   Chapter 9, Problem 34P

Chapter
Section
Textbook Problem

Wafer flowing through a garden hose of diameter 2.74 cm fills a 25.0-L bucket in 1.50 min. (a) What is the speed of the water leaving the end of the hose? (b) A nozzle is now attached to the end of the hose. If the nozzle diameter is one-third the diameter of the hose, what is the speed of the water leaving the nozzle?

(a)

To determine
The speed of water leaving end of the hose.

Explanation
The volume flow rate is defined as V/t=Av and speed of the water leaving end of the hose is v=V/At . The area of cross section of the hose would be A=πr2=π(d/2)2=πd2/4 and this is used in the expression of speed of the water for the area of cross section.

Given info: The diameter of the hose is 2.74cm and volume of water flows in a minute is 25.0L .

The formula for the speed of water at the end of the hose is,

v=Vπ(d2/4)t

• V is volume of water.
• d is diameter of the hose.
• t is time for fill the bucket.

Substitute 25.0L for V , 2.74cm for d , and 1min for t to find v

(b)

To determine
The speed of water leaving the nozzle.

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