, find an expression for the radius of the stream as a function of y.
(b) If water flows out of a vertical pipe at a speed of 1.20 m/s, how far below the outlet will the radius be one-half the original radius of the stream?
ANSWER:Step 1 of 6
(a)
As liquid flowing in a vertical pipe comes out with the speed and the radius of the stream of liquid is
just as it leaves the pipe.
1. Taking into account the free fall as it leaves the pipe, we need to derive the expression for speed of liquid as a function of distance y as it falls.
2. By using this equation in continuity equation, we need to get the expression for the radius of the stream as a function of distance y.