Consider a column of water as it falls from a faucet. The opening in the faucet has radius ro and the water comes out with initial velocity vo. Define y to be the distance below the faucet. As the water falls (y increases), it accelerates due to gravity and the stream narrows. a) Assuming streamline flow, find an expression for the velocity of the water for any distance below the faucet. b) The stream obeys the continuity equation. Use this to determine the radius of the stream as a function of y. c) At what distance 9₁/2 will the radius of the stream be half its original radius? At what distance Y1/3 will it be a third? d) Compare y₁/2 and y₁/3 for v0 = 1 m/s and vp = 0.1 m/s (use g = 10 m/s²).

Consider a column of water as it falls from a faucet. The opening in the faucet has radius ro and the water comes out with initial velocity vo. Define y to be the distance below the faucet. As the water falls (y increases), it accelerates due to gravity and the stream narrows. a) Assuming streamline flow, find an expression for the velocity of the water for any distance below the faucet. b) The stream obeys the continuity equation. Use this to determine the radius of the stream as a function of y. c) At what distance 9₁/2 will the radius of the stream be half its original radius? At what distance Y1/3 will it be a third? d) Compare y₁/2 and y₁/3 for v0 = 1 m/s and vp = 0.1 m/s (use g = 10 m/s²).

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Fluid Dynamics

The study of the flow of gases and liquids, usually in and around solid surfaces, is known as fluid dynamics in physics and engineering. Fluid dynamics, for example, can be used to evaluate the movement of air through an airplane wing or the surface of a vehicle. It can also be used in ship design to increase the speed at which ships pass through water.

Question

Consider a column of water as it falls from a faucet. The opening in the faucet has radius ro and the
water comes out with initial velocity vo. Define y to be the distance below the faucet. As the water falls
(y increases), it accelerates due to gravity and the stream narrows.
a) Assuming streamline flow, find an expression for the velocity of the water for any distance below the
faucet.
b) The stream obeys the continuity equation. Use this to determine the radius of the stream as a function
of y.
c) At what distance ₁/2 will the radius of the stream be half its original radius? At what distance Y1/3
will it be a third?
d) Compare 1/2 and Y1/3 for v0 =
= 1 m/s and v0 = 0.1 m/s (use g
= 10 m/s²).

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