Physics

Physics · mechanics

Problem

b. Assume that the stream of water falling from the faucet is cylindrically symmetric about a vertical axis through the center of the stream. Also assume that the volume of water per unit time exiting the spout is constant, and that the shape of the stream of water is constant over time. In this case, the radius

r

of the stream of water is a function of vertical position

y

. Let the radius at the faucet be

r_{0}

. Using your result from part (a), find

r(y)

. If

r(y)

is not constant, it implies that the water has some radial velocity during its fall, in contradiction to our assumptions in part (a) that the motion is purely vertical. You may assume throughout the problem that any such radial velocity is negligibly small. Given constants: ## String Cheese Context question: a. When a faucet is turned on, a stream of water flows down with initial speed

v_{0}

at the spout. For this problem, we define

y

to be the vertical coordinate with its positive direction pointing up. Assuming the water speed is only affected by gravity as the water falls, find the speed of water

v(y)

at height

y

. Define the zero of

y

such that the equation for

v^{2}

has only one term and find

y_{0}

, the height of the spout. Context answer:

y_{0}=\frac{-v_{0}^{2}}{2 g}

v=\sqrt{-2 g y}

Browse the problem library