A liquid flowing from a vertical pipe has a definite shapeas it flows from the pipe. To get the equation for this shape, assumethat the liquid is in free fall once it leaves the pipe. Just as it leavesthe pipe, the liquid has speed v0 and the radius of the stream of liquid is r0.(a) Find an equation for the speed of the liquid as a function of the distancey 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) Ifwater flows out of a vertical pipe at a speed of 1.20 m/s, how far belowthe outlet will the radius be one-half the original radius of the stream?

A liquid flowing from a vertical pipe has a definite shapeas it flows from the pipe. To get the equation for this shape, assumethat the liquid is in free fall once it leaves the pipe. Just as it leavesthe pipe, the liquid has speed v0 and the radius of the stream of liquid is r0.(a) Find an equation for the speed of the liquid as a function of the distancey 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) Ifwater flows out of a vertical pipe at a speed of 1.20 m/s, how far belowthe outlet will the radius be one-half the original radius of the stream?

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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 v0 and the radius of the stream of liquid is r0.
(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?

Expert Solution